orimath

I am moving my blog to Orinetz

2009-04-11T00:15:00.000-07:00

I want to tell readers of my blog that I am going to move my major blogging effort to Orinetz Network. Blogspot is a nice place for blogging, however a web-programmer and linguist need more freedom to express himself. I need a place where I can effectively express myself in more than one language.

That is why I decided to purchase a domain and start a new website there. I had uploaded several web application to orinetz. In the mean time, there are Blog, Question and Answer Forum, Online Gravity Simulator and Programmable Comics in Orinetz Network.

I am especially proud of the new Gravity Simulator. Compared to the old one mentioned several times in this blog, the new Gravity simulator have many advantages:

It is browser based, you only need your browser to run it
It is collision capable simulator
It is multilingual - at the moment there are only two languages in Orinetz Network though
Space objects are drawn to scale
Anyone may make their planetary system there

All in all, I believe that this Gravity Simulator is already far more realistic than its older counterpart. This is my first step toward making Orinetz as a multilingual science fiction directory. In the future I plan to make more browser-based applications related to science fiction and applications related to learning new languages. This also add something in the list of programming languages I ever used to make gravity simulators.

Orimath Referral and Reselling Business

2008-10-23T23:14:00.000-07:00

Lately I had added a new marketing module in my website www.orimath.com. This new marketing function will enable anybody who have PayPal account to get extra income by referring my products to their friends or resell my products in their website or blog. If someone buy a product in my website, they will get a share. All they have to do are :

After they get the referral code, they can either put the codes in their email and send them to their friends, or they can put referral link in their blogs, websites, or social network profile.

Example of Referral Hyperlink

a step-by-step Mathematic Solver

Example of Referral Banner

Beside referral links, orimath.com also provide resellers with reseller buttons. By putting these referral buttons in their own websites or blogs, resellers can sell my products direcly from their websites or blogs. Resellers will also get a portion of the sales generated by their reseller buttons. Clicking these buttons will redirect you to PayPal to pay for the products. After purchase is made and paid, you will be sent to my download page to download the products you had paid for.

Example of Reseller Buttons

Oh and last but not least. I just added a new product into orimath. A polynomial solver. This could help you to solve and learn how to solve polynomial using various numerical method. See this link for more into about the product.

Shopping Cart,Multi Download and Discount in Orimath.com

2008-09-26T08:57:00.000-07:00

After adding Fractal Gallery into Orimath.com, today I work to upgrade the purchasing and download system. Now any users who wish to buy more than one item wont need to surf around between Orimath.com and PayPal. Just check-up several items that you wish to purchase and put them into your shopping cart. No login is required.

Now, users can grab several items at once

Orimath.com shopping cart system

Have you finished your shopping in Orimath.com ? You just need to click that Buy Now button. You will be automatically be brought to PayPal to pay your purchase. By purchasing more than one item in Orimath.com you will get USD 0.15 discount per item, starting from the second item you put into your shopping cart.

This is the Multiple Download page

After finishing the payment procedure using PayPal, user will be redirected back to Orimath.com. Meanwhile in Orimath.com, the purchased product will wait for user to download them. Just click once in each picture and user will get the product they bought.

This upgrade have been installed, checked for validity and ready for use. I will have to say thanks for Sonata, who had helped me as the tester and everyone who had visit my site. Thanks to all of you. :)

System Update in Orimath.com

2008-09-24T07:46:00.001-07:00

Orimath.com is the website I used to sell Orimath Quadratic Solver, which is basically a commercial version of the Quadratic Solver I used to answer questions in Yahoo!Answer. The website used to sell only one product, there is practically no other software other than the Orimath Quadratic Solver itself. But that already changed.

Yesterday Orimath.com got a facelift. The index page had been changed to fit more with its role as a webstore. I added a new feature called Fractal Store.

At the moment this post is written 8 fractal patterns are being sold in the web. The pattern is sold as programs capable of rendering the fractal in any resolution. User can also explore the fractals in any range they want to, this would give users freedom to choose which part of the pattern they want to render into high resolution fractal image.

However, since fractal rendering is a time consuming process, it is advised that exploration should be done in low resolution. Should users find certain part of the fractal interesting, they can take high resolution shoot on that particular part.

Newton Fractal and Durand Kerner method

2008-09-16T12:20:00.000-07:00

Newton Fractal and Durand Kerner method

I had known about Newton Fractal for a long enough time, even before I wrote the code for RTC7681 and RTC7683. But it is impossible to do, as long as I don't know what numerical method people use to get the complex roots of complex polynomial function.

Anyway I just decided to ask the question in Yahoo!Answer recently and several people was kind enough to answer my question. Too bad I can only choose one best answer. Internet is a really helpful thing to have, just imagine how many knowledge do millions of user around the world can have. So I just need to transform Durand-Kerner method into computer code and voila I have my Newton Fractal.

All pictures showed below is a actually Newton Fractal plot of the same complex polynomial function, but different pictures showed different level of detail. The complex polynomial function used is f(x) = x⁸ + x⁶ + 5i x⁵ + ( 3 + 2i )x⁴ + ( 3 + 5i )x² -1. The value of a used is 1 + 1i.

The picture above is the Newton Fractal plot of the complex polynomial function mentioned earlier. The plot range is between -300-300i and 300+300i. Even though this is the least detailed plot of the fractal, this one is drawn the latest as that was the last thing I am curious about. If I wasn't too curious about the geometry of the Newton Fractal in big range, I would probably never care to plot it. Anyway the prospect of being able to get the same small detail in big scale win my curiousity.

This particular Newton Fractal was plotted with plot range between -3-3i and 3+3i. So this one have about 100 times more detailed, than the previous Newton Fractal plot result. This is the first plot I told my cute little computer to execute, as that is the range I used to test the program with different polynomial function and a value.

Curious what would happen if we take a look on those little blob in plot range between -2.3-0.3i and -1.7+0.3i ? I was curious as well. So I decided to spend about 8 hours of my computer time to plot the function in high resolution ( 8000x8000 pixels² ). I have ordered the ( 70x70 cm² glossy paper print of the plot result and planned to use it as a poster in my room. Too bad I can't share either the 183 MB BMP file or 20.7 MB JPG File due to the upload speed where I live. But if you click the image, you can still view it in 2000x2000 pixels² detail.

Extreme Resolution

I was still curious about bigger picture of the Newton Fractal, so I decided to do more experiments. The first extreme experiment result was the picture above, depicting the plot result with range between -3e5-3e5i and 3e5+3e5i. It seems that the greater range we go, the less detail we can expect to get.

And on the range of -3e8-3e8i and 3e8+3e8i, you will get no complex picture at all. See the picture above and you will realize that the pictur consist of only 5 different color, instead of 8. This means that in the big picture of things, the probability to get 5 roots out of 8 from x⁸ + x⁶ + 5i x⁵ + ( 3 + 2i )x⁴ + ( 3 + 5i )x² -1 = 0 using Newton-Raphson method is great. To get the other 3 roots however will be almost impossible.

On the other hand, it is not easy to get a plot result with good complexity on the micro scale either. Most of the time you are going to Fall into the Sea, but by using a numerical method called Bisection combined with low resolution exploration, we can expect to arrive in some Island of Complexity. The plot result above for example, was drawn with plot range between -2.2113+0.0002i and -2.2117+0.0006i.

Who is the god of a simulated reality ?

2008-09-11T23:06:00.000-07:00

I have been interested in stories about deities since I was small, and lately I asked lots of questions about this in several internet forums. I am a Christian myself, but I would state that there is no observational evidence about the existence of what we called gods. Some people would say that there is no observational evidence for the inexistence of gods as well, but this argument can be easily countered by the fact that there is no observational evidence about the existence of unicorns and flying sphagetti monster as well. This of course won't mean that gods doesn't exists, but it does mean that the existence of gods is as hypothetical as the existence of either unicorns or flying sphagetti monster.

So what is a possible solution when there are no conclusive evidence ? We should look at how we prove the existence of something hypothetical. A hypothetical object could be proven to be exist, even if they are not visible, by observing whether their predicted effect could be observed in experiments. Of course to do so we have to be clear on the properties of the hypothetical object we are going to look for. In this case I tried to look for possible definitions of gods in case of simulated reality.

So I put my question in a science fiction forum about what they think regarding the gods of a simulated reality. This is a reply from David Jackson, a fellow member of Orions Arm mailing list who happen to run a digital fiction blog. I find his reply to be somewhat insightful, so lets hear how he define a god :

Well ... let's see. What constitutes a god?

IMO, a true god should be the ultimate agent of creation for a thing. He need not craft ever detail of that thing -- it is enough to initiate the creative spark that subsequently develops into the finished product.
Likewise, he need not have absolute authority over the development of the thing once it gets going, but he SHOULD have the power to dictate arbitrary changes and have those changes proceed/develop according to the pre-existing nature of the thing and the overall influence of the change itself.
A god need not be omnipotent, IMO. It is enough that he should be able to obtain a particular piece of information he desires when and if knowing it becomes important.
A god should have power over the future of a thing even after it has left the cradle. So he should be able to recall it for further changes on a whim, terminate the thing outright, suspend its development indefinitely, etc.

So that is David Jackson definition of a god. Then he go on to explain his points whether each objects in a simulated reality could be considered as a god. Since I am the one who make the poll in the Great Big Group, I think I will have to explain why I included each option for my friends there to choose. Green colored text is my reason to include the option as a god candidate, Blue colored text is David Jackson's argument.

So ... how do these criteria match our godly candidates?

The programmer who made the program

It is clear, programmers made the program. Programmers are godlike in the sense that they are the creator deity of the simulated reality. Most people I asked in other forum would choose this option. Programmer is the one who create the environment and the very law that the universe where simulated reality run have to obey. But David Jackson have better knowledge about software development than I am.
Well, he certainly created the program, and has some degree of arbitrary power over its development. But, in the real world, a programmer actually tends to have very little freedom within a project. He is handed a set of goals to accomplish, and sets about accomplishing those goals to the best of his ability. Good managers will give good programmers considerable leeway in designing and implementing their programs ... but programmers without any direction whatsoever are a bad idea.

Anyone who run the program and play

The program have left its cradle and people who may not know anything about how the program is written, puchased the program and play it. The player have full control on the lives of any creature in the simulated reality, and the programmer will not interfere. Players in this sense are gods, just like Odin, Osiris and Zeus are gods.
He is constrained by the nature of the program, warts and all. Since he has no authority over the nature of his experience regarding the program and no ability to dictate arbitrary changes, I'd say he's out as a god.

The computer where the simulation is run

My reason to include this option is they are the one that make sure the law the programmer had made is always obeyed in simulated reality universe.
Basically this is the same as the person who runs and plays the program. They experience different aspects of the same process. A user is just as much a part of a program's process flow as the CPU is ... so by the same argument, no, the computer is not a god. It's merely an environment.

The simulation software

This is the very law of the simulated reality universe itself. If the simulated universe can evolve, this is the very equation that govern how the evolution are being done.
Am I a god of myself? Considering how a bad cold can knock me down ... I'd say no. Likewise, the first time a segfault brings the simulation to its knees, it pretty much loses all claim on godhood.

The harddisk

My reason is the harddisk store the deeds of all creature in the simulated reality universe. The harddisk know everything and is closer to omniscience (relative to the simulated reality) than even the programmers themselves.
Part of the environment. Not even a directive part of the environment, so, no.

The server admin

Well, some of them say they are gods, so I included them here :)
Have you met many server admins? They only think they're gods.

The memory (RAM)

This is the very environment where creatures inside the simulated reality lived and evolved.
Same basic principle as the hard disk, so no.

Conclusion

When all is said and done, I'd have to say that the project manager or designer is the closest thing to a god I can think of when it comes to a software project. He is tasked with identifying a need, formulating a plan to address that needs, and delegating the implementation of that plan to his programmer peons. Depending on his position in the company, he may be able to initiate holds and recalls of the product. If he is forward-thinking, he can direct his programmers to include the kinds of "kill switches" Microsoft builds into all its products to obsolete them after some amount of time in-market.

Sure ... every now and then some hacker comes along with a crack to disable your kill switch ... but, then, Adam bit that apple. So a PM still has at least as much claim to godhood as Yahweh.

Example of Chaos in Rule 23-3

2008-08-19T21:19:00.000-07:00

The evolution property of Cellular Automata Rule 23-3 known as Conway's Life have been known to be chaotic. This means a small change in initial condition, will have a big effect on the evolution of said world.

This Morning (August 10th 2008,1 AM (GMT+8)) I had been lucky enough to observe this particular property of Rule 23-3 while doing some experiments involving 21 Conway's Worlds.

The experiments involved 7 worlds with worldsize of 30 x 30 pixels, 7 worlds with worldsize of 60 x 60 pixels and 7 worlds with worldsize of 120 x 120 pixels. The main objective of the experiments was to determine the average longevity of Conway's world in relation to the worldsize of said Conway's world.

What interest me the most was an unusually high longevity observed in one world with worldsize of 120 x 120 pixels. This particular initial condition below, was shown to have longevity of 9150 cycles.

Initial Condition	Death Condition

This unusually high longevity (about 2.135 Standard Deviation from the mean value) had made me wonder about the rarity or abundance of Conway's world with such long lifetime. So I alter the initial condition by killing one live cell from the original initial condition above. This had decreased the lifetime of the world down to 3059 cycles.

Initial Condition	Death Condition

Since killing one live cell in the initial condition made the longevity of the world being near to the mean longevity value, this might means that initial conditions that produce world with high longevity value to be rare. But more experiments must be done before taking any further conclusions.

If you are interested to help calculating the average lifetime of a Conway's world with certain worldsize, just download the program and do some experiments by yourself. Submit your experiment results to this particular maling list Yahoo!Groups : Cellular Automata Research.

My website : www.tmvfood.com

2008-08-02T06:02:00.000-07:00

July 2008, is a month full of web programming work. My partner in web busines, Lucy Rahayu had asked me to make 2 new websites. One of them is www.tmvfood.com. This website is basically selling frozen foods like dumplings and meatballs, produced by an Indonesian food company named TMVFood, owned by one of our friends.

Lucy is the one doing the web design and marketing work, while I do the programming and webmaster work. We are new in this business and this is the first time we make a complex website for e-commerce purpose, so it is natural that we got some difficulty during the process of making this website. Both of us don't know from the start what facility an e-commerce website should have.

I have to think not only about the code, but also how to integrate the links to the design, so the website esthetic value is preserved. I have to admit that Lucy is a good web designer anyway.

Shown above is the product menu page of www.tmvfood.com. At the time this entry is being written, there are only three products there. The owner of TMVFood plans to add more products later.

Click any picture in the product menu page and you will be redirected into a page containing the full detail of said product. Shown here is Chicken-Shrimp Dumplings, or "Siomay Ayam Udang" in Bahasa Indonesia.

This page contain details about the product and the price of said product. Anyway the more you buy a kind of product, the less each unit of them will cost. This page also have price list stating how much a product will cost, given the amount of product you buy.

This website also contain some delicious recipes. The one shown above is "Sup Bola-bola".

And finally if you are interested to ask us some questions, we have a contact page. Just write your name, email address (we will need it to send our replies) and your message. We will reply your message as soon as possible.

Mathematical Basis of RTC7683

2008-08-02T03:58:00.000-07:00

Download RTC7683 here

Problem Description

I had made an attempt to do the math for relativistic rocket in my previous blog post. However it turns out that the calculations in said post turns out to be wrong. I got to know why it is wrong when I looked for information from Yahoo!Answer, Physic Forum and Adam Getchell. I initially planned to used the information for upgrading RTC7681 to RTC7682. It turns out that in the previous post, I ignored conservation of linear momentum and thus the whole mathematic attempt is wrong. I will have to redo the calculation, this time including Conservation of Linear Momentum.

Anyway, this is the problem description :

A Spaceship with empty ress mass of MShip have fuel capacity of MFuel. The Ship's engine is capable of burning some amount of the fuel per unit time ( FBT ), turning them into kinetic energy per mass unit ( EPM ). The Spaceship is assumed to use Photon Drive as suggested in Baez Relativistic Rocket FAQ.

Actually I want to make SRF Exhaust Velocity variable, but it turns out to be more complex than I had initially thought. It is easier to assume that the SRF Exhaust Velocity to be c, as lightspeed is frame invariant. Anyway if anyone who read this post know how, I will be more than thankful if you want to tell me.

Conservation of Mass-Energy and Conservation of Linear Momentum

To calculate anything about rocket, we have to consider both Conservation of Mass-Energy and Conservation of Linear Momentum. Anything else about the rocket can be derived, if we can model how Mass-Energy and Linear Momentum is conserved in our model.

Equation RTC7683-1.Conservation of Mass-Energy

Equation RTC7683-2.Conservation of Linear Momentum

To get rid of EXE ( Exhaust Energy ), we would use equation RTC7683-2 to derive what EXE is equal to.

Equation RTC7683-3.Exhaust Energy Equation

Equation RTC7683-4.Equations derived from both Conservation

Function v(t) and t(v)

To get the IRF Velocity of the ship over time, we have to turn Equation RTC7683-4 into Quadratic Equation over v.

Equation RTC7683-5A.Quadratic Equation on v

Equation RTC7683-5B.The a,b,c part of
Quadratic Equation in Equation RTC7683-5A

Equation RTC7683-5C.Velocity as Function of Time

For the program RTC7683, we are going to need calculating the time required to reach certain velocity in order to calculate the time required for deceleration.

Equation RTC7683-6A.Quadratic Equation on t

Equation RTC7683-6B.The a,b,c part of
Quadratic Equation in Equation RTC7683-6A

Equation RTC7683-6C.Time as Function of Velocity

Coordinate and Proper Acceleration

Coordinate Acceleration is the second derivative of displacement as observed in a reference frame over time.

Equation RTC7683-7.Coordinate Acceleration

Proper Acceleration is the amount of acceleration an accelerometer inside the ship would measure.

Equation RTC7683-8.Proper Acceleration

Download RTC7683 here

Update on Cellular Automata Programs

2008-07-02T22:32:00.000-07:00

I had updated my cellular automata programs. The previous version seems to have problem with the width of the screen in computers without some Japanese fonts installed.

The new links is here :

Cellular Automata v1

Cellular Automata v2

The Cellular Automata v1 is a program to simulate single state cellular automata. Thus the color of each cell could only be black or red (or other color, if you choose so.

The Cellular Automata v2 is a program to simulate multiple state cellular automata. The rule required are a bit more complex than the one for Cellular Automata v1. But once you find a good rule, you could have more fun. The Cellular Automata v2 package have three rules inside in (*.rul) files.

Unfortunately I am really busy with my web programming work, that I have no time left to do any deeper research on it. Anyway I am going to have some good surprise for programmers in the near future. Have fun!

My Enterpreneurship Attempt

2008-06-29T13:46:00.000-07:00

Since I am currently starting my new business, I thought it should be useful for me to read more about investing. Well, someone like Warren Buffet started investing in financial terms from very young age, most of us don't. So I run into this particular link, and that reminds me about my own enterpreneurship attempts.

Personally I had loved math since I was 7 ,learned programming since I was 14 and start being serious learning my religion since I was 13. Not really an advantage for me during high schools, since we was not taught programming and won't get any points for it. But after being memed by my father since I was five about he having a system working for him, and he only had to command the system to fulfill his wishes, I know that programming is the path I should go.

It turned out that I was right. During university my programming skill help me greatly to understand most of the math taught ( and not taught ) to me. I don't need to derive mathematic equations myself, since the computer can do it for me, but the most helpful part is the computer's calculation speed and graphing capability. I don't know if anyone can turn hundreds 3D points into a graph in their mind, but I know I can't, that is where programming can be a really useful thing to know.

I think that was an investment in my part. But my friend told me something that I can't deny, "Fendy I am amazed how you can make hundreds of programs, but still make no money from your skill". Well, it is not really that I am not trying to. But some months before that, I just lost my first entrepreneurship attempt, after I worked the whole 6 months to make the full system without receiving any payment, during the beginning of the commercialization.

That was really a shock to me. That system was like my own child, I weave every part of its DNA, hoping that one day the system would grow and become sentient on its own right ( I designed the system so it could grow and evolve, evolution sometimes is the only way to answer some mathematic problems, extrasolar planet finders being one of its application, you will need a GRAPE to do accurately it however ). I had read OA during those times and some ideas leading to the creation of the system was based on things written there ( Have to thanks Todd a lot for some discussion about sexuality in the OA main list, that was really helpful ). Having nothing to do anymore in Jakarta, I have pack up and go back to my hometown Surabaya, and here I am until now.

In Surabaya, I spent several months writing things in my blogs, answering questions in Yahoo!Answer and taking some Japanese courses. It is funny though that during these downtime, I learned lots of new things from the internet, made several simple programs every month. One day when I was answering questions, I notice that there are certain questions that I can answer very quickly in detail, if only I have the right program to do it. I spent two days to do the code and start answering questions in detail in short time.

Then my friend come and asked me, "Why dont you sell it for $2 ? I can market it for you.", that surely reminded me on the thread a net friend of mine, Chris had started in Great Big Group some months before, my answer at that time was "lets start immediately." So I spent some weeks learning how PayPal works and start selling programs in my website, while my friend take care about the web design and marketing part. The result was not great yet, but one ideas done make more ideas come out. Robert Kiyosaki said in his books, that most people lost two or three companies before they own the one that made them filthy rich. And information age, provide a way to own a company at the cost of less than $50, the only thing required is idea alone and in my case I got more idea after I execute an idea.

So here's some lesson I learned and wish to share with everyone who read this post :

Starting a business is more about people than about money.
Don't be afraid to fail. Had I didn't do my first entrepreneurship attempt, I won't know how to do web-programming at all.
Work even when you are not being paid. Someone who never want to work without being paid, are not going to be paid when they are not working.
Don't waste your breath to curse or blame someone. Each breath worth a lesson to learn.

I really hope that everyone who read this particular entry could start being creative and found their own business. There are countless number of web-based business that already helped billions of people in the planet to live their lives. Some of them like PayPal, Google, Yahoo!, GNU Project and FSF had spent billions of dollars and millions work hours to place the foundation and infrastructure required, to ensure that all creative, talented and brave entrepreneurs in the information age to start their business for less than the cost of a bag of peanuts. So what hold you down ? Feel free to contact us, in case you need some help setting up your web-based business.

RTC7681 Graph Plotting

2008-05-13T21:45:00.000-07:00

Download RTC7681 here.

The mathematic detail of calculation provided by RTC7681 is provided here.

This post will focus on what kind of graphs RTC7681 is capable to produce. In short, RTC7681 is a calculator that calculate in detail the value of various variables involved in a relativistic travel. Instead of simply relating the maximum speed to various variables, RTC7681 also take the fact that the mass of fuel used to provide acceleration decrease over time during both acceleration and deceleration phase into consideration. The consideration about fuel mass depletion during both acceleration and deceleration phase is intended to provide more detail about the nature of relativistic travel, since there seems to be statistically significant percentage of people ( including me in the past ), who have wrong impression about the mass dilation as mass increase from nowhere. The mass increase during relativistic travel, actually did not come from nowhere, it come from the potential energy stored initially in the ship as fuel.

The examples of the graph below depicts the change in several variables value during relativistic travel for a spaceship massing 1 metric tons, carrying 10 metric tons of fuel, with engines capable of burning 0.08 kilograms of fuel per second and convert the fuel mass into kinetic energy at 0.1 efficiency ( 8.987551 10¹⁵ Joule / kg = 0.1 c² ).

Changes in Velocity over time

The spaceship's velocity during a relativistic travel is not always constant. During both the acceleration and deceleration phases, the velocity changes as the spaceship accelerate or decelerate. The mass dilation effect increase the total mass, while burning the fuel for acceleration decrease the mass. Since the amount of fuel burned during both acceleration and deceleration phase is assumed to be constant, the change in mass affect the change in the amount of acceleration the engines are capable to provide.

Changes in Velocity over time
( Fuel Burned during Acceleration Phase 50%)

Changes in Velocity over time
( Fuel Burned during Acceleration Phase 76.833%)

Changes in Acceleration over time

The amount of fuel burned during both acceleration and deceleration phase are assumed to be constant. However since the total mass of the spaceship changes due to loss of mass by fuel and dilation of mass due to relativistic effect, the spaceship's acceleration provided by the engine do change over time during both acceleration.

Changes in Acceleration over time
( Fuel Burned during Acceleration Phase 50%)

Changes in Acceleration over time
( Fuel Burned during Acceleration Phase 76.833%)

IRF Distance Travelled over time

IRF Distance Travelled, is the distance travelled by the spaceship over time, as observed by an observer in an Inertial Reference Frame (IRF). Said observer in Inertial Reference Frame could be in the origin or in the destination point. The distance travelled by the spaceship is the result of finite integration of its velocity function over time.

Distance Travelled over time
( Fuel Burned during Acceleration Phase 50%)

Distance Travelled over time
( Fuel Burned during Acceleration Phase 76.833%)

IRF Ship's Mass over time

IRF Ship's Mass is the mass of spaceship as observed by an observer in an Inertial Reference Frame (IRF). Said observer in Inertial Reference Frame could be in the origin or in the destination point. Since the velocity of the ship change during both acceleration and deceleration phase, observers in Inertial Reference Frame are going to observe change in the amount of mass dilation during these both phases.

IRF Ship's Mass over time
( Fuel Burned during Acceleration Phase 50%)

IRF Ship's Mass over time
( Fuel Burned during Acceleration Phase 76.833%)

SRF Fuel Mass over time

SRF Fuel Mass is the amount of fuel available in the spaceship over time, as observed by observers inside the Ship's Reference Frame (SRF). Since the amount of fuel burned per unit time is assumed to be constant in this model, we should not expect anything other than two linear graphs with equal gradient, separated by a horizontal line.

SRF Fuel Mass over time
( Fuel Burned during Acceleration Phase 50%)

SRF Fuel Mass over time
( Fuel Burned during Acceleration Phase 76.833%)

IRF Total Mass over time

IRF Total Mass is the mass of the ship added with the mass of fuel still available in the ship, as observed by observers in an Inertial Reference Frame. Said observer in Inertial Reference Frame could be in the origin or in the destination point. Preservation of energy will make it impossible for the spaceship to gain mass without losing its fuel mass.

IRF Total Mass over time
( Fuel Burned during Acceleration Phase 50%)

IRF Total Mass over time
( Fuel Burned during Acceleration Phase 76.833%)

Download RTC7681 here.

Mathematical Basis of Relativistic Travel Calculator RTC7681

2008-05-12T19:57:00.000-07:00

Problem Description

Download Relativistic Travel Calculator RTC7681 here

Relativistic Travel Calculator RTC7681 is a software intended to calculate various variables and graph various function over time related to relativistic travel. The variables used in this blog entry are :

-	MShip	:	The rest empty mass of the spaceship intended to be used.
-	MFuel	:	The rest mass of the fuel provided for the spaceship.
-	FBT	:	Amount (mass) of fuel burned per unit time.
-	EPM	:	The amount of energy provided per unit mass of fuel burned.
-	DistanceOfDestination	:	The distance between spaceship's destination and its origin.

The calculation done in RTC7681, assumes that :
- The spaceship travel in linear trajectory.
- The spaceship always use the same engine capacity for both acceleration and deceleration.
- Friction with interstellar medium is ignored.
- The total rest mass of the spaceship is decreasing as the spaceship engine burn the fuel.

Below are the definition of several terms used in this blog entry :

-	IRF	:	Inertial Reference Frame, any IRF values are measured by observers in the origin.
-	SRF	:	Ship's Reference Frame, any IRF values are measured by observers inside the ship.
-	Acceleration Time	:	The time required by the spaceship to accelerate to an intended maximum IRF velocity.
-	Acceleration Distance	:	Distance travelled by the ship during Acceleration Time.
-	Deceleration Time	:	The time required by the spaceship to decelerate to zero IRF velocity.
-	Deceleration Distance	:	Distance travelled by the ship during Deceleration Time.

Function of Velocity, Time, Distance and Acceleration

In order to find the function that relate these variables, we have to remember a concept called energy preservation. To gain kinetic energy, something have to lose its potential energy. The potential energy of the ship is stored as mass of fuel, while the kinetic energy of the ship as a whole depend on the total mass of the ship and fuel, multiplied by the square of its velocity, dilated by the mass dilation caused by relativistic velocity. From the equivalence between ship's potential and kinetic energy, we got we got :

Equation RTC7681-0. Energy Preservation

Equation RTC7681-1. Energy Preservation

To Solve this for v and t, we have to do the following steps :

Equation RTC7681-2. Energy Preservation

Equation RTC7681-3. Energy Preservation

Equation RTC7681-4. Quadratic Equation relative to v

Since equation RTC7681-4 is a Quadratic Equation relative to v, we can use any technique used to solve a Quadratic Equation , to solve it for v. Assuming that v is positive, we got the function of v over t below :

Equation RTC7681-5. Function of velocity over time

function TForm1.CalculateVelo(const EPMA,FBTA,MS,MF,t : double ) : double;
var P1,P2,PL,t2,FBT2,EPM2 : double;
begin
   FBT2:=FBTA*FBTA;
   EPM2:=EPMA*EPMA;
   t2:=t*t;
   PL:=((2*EPMA*FBTA*t*c2*(MF+MS))-(2*FBT2*EPMA*t2*c2)+(FBT2*EPM2*t2));
   P1:=sqrt(abs(PL));
   P2:=c2*(MF+MS)+FBTA*(EPMA-c2)*t;
   CalculateVelo:=P1*c/P2;
end;

Equation RTC7681-5 in Delphi Code

By turning equation RTC7681-4 to it's alternative form below, we can easily see that equation RTC7681-4 is a Quadratic Equation relative to t.

Equation RTC7681-4B. Quadratic Equation relative to t

So assuming that t is positive, we got the function of t over v below :

Equation RTC7681-6. Function of time over velocity

function TForm1.CalculateTime(const EPMA,FBTA,MS,MF,v : double ) : double;
var P1,P2,P3,v2,EPM2 : double;
begin
   v2:=v*v;
   EPM2:=EPMA*EPMA;
   P2:=c2*EPM2*(c2-v2);
   P1:=EPMA*(c2-v2)+v2*c2-sqrt(P2);
   P2:=c2*(MS+MF);
   P3:=((v2*EPM2)+(v2*c2*c2)-(c2*EPM2)+(2*c2*c2*EPMA)-(2*v2*EPMA*c2))*FBT;
   CalculateTime:=P1*P2/P3;
end;

Equation RTC7681-6 in Delphi Code

Acceleration and Deceleration Distance over time can be calculated using numerical integration below of the equation below :

Equation RTC7681-7. Function of Acceleration Distance over Time

function Torm1.CalculateDist(const EPMA,FBTA,MS,MF,t0,t1 : double ) : double;
var Acc,DT,Y0,Y1,lt : double;
    hi : cardinal;
begin
   DT:=(t1-t0)/400;
   lt:=t0;
   Y0:=CalculateVelo(EPMA,FBTA,MS,MF,t0);
   Acc:=0;
   for hi:=1 to 400 do begin
      lt:=lt+DT;
      Y1:=CalculateVelo(EPMA,FBTA,MS,MF,lt);
      Acc:=Acc+0.5*(Y1+Y0);
      Y0:=Y1;
   end;
   Acc:=Acc*DT;
   CalculateDist:=Acc;
end;

Equation RTC7681-7 in Delphi Code

While the amount of acceleration and deceleration over time is the differentiation result of v over t.

Equation RTC7681-8. Function of Acceleration over time

Maximum Amount of Fuel Expended during Acceleration Time

The amount of fuel expended during acceleration time should never exceed a certain value or the ship will not be have enough fuel later during deceleration time. The maximum mass of fuel expendeable during acceleration will be called MPF here on. To find the value of MPF, remember that the proportion between the amount of fuel required to accelerate an object and the mass of the object, is always the same for the same velocity. Which means :

So, if the spaceship is intended to stop in its destination, the amount of fuel expended during acceleration should never be greater than MPF.

Exception in Acceleration Distance

Sometimes after some calculation, amount of fuel required to be expended during both acceleration and deceleration phase are not as great as we first intended them to be. In such situation, the amount of fuel required to be expended must be recalculated. The recalculation will involve solving equation RTC7681-9 for t0 and t1 :

Equation RTC7681-9. Exception Handling Formula

The variables in the equations above are :

- t0	:	Length of Acceleration Phase.
- t1	:	Length of Deceleration Phase.
- MFuel₀	:	Initial amount of fuel when the spaceship start accelerating.
- MFuel₁	:	Initial amount of fuel when the spaceship start decelerating.

We also have to mind the fact that the Initial amount of fuel when the spaceship start decelerating is equal with the Initial amount of fuel when the spaceship start accelerating subtracted with the amount of fuel burned during Acceleration Phase.

MFuel₁ = MFuel₀ - FBT t0

Download Relativistic Travel Calculator RTC7681 here

Orimath Quadratic Equation and Function Solver

2008-05-05T09:29:00.000-07:00

Orimath Quadratic Equation and Function Solver is a software capable of solving basic mathematic problems related to quadratic equation or quadratic function. In this sense, Orimath Quadratic Equation and Function Solver can act as both a Quadratic Equation Calculator and a Quadratic Function Calculator.

The picture depicted above is the main part of the Quadratic Equation and Function Solver. The main interface is designed so user can define their problem easily and checks out what questions about the quadratic equations or quadratic functions, the Quadratic Equation Calculator have to solve for them.

Unlike its freeware counterpart, this new Quadratic Equation Calculator is capable of telling the steps required to get the answer in user friendly HTML interface. This make the program good and useful for students who have problem with their mathematic homework, students who want to learn more about quadratic equations and quadratic functions, and teachers who want to make some problems for their students to solve.

The program is also capable of plotting the quadratic function neatly. The plotting interface also allow students to looks for the value of y(x) for a given value of x, making it easier to plot or graph a quadratic function.

Visit Us at www.orimath.com

Plotting Quadratic Function

2008-05-05T09:23:00.000-07:00

A picture can speak thousands words, that is exactly the reason why plotting a function is a good way to understand the properties of said function. To understand some properties of quadratic function, we have to see how the quadratic curve is shaped or located if each constants in y(x) = ax² + bx + c is modified. The program used to plot the quadratic functions is Orimath Quadratic Equation and Function Solver.

The picture above shows how the shape of the curve change if the value of a is modified. Modifying the value of a will dilatate the curve relative to the x-axis.

The picture above shows how the position of the curve change if the value of b is modified. Modifying the value of b will move the position of the curve diagonally.

The picture above shows how the position of the curve change if the value of c is modified. Modifying the value of c will move the position of the curve vertically along the y-axis.

Take a look at our Orimath Quadratic Equation and Function Solver.

Mathematical Artwork Thumbnails

2008-04-26T05:51:00.000-07:00

The images below are thumbnails of mathematical artworks I had made. Click the image for greater resolution.

Intelligent Design Conjencture derived from Theory of Evolution

2008-04-11T12:25:00.000-07:00

In order for the following Intelligent Design Conjencture to be true, several condition must be met :
- Theory of Evolution must be true.
- Evolution is Turing Complete.
- Evolution go faster in faster computational medium.
- Hard Artificial Intelligence are feasible.

A good scientific theory must be able to make prediction, which can be evaluated by observation.

The theory of evolution is a good scientific theory, its claim have been verified by observation of fossil records from the past. Theory of evolution predicts that some sentient beings given enough time is going to evolve intelligence, and human is but an example of such thing.

The time required for humanity from when they gain full-sapience to modern technology is roughly 200,000 year.

Evolution from sentience to partial-sapience or full-sapience require billions of years, and not all species succeed reaching it.

Given that a species capable of full-sapience, have good probability of existing and continue to develop their technology in the timeline required for sentient species to evolve sapience, it is highly probable that a species will observe powers possessing greater intelligence, by the time they reach sapience.

Which means that if we take a random sapient species evolving naturally from a universe-sized box, most of them are going to observe powers possessing greater intelligence, by the time they reach sapience.

A technological civilization of a sapient species may catalyze the evolution of other sapient species, either via natural intelligence catalization or artificial intelligence catalyzation.

This intelligence catalyzation process may be deliberate or non-deliberate.

Deliberate natural intelligence catalyzation happen if the technological species provolve, train or teach less developed sentient beings, to develop their technological capability.

Non-deliberate natural intelligence catalyzation happen if the less developed sentient beings watch and learn what already technological species does.

Deliberate artificial intelligence catalyzation happen if the technological species create artificially created intelligent agent having full-sapient capability.

Non-deliberate artificial intelligence catalyzation happen if the artificial intelligence results from unexpected result from an experiment conducted by technological species.

If a technological species happen to discover space travel, the extreme difference of condition between worlds may force them to deliberately catalyze the evolution of new intelligent species, for their economic or memetic purpose. Which means that a naturally evolved technological species, may catalyze the evolution of more than one sapient species.

Since evolution process go faster in faster computronium, most species are going to be the result derived from evolution inside faster computronium.

Naturally evolved brain is a faster computronium than natural chemical process and biological evolution of pre-sapient beings. The development of technology means increase in computation demand, which fuel the development of even faster and more effective computronium.

Which means that if we take a random species in this universe, there are higher probability that they are result of evolution in the ideosphere of a technologically advanced species, rather than purely the result of natural evolution.

Which means that if we take a random species in this universe, there are higher probability that they are created by a technologically advanced beings ( very far more advanced than the created species, bordering on godlike ), rather than the result of natural evolution.

Quadratic Equation Solver

2008-04-10T08:22:00.001-07:00

Download a free Quadratic Solver here!!

Quadratic Equation Solver, is an educational program made to explain ways used to solve various problem related to quadratic equations.

The problems it capable of solving is the one, in the patterns like below :
-> x² + 4x + 6 = 0 , 2x² + 6x + 7 = 0
-> x² + 6x + 6 = 12 , 3x² + 1x + 1 = 25
-> x² + 2x = 30 , x² + 33 = -5x
-> x² = 25 , x² = -25
-> ( x - 3 )( x + 6 ) = 23 , ( x + 5 )( x +2 ) = 33
-> ( x - 3 )( x + 6 ) = 2x² + 25
-> etc

And from those equation, the program is capable of deriving the value of :
-> Determinant ( b² - 4ac ).
-> The roots ( x1 and x2 ) by using quadratic (abc) formula.
-> The roots ( x1 and x2 ) by using factorization.
-> Determining values like x1+x2 ( Sum of Roots ) , x1*x2 ( Product of Roots ) , x1-x2 (Difference between Roots), etc.

In order to understand about how Quadration Equation Solver works, just download the program and follow this tutorial.

After you open the program you will be presented several interesting mathematical applications and scientific topics. The URL can be clicked if you are interested about the article.

But if your primary goal is to solve a Quadratic Equation, you better continue to "Quadratic Solver" page.

Solving x² + 5x + 4 = 0 using factorization

There you will be presented several type of Quadratic equation, the program capable of solving. In the example above, I requested the program to solve x² + 5x + 4 = 0 ( watch, which radio button is on ), using factorization method ( watch, which check box is checked ). Then I click "Solve the Equation" button.

Factoring x² + 5x + 4 = 0

Unlike most Quadratic Solver, this program will tell you the ways required to get the answer, in detail.

So now, how can I ask for the value of Sum of Roots ( x1 + x2 ) and the value of Product of Roots ( x1x2 ), from equation like -x² + 3x + 4 = -2x²-2x ?

Just light up the second radio button to choose the form of equation you want to solve ( cyan ), and choose what you want to know from that equation ( red ). Then click "Solve the Equation" button.

And the program will tell you how to get the answer, like the example above.

If you happen to have some free time, re-visit my blog in the future to give some comment or advice about the program, by clicking the URL above inside the program.

You may also copy the program to your friends for free, but you may want to remind them to download the latest version directly from this blog.

Have fun using the program. :D

Provolution and Fongoli Chimps

2008-04-07T22:11:00.000-07:00

Some animal lovers have known for a long time, that animals are not as stupid as people usually think of. It seems that this claim is not merely a hoax. The definition of a useful scientific theory, is that it must make a predictions, which can be verified by observation, and the theory of evolution, predicts that there are possibility that other sentient beings on Earth may someday become intelligent species, just like human.

When I was a 10 years old child, I made a comic series, which only I and my siblings read. The settings of the comic are about millions of years in the future, when human had perished, while arks filled with different species of animals was sent to the space. My comic was largely influenced by the polular anime and manga at that time, Doraemon (by Fujiko F Fujio) and Astro Boy (by Ozamu Tezuka). Even now, I still think that everybody, even adults, should watch the anime. There are some good memetic content in both manga, which later I recognize as transhumanism, when I come across a website, called Orion's Arm.

Kind of cartoon I draw when I was 10 years old.

Funny enough that in high school I grow to become a religious, there is a path that I feel must follow, which lead me to become a member of my high school's religious community. There, I met two of my best friends, who are still my best friends until now. At that time, I learned about Creationism, and even my first paper, I wrote in high school is about Creationism, opposing my previous evolutionary worldview. Creationism told that every living being in Earth was created to be perfect, during my study of programming, I learned that a perfect system, must be able to change and perfectly adapt to environmental change. So did I abandon Creationism ? Well, no, but I will tell more about that in later post.

So when I met a website called Orion's Arm, I was drawn to it by a concept called provolution, which basically means that you can make humanoid form of any animal and give them intelectual capability as well ( unplifting ). I suspect that this meme had infected me since fairy tales depicting talking animals was told to me.

Article about Fongoli Chimps from National Geographic website.

But this may not be just a fairy tale, since I read an article about Fongoli Chimpanzee ( Pan troglodytes verus ), written by an Assistant Professor of Antropology Jill Pruetz ( blog ), from Iowa State University.

In the article, it is said that Fongoli Chimps, had begin to hunt bush babies ( Galago senegalensis ) by using spears they made from the branches of local tree. What surprised me, is the fact that in the article, it is mentioned that the chimps sharpened their spear, before using them for hunting, which is a proof that they had invented tool making by themselves. The article is also present in Iowa State University news service and her paper. The spear the chimps used can be seen in her paper.

Funny enough that there are some difference between what happened with the chimps, and what mostly believed to be happened in human evolution. It is believed that in case of human, it is the male who hunt, while the female looks for vegetables, but in case of Fongoli Chimps, it is female who go and hunt. May be they haven't invented agriculture, yet. A more funny thing is the fact that the method of making spears seems to be more complicated, the younger the chimps are, which show that there are some ongoing technology development on the play.

The issue that I am currently interesting of is "what humanity, as their older full-sapient siblings should do ?". Should we let them develop their own technology at their pace, or should we teach them what we know ? Are we going to enter an age, where animals can talk and interact with us as equals ? Will our world become like how it be in the fairy tales ? Will one day we see chimpanzee and human, learning the same thing in the same school and classroom ?

I will be interested to know different reaction from different people, feel free to make an educated comment.

Characters from Utawarerumono, an anime depicting a world where animals have become humanoid sapient beings.

Cellular Automata

2008-04-03T01:41:00.000-07:00

Several days ago, I read an entry about Cellular Automation in Wikipedia, which links to a page titled Conway's Game of Life. In that page I learned that there is a simple rule in Cellular Automation, capable of generating complex pattern. Since I had been interested in the concept for a long time, I made the program yesterday (April 1st 2008).

There are many rules, which can be used in a Cellular Automation program. A Cellular Automation's rule have to mention what neighborhood condition should be fulfilled, to make a cell born, unchanged, or dies. The image above for example, is generated using rule 1/1, which means that for each cell, having one neighbor is going to come to life, but will die of loneliness if it have no neighbor, or die of overcrowd if it have more than one neighbor.

You can see the lexicon of rules, and the possible outcome in this Index of Rule.

Gosper's Glider Gun (Rule 23/3)

One of the pattern in Cellular Automation that I'm fond of is Gosper's Glider Gun which use Rule 23/3. The Gun, continuously produce a glider, which is a pattern capable of traversing the map. Since the glider is going to leave away, as soon as its pattern emerged from the reaction in a Gosper's Glider Gun, the Gun appear to shoot, with a glider as its ammunition.

I used Gosper's Glider Gun, to make a pattern consisting of 16 Gosper's Glider Guns, to make a Collider above. The collision between glider are unpredictable. Sometimes they explosively annihilate, sometimes they calmly annihilate, depend on how they collide.

The Collider is not stable, it will slowly degenerate itself to become the pattern above. The pattern above consist of only p1-oscillator and still lives. ( For definition of p1-oscillator and still lives, see this
Lexicon Of Life ).

I had made the X-Collider above as well, using 16 Gosper's Glider Guns in 4 different phase. The X-Collider, will continue to make a lot of glider collisions, and exhibit chaotic behavior. Whether these will result in degeneration or oscillation, is yet unknown. I haven't tried to play it long enough.

By merging different pattern I found in this Lexicon Of Life, I made the Space station above from components such as gliders, glider duplicators, octagon IIs,
octagon IVs, non-monotonic spaceships, and sparky spaceships. ( See the definition of each component in the Lexicon Of Life )

Download Cellular Automata Installer here.

Credits

A Strange Mushroom ( Zombie Hand )

2008-03-31T21:10:00.000-07:00

Some days ago, a strange plant grow itself in my garden. I know that Indonesia is a country rich in biodiversity, but most people, including me are ignorant about it. Anyway, Indonesia's biodiversity, never failed to make me wonder about how creative the nature is.

Because of the spongy structure of the strange plant, we decide that is is some kind of mushroom. The shape resemble a zombie hand, digging itself out from the its grave, which is the reason why I decide to give it it's current name, Zombie Hand. Another reason for it's current name we gave to it, is because we suspect, that the origin of this plant is its seed that had been dormant for years, inside the compost we purchased and place in that particular area of my garden.

The strange plant, attracted the attention of my whole family because it smell so bad, like dead fish or dead rat. Our curiousity however, doesn't let us to remove it, because it may turn out to grow into some interesting plant.

Some of my employees, told me that this plant have also grown in their home, but their version of the same plant is more colorful than the one grown in my garden. They also said that this kind plant, which grow in their home, also emit somehow unpleasant smell.

I would like someone to identify what is the scientific name for this strange plant, along with the name of their ordo, families, and genus. Everyone in my home is curious abot this particular plant.

What will happen if moon have its own moon ?

2008-03-21T00:11:00.000-07:00

There was a question back in Yahoo!Answer, which catch my interest. The question was, what will happen if the Moon have a moon. Actually there can be more than one answer to this question, or may be there are unlimited number of answer to this question, since there are so many possibilities on the mass, the initial position vector and the initial velocity vector of the moon of the Moon.

For the sake of simplicity lets assume, that the name of the moon of Moon is Usagi( うさぎ , means rabbit, refering to old belief that there are rabbits in the moon ), which mass is 2.3221E20 kg, or about 3.88688E-5 Earth Mass. Then we can predict what is going to happen by using NCGS or PPNCGS Gravity Simulator

Stable moon of Moon

For Usagi to orbit Moon in stable orbit, it may not be too far from the Moon, or Earth gravity field is going to disrupt the orbit.

For example, if the distance of Usagi and Moon is about 24544 km, and the orbital velocity of Usagi is 447.559 m/s, the orbit of Usagi around Moon is going to be stable.

Geocentric orbit path

Lunacentric orbit path

Unstable moon of Moon (Newtonian Simulation)

1. Geocentric Trajectory

But if Usagi is too close to Earth, then Moon is not going to have its own moon for a long time, since the orbit of Usagi is not going to be stable.

For example, if the distance of Usagi and Moon is about 64544 km, and the orbital velocity of Usagi is 275.991595 m/s, the orbit of Usagi around Moon is going to be unstable.

Usagi is going to escape it's Lunacentric orbit right away, since earth have higher mass and thus, stronger gravity field. Between time 0 until month 8 day 22, Usagi will orbit Earth twice in not so eccentric orbit, and twice in highly eccentric orbit.

Then between month 8 day 22 to year 1 month 7 day 5, Usagi will orbit Earth several time, inside the Earth-Lunar space, then move to higher orbit, and orbiting earth 5 times.

During the period between year 1 month 7 day 5 to year 2 month 9 day 22, Usagi will continue to orbit earth chaotically, moving between orbits in Earth-Lunar space.

During the period between year 2 month 9 day 22 to year 3 month 5 day 20, Usagi will orbit earth, as high as the Moon itself.

2. Lunacentric Trajectory

In order to gain more understanding about what is happening, we should see it from different point of view, that is why we need to see the orbit of Usagi, from Moon's point of view.

As we could see, Usagi is going to be pulled right away by earth gravity, form its Lunacentric orbit. Notice that the path of Usagi is chaotic since the first time, up to month 2, until it escape to higher orbit, with higher eccentricity.

Since between month 2 and month 8, Usagi didn't orbit Moon anymore, but orbit Earth in highly eccentric orbit, while the Moon continue to orbit Earth as if nothing happened, the path of Usagi relative to Moon, show retrograde motions, just like the path of any bodies relative to other bodies in a celestial sisterhood.

The path of Usagi relative to Moon, during month 8 to month 12, take my interests, since the plot result of Usagi's motion, somehow draw a face in the space between moon and earth. Looks like the face of a cute dog to me.

Between month 12 and year 1 month 11, Usagi orbit earth in relatively stable orbit. In that period, the path of Usagi relative to Moon, show common retrograde motion.

Instability begin to occur in Usagi's path after year 1 month 11. During the period between year 1 month 11 and year 3 month 5, Usagi continue to exhibit chaotic movement, sometimes dangerously close to Moon.

Unstable moon of Moon (Post-Parameterized Newtonian Simulation)

After trying to simulate what is going to happen using NCGS, I am curious abuot what is going to happen if I use my other Gravity Simulator, the PPNCGS which take relativistic effect into account.

Just link the simulation result of NCGS, the PPNCGS simulation result also shows, that Usagi is going to "take off" to higher Geocentric orbit, in month 2.

But the simulation result after that predict different movement of Usagi. PPNCGS simulation result, predicts that Usagi is going to orbit Earth in highly eccentric orbit, for about 5 times, during the period of time between month 2 to year 1 month 3.

Then PPNCGS simulation result, predicts that Usagi is going to orbit Earth in close orbit, during the period of time between year 1 month 3 to year 1 month 7, Moon gravity field, throw Usagi away from its orbit.

Between year 1 month 7 and year 2 month 9, Usagi is going to occupy different orbit, around Earth, changing its path as it encounter Moon in close distance, and being thrown by Moon's gravity field.

After year 2 month 9, Usagi is going to orbit earth in close distance, until the 2.3221E20 kg object finally collide with Earth in year 3 month 3.

GeoScene 2D Fractal Generator

2008-02-24T21:00:00.000-08:00

GeoScene Fractal Generator, is a program I made in 2006 using Julia Set generation algorithm, as a part of my thesis for my bachelor degree. I used it at that time to generate some kind of geographical irregularities, as part of the input used by my seawave simulation program.

Later, I also used the program to make different kinds of mathematical arts. Which you can see in my deviant art gallery. The icons I used as part of my banner in my Mathematical Programming Tutorial Website is also generated using this program.

How to Use GeoScene Fractal Generator ?

Before you can use the program, you have to download the program here. Then you can activate the program and see the following screen.

If you set the Multiplier in Limit section by 20, and click ADD Generate button in Coloring section, you will see a fractal generated using the equation : green(z)=1-z^2, where z is a complex number.

The Polynomial and Coloring Section

Now, clear the screen by clicking Clear Color button in Coloring section.

Then lets try to make a Fractal by using the following polynomial :

f(z)=(0.3 + 0.2 I) z² + (4.2 - 0.9 I) z + (-2.3 + 0.2 I)

These are the thing you should do :
- Set the C(n) value in the Polynomial Section, just like the function described above.
- Set the Coloring to Red
- Set the Multiplier value in Limit section to 60
- Click ADD Generate Button

Then :
- Set the Coloring to Green
- Set the Multiplier value in Limit section to 40
- Click ADD Generate Button

At last :
- Set the Coloring to Blue
- Set the Multiplier value in Limit section to 30
- Click ADD Generate Button

And the picture above is what you would get, after doing the procedures stated above.

How to Clear the Screen ?

Set the coloring to RGB and click Clear Color.

Random function

The purpose of Random button in Polynomial Section, is for generating a random polynomial function. After clicking the Random button and clicking the ADD Generate button, you can get a picture like below.

Matrix Size

Matrix Size is the actual height and width of the generated fractal. By Enlarging the size of the matrix, we can see more detail in the generated fractal.

Polynomial with Higher Order

The Add button in Polynomial section, is used to increase the order of the polynomial function, used to make the fractal. Higher order fractals usually are more complex than lower order fractals.

If you click the Save Julia Set Image button, below the image, you can save the currently shown picture as a bitmap image. The example below have been saved in PNG format.

* Download Geoscene Fractal Generator here
* See some generated fractals in my Deviant Art gallery

Image Transformer

2008-02-23T03:25:00.000-08:00

Image Transformer is an application capable of doing Computer Vision related image transformations. The primary feature of the program is edge detection and color separation.

As Image Transformer is designed for research, the interface is constructed so the user can change the matrix value and greyscale definition of each transformation operator. The user can also put wieght on the result of different transformation, in a TransColor matrix, to create a custom transformed image.

Download Image Transformer here

Edge Detection

Edge detection is one of the basic operations in computer vision. By detecting the edges from a bitmap file, we can differentiate between different regions that exist inside an image. By knowing the position of some regions in an image, an image recognition application can work faster, because it only need to consider the pixels value inside a certain region, instead of considering all pixels value in the whole image.

In order to detect the edges in an image, several transformation operators can be used. The following example uses Laplace operator.

And the example below is drawn using Robert's operator.

We can assign a different transformation operator by entering the matrix values and grayscale definition in the Transformation page. Then we can associate weights on the results of different operators, on the Transcolor List page. The resulting transformed image in the Picture page will be the result of the weighted addition of different operator results from the Original Image.

Color Separation

By manipulating the matrix values and grayscale definition of an transformation operator, it is possible to separate different colors of an image. The Original Image used in this example is an Orphys Fractal, which is separated into its Red and Green parts.

This is done by using the "Take Red" and "Take Green" transformation operators, which are available by default in the Image Transformer.

Download Image Transformer here

Animals Equations

2008-02-20T05:59:00.000-08:00

This is a list of mathematical animals, I made several years ago using a software called Maple. The animals are usually drawn by assembling several abzoloid class of equations. The command used is implicitplot3d from plots package. See my website for more detail.

The Elephant

Big, strong and mighty, yet gentle and peaceful animal. Elephant is my favourite animal since I was 7 years old. In fact this is the first animal equation, by which I earned my reputation as mathematical artist in my university, back in 2002. In fact most people recognize me by the elephant I drew, along with the equation I place around the elephant.

The cat

I draw the cat in 2003, when I watch a Japanese anime titled Ultra Maniac. In that anime, there is a cat called Rio, and I think he is kinda cute. Moreover, I am a fan of Yoshizumi Ayumu-sensei, and have enjoyed several manga and anime based on her work. I hope I can meet her one day.

The Lion

Lion is often depicted as the king of jungle. I ever see one when I visit South Africa with my family. It is one of the famous big five there. The mane, which is part of its body, differentiating it from the rest of the cats family, is the tricky part, which require more than assembling abzoloid class of equation.

The Girrafe

Girrafe's long neck, have earned the species its famous reputation. In fact it is one of the animals, most children can easily recognize if they meet one. I often saw them in the local zoo, when I was small.

The antelope

Antelope is famous for its male's horn, which they use to fight other males in the mating season. I draw this one in 2007 along with the lion and the girrafe.

Repeating same animals for infinity

By using the nature of function based on arccos(cos(x)), it is possible to plot the same animals for infinity, along the x axis. The same can also be done for other axes. Showed in the picture below, are the basic animal equation and two types of iteration.

Conclusion

I often hear from my classmates back in high-school, that the part of brain used for arts and mathematic are different. Most of them also suggest that it is impossible to be good at both of field. I believed that at that time, but after I enter university and learned that even a software which purpose are for mathematic, can be used for the sake of art, I don't think that belief is entirely true.

There advancement in science have made it possible for new kinds of arts to spring out. There are even some kind of arts which require computers to make, for example fractals and animal equations. This has led me to believe that, two or more different subjects may have a meeting point, where a lot of possibility can be studied. It turn out that I was right.

It is always interesting for me to find more and more knowledge, as I understand why elderly always say that learning is a way to know what you don't know, if you never learn, you never know what you don't know. There is a lot of things that can come out from the understanding of this sentence alone.

Japanese Writer Application

2008-02-13T09:40:00.000-08:00

Introduction

Since the first time I studied Japanese, I had have a hard time looking for application programs, which can be used to write in Japanese. It seems that there aren't many people learning Japanese in my country, or they who currently learning, never bother wanting to write anything in Japanese in a computer.

The problem is, I have some Japanese friends, and sometimes when we exchange mail over the internet, some transliteration mistake happened many times, rendering our mail unreadable. We have tried to overcome this problem by exchanging romaji email or sending kanji as picture, but each of those solutions have their own drawbacks.

Exchanging romaji email will do little to improve my Japanese literation. Unlike most people who just want to be able to speak in Japanese, I want to be Japanese literate. I want to read many kinds of book written in Japanese, in their original language. Everyone with more than single language capability know, how many meaning are lost in translation process. Not to mention there are some knowledge that can only be obtained if you understand a language, because that knowledge are never translated to other language, or simply can't be translated to other language without losing their meanings.

Exchanging picture, while can be one of the good solution, also has its own drawbacks. The size of a picture file is far greater than a text file is a no brainer for every computer literate individual.

Therefore when I found out that making a Japanese Writer program is quite easy, I jump on the chance to make one. Now, the program can be downloaded for free in the link below.

Download Japanese Writer

By using this program, different users just have to exchange their Japanese Writer File (*.jwf) between their net friends.

I hope this program can help anybody to conversate with their Japanese speaking friends, or with their friends who want to improve their Japanese literation as well. For myself, I hope that I can have more Japanese friends, as the very reason for me to study language is to make more friends, and to understand the relationship between different culture in our blue planet.

Additional Note

For Japanese Writer to work, set you windows non-Unicode language to Japanese by following these easy steps :

Go to Control Panel.
Choose "Regional and Language Settings".
Choose "Advance".
Choose "Japanese" in "Language for non-Unicode programs".
Japanese Writer is ready to be used.

An Example of Orphys Fractal

2008-02-09T21:43:00.000-08:00

It is suggested to read Introduction to Orphys Production Line and Shipping Schedule Optimation, before reading this entry.

Heuristic Constants in Optimation Program

The effectiveness of the optimation algorithm used in Orphys Production Line and Shipping Schedule Optimation (OPLSSO) , is affected by a set of heuristics. These measure of effectiveness, is often called fitness in Genetic Algorithm terms. By plotting the value of several objective functions into a two dimensional map, given a set of heuristic values, it is possible to compare the effectiveness of each set of heuristics.

As the number of heuristic values in Orphys PLSSO is more than two, the actual map is multidimensional. Since the computation resources I have is limited, I can only plot some two dimensional manifold inside the multidimensional map. The mathematic detail of what is plotted is given below.

For example an optimation algorithm have a set of objective values : Z₁, Z₂, Z₃, ...... , Z_k
The values of these objective values depend on a set of heuristics : h₁, h₂, h₃, ...... , h_n
A function F, will map a set of heuristics to the set of objective values as follow : [ Z_1..k ] = F( h_1..n );

Where k is the number of objective values and n is the number of heuristics used.

Since we have to plot a two dimensional map with two axis x and y, we have to make the value of the set of heuristics to depend on the value of x and y in linear manner :
h₁ = a₁ x + b₁ y + c₁
h₂ = a₂ x + b₂ y + c₂
h₃ = a₃ x + b₃ y + c₃
.
.
.
h_n = a_n x + b_n y + c_n

Now the function F will map the value of x and y to the value of [ Z_1..n ], like below :
[ Z_1..k ] = F( a_1..n x + b_1..n y + c_1..n );

The Objective Values of Orphys Production Line and Shipping Schedule Optimation

In case of Orphys PLSSO, the set of objective values are :

1. Total Production Line Time Used

How many Production Line Hour are used if a set of heuristics is used to control the algorithm used in Orphys PLSSO, according to the schedule produced by a set of heuristics ?

The coloring used in the map below is HSV, with red denoting an area where the sets of heuristics produce a schedule with lowest amount of Production Line Hour used, and purple denoting an area where the sets of heuristics produce a schedule with highest amount of Production Line Hour Used. The less Total Production Line Hour used, the more favourable the schedule produced is.

2. Total Overtime Hour Used

How many hours must the Production Lines in the case must works outside normal workhour, so customer's demand can be fulfilled on time, according to the schedule produced by a set of heuristics ?

The coloring used in the map below is HSV, with red denoting an area where the sets of heuristics produce a schedule with lowest amount of Total Overtime Hour Used, and purple denoting an area where the sets of heuristics produce a schedule with highest amount of Total Overtime Hour Used. The less Total Overtime Hour used, the more favourable the schedule produced is.

3. Total Production Line Salary

How much money must be spended to pay the salary, according to the schedule produced by a set of heuristics ? This value include the normal workhour salary and overtime payment.

The coloring used in the map below is HSV, with red denoting an area where the sets of heuristics produce a schedule with lowest Total Production Line Salary, and purple denoting an area where the sets of heuristics produce a schedule with highest Total Production Line Salary. The less Total Production Line Salary is required, the more favourable the schedule produced is.

4. Total Inter-Warehouse Shipping Cost

How much money must be spended to move the products from factories to warehouses or between warehouses, according to the schedule produced by a set of heuristics ?

The coloring used in the map below is HSV, with red denoting an area where the sets of heuristics produce a schedule with lowest Total Inter-Warehouse Shipping Cost, and purple denoting an area where the sets of heuristics produce a schedule with highest Total Inter-Warehouse Shipping Cost. The less Total Inter-Warehouse Shipping Cost is required, the more favourable the schedule produced is.

5. Total To-Customer Shipping Cost

How much money must be spended to send finished products from company's warehouses to customers on time, according to the schedule produced by a set of heuristics ? This value is affected by the amount of time left ( relative to deadline ) when the products that customers ordered is finished, the cost of the shipping means required to deliver the products on time, and the amount of products delivered.

The coloring used in the map below is HSV, with red denoting an area where the sets of heuristics produce a schedule with lowest Total To-Customer Shipping Cost, and purple denoting an area where the sets of heuristics produce a schedule with highest Total To-Customer Shipping Cost. The less Total To-Customer Shipping Cost is required, the more favourable the schedule produced is.

6. Order Fulfillment Cost Grand Total

Order Fulfillment Cost Grand Total is the predicted sum of all money used in all activity required to fulfill customer's demand. This cost is the sum of production line salary, inter-warehouse shipping cost, and to-customer shipping cost. So this value is the ultimate objective value of Orphys PLSSO.

The coloring used in the map below is HSV, with red denoting an area where the sets of heuristics produce a schedule with lowest Order Fulfillment Cost Grand Total, and purple denoting an area where the sets of heuristics produce a schedule with highest Order Fulfillment Cost Grand Total. The less Order Fulfillment Cost Grand Total is required, the more favourable the schedule produced is.

By comparing the maps of different objective values to Order Fulfillment Cost Grand Total map, we can understand which cost is dominant in a company. By understanding which cost is dominant in a company, the management team of a company can reduce the total cost by focusing on how to reduce the dominant cost. For example, since the map for Order Fulfillment Cost Grand Total is roughly the same with Total To-Customer Shipping Cost map ( in this example ) , we can infer that To-Customer Shipping Cost is the dominant one, and company's management team can focus their cost cutting efforts, by finding new means for shipping their finished products to customer.

Download an Example of Orphys PLSSO Schedule. ( HTML )

Orphys Production Line and Shipping Schedule Optimator

2008-02-01T04:53:00.000-08:00

Introduction

Orphys Production Line and Shipping Schedule Optimator (Orphys PLSSO) is a program cluster made to help management team in a company to manage, how customer's demand is fulfilled, using any available company's resources, in the least costly way.

Orphys PLSSO is capable to automate and optimalize the production and shipping schedule for manufacturing companies with multiple factory and multiple warehouse. As the program cluster it is capable of trying different possible schedule based on some heuristic value in a short time, and tell the production management team the least costly schedule found.

Assumption

In order to do its task, the program make several assumption about the company :

the company have one or more factories.
the company have one or more warehouses.
the company may have one or more production lines in a factory.
the company have more than one means to transport their product to customer.
each factory have a storage area for finished product, which are warehouse in their own sense.

Several assumption about the production lines :

raw materials inputed into a production line, will yield finished products.
a production line may consist of several machine and tools.
a production line can't use other production line's resources (machine or tools).
production lines will have some lag time, if asked to produce a product it is not currently producing (setting time).

And several other assumption about the company's customer :

customers want to get their ordered product on time.
customers will give the company a deadline, to produce and ship their product.
customers may be located in different geographic area (cities, state, country).

What Schedule and Report can Orphys PLSSO make and optimize ?

Basically Orphys PLSSO can be used to produce several kind of schedule and report :

Download an Example of Orphys PLSSO Schedule. ( HTML )

Production Schedule, tells company management teams, at what time a production line must :

start producing product A. ( production )
change the production line's setting to produce product B. ( setting )
start producing product B. ( production )
change the production line's setting to produce product C. ( setting )
and so on.

Overtime Schedule, tells company management teams, in which day and how long a production line must work outside normal workhour (overtime). This feature can be disabled if the company policy don't allow overtime.

Inter-Warehouse Shipping Schedule, tells company management teams, when a finished product must be moved from a factory to a warehouse, or must be moved between warehouses.

To-Customer Shipping Schedule, tells company management teams :

when a finished product must be shipped to customer.
which shipping or transportation method must be used ( truck, ship or airplane, for example).
how much shipping days is needed.
when customer will recieve the shipped product.

Transport Cost Detail, is a detailed report about how demand on a set of product, is fulfilled by the production and shipping schedule generated by Orphys PLSSO. The report also tells the cost required to ship a customer's set of ordered product.

Estimated Cost, is a short report about the estimated cost involved, if the current plan is executed. The calculated costs are :

Inter-warehouse Shipping Cost ( Per Warehouse ).
To-Customer Shipping Cost ( Per Warehouse ).
Production Lines Salaries ( Per Factory ).

Download an Example of Orphys PLSSO Schedule. ( HTML )

Learn More about Orphys :

What is an Orphys PLSSO Program Cluster consists of ?
What is the Input required ?
About Oprhys

Orphys PLSSO Program Cluster

Orphys Production Line and Shipping Schedule Optimator (Orphys PLSSO) is a program cluster made to help management team in a company to manage, how customer's demand is fulfilled, using any available company's resources, in the least costly way.

Orphys PLSSO is capable to automate and optimalize the production and shipping schedule for manufacturing companies with multiple factory and multiple warehouse. As the program cluster it is capable of trying different possible schedule based on some heuristic value in a short time, and tell the production management team the least costly schedule found.

Orphys PLSSO is not a single program, it is a system consisting of several programs, They are :

Orphys Optimalization and Learning Server (OOLS)
Orphys Input Module
Orphys Web-based Interface

Orphys Optimalization and Learning Server (OOLS), is the brain of Oprhys PLSSO system. For Orphys PLSSO System to work, this OOLS program must simply be activated. When a company want to use Oprhys PLSSO system to optimize their production and shipping schedule, Orphys Web-based Interface will tell OOLS to make a schedule. When there is no request for any optimation, OOLS will learn from previous cases, about how to optimally optimize the company's production and shipping schedule.

Orphys Input Module, is one of two interface by which end-user can request OOLS to make and optimize a company's schedule. Orphys Input Module will ask end-users some information about the company, and turn the information into five files ( *.fac ; *.nmf ; *.fwhc ; *.ord ; *.nona ), which must be inputted later into Orphys Web-based Interface to make a schedule.

Orphys Web-based Interface, is the other interface by which end-user can request OOLS to make and optimize a company's schedule, by inputting the five files ( *.fac ; *.nmf ; *.fwhc ; *.ord ; *.nona ) generated by Orphys Input Module. This Web-based Interface is also useful for viewing the created schedule and report.

Download an Example of Orphys PLSSO Schedule. ( HTML )
Learn More about Orphys :

Introduction to Orphys PLSSO
What is the Input required ?
About Oprhys

Orphys Input Module

Orphys Input Module is a program, created as an interface for an end-user, to enter the information about company's resources and customer's order, that must be scheduled properly to avoid high fulfillment cost.

There are several information that must be provided for Orphys PLSSO to make a optimized schedule, they are :

Environment Configuration

Number of City and names of the Cities
Number of Shipping Service available, and their names
Shipping Service Cost and Time Matrix

Product Configuration

Machinery and Tools required to make a product
Data of Product and the Production Line Setting required to make a product

Customer and Ordering

Customer Data
Port To Customer Cost Matrix
Nota and Nota Detail Information

Factory Configuration

Number of Factories and Basic Factory Data
Initial Production Line Configuration

Warehouse Configuration

Current Warehouse Configuration Data
Warehouse To Shipper Cost Matrix
Warehouse's Finished Product Stock Matrix

Notice, that most page have a save and load buttons. These buttons are used to save or load some parts of the company information for later use. After saving some parts of company information, end-users can load the saved information by using load buttons, without the need of rewriting the information from scratch.

To convert the information into five files ( *.fac ; *.nmf ; *.fwhc ; *.ord ; *.nona ), which is required for OOLS to make and optimize a schedule, open the conversion page, and click write button. Conversely you can also read company's information from five file format, by clicking read button in conversion page.

Download an Example of Orphys PLSSO Schedule. ( HTML )
Learn More about Orphys :

Introduction to Orphys PLSSO
What is Orphys PLSSO Program Cluster consists of ?
About Oprhys

About Orphys

Orphys Production Line and Shipping Schedule Optimation, is a program I made to help manufacturing companies schedule their production and product shipping. The assumption had already been listed above.

If any reader here is interested to implement Orphys PLSSO in their company, just contact me by email.

Parameterized Post Newtonian Collision less Gravity Simulator

2008-01-24T05:58:00.000-08:00

Parameterized Post Newtonian Collision less Gravity Simulator (PPNCGS) is a program made to simulate the interaction between celestial bodies due to a force called gravity. The principal gravitational force on the celestial bodies is modeled by considering those bodies to be point masses in the isotropic, parameterized post-Newtonian (PPN) n-body metric. The equation used in PPNCGS is written in my previous posting "Plan 1 for Parameterized Post Newtonian Collision less Gravity Simulator" derived from equation [8-1] from http://iau-comm4.jpl.nasa.gov/XSChap8.pdf .

Collisions between bodies is assumed do not occur, for the same reason stated in NCGS design.

In addition to the usual information needed to run a simulation with NCGS, PPNCGS need several more information, they are :
- Speed of Light ( c )
- PPN parameter measuring the nonlinearity in superposition of gravity (Beta).
- PPN parameter measuring space curvature produced by unit rest mass (Gamma).
- For general relativity the value of Beta=Gamma=1.0

Comparative Study in Weak Gravity Field

The first comparative study of PPNCGS and NCGS will involve a planetary system with weak gravity field. The fictional system that we use to study is Erinton system. Erinton System consists of a star Erinton with mass of 1.5076 Solar Mass, and a planet named Eivalia with mass of 5.7665 Earth Mass orbiting it from a distance of 1 AU. The Initial orbital speed of Eivalia is 0.0003849 c. (see or click image for more detail)

Erinton System initial condition

Both NCGS and PPNCGS simulations are run to simulate the system for time length of 1 years, with time-step accuracy of 360 seconds.

Comparison between the simulation result

of NCGS and PPNCGS in weak gravity field.

Since the gravity field is weak, there is almost no difference between two simulation, although if we view the result in detail below, there is small difference between the position predicted by NCGS and PPNCGS.

Small difference in prediction position

Comparative Study in Strong Gravity Field

The next comparative study of PPNCGS and NCGS will involve a planetary system with strong gravity field. The fictional system that we use to study is Incada system. Incada System's primary star is Incada with mass of 1507.6 Solar Mass, which is orbited by a planet named Incada B with mass of 5.7665 Earth Mass, from a distance of 0.000733 AU. The Initial orbital speed of Incada B is 0.3 c. (see or click image for more detail)

Incada System initial condition

Since the gravity field of Incada is strong, and Incada B is orbiting its primary in very close orbit in relativistic speed, the simulations have to be run with time step accuracy of 0.003 seconds, to simulate the system behavior in a time length of 4 minutes 22.8 seconds.

Comparison between the simulation result

of NCGS and PPNCGS in strong gravity field.

The difference between two simulation result are huge since the gravity field involved is strong. While Newtonian simulation result shows elliptic orbit, taking General Relativity into account somehow causing the orbit of Incada B to become chaotic.

Download (PPNCGS and NCGS)'s (Program and Source Code) here

Attention : I have made a 3D online simulator in Orinetz.com which is Newtonian and collision capable. Here's a link to Planets only Solar System Simulation and Planet and Satellites Solar System Simulation.

Making Arithmetic function from Logical function ( Pascal, C )

2008-01-22T00:19:00.000-08:00

When I was in 12th Grade High School, I asked myself how a computer can do arithmetic. I had already programming Pascal since I was in Grade 7th, and I don’t know much about logic gates, yet at that time. But I know that in its very basic form, computer can only do logical operation such as AND, OR, NOT, XOR, SHL and SHR, so I asked myself, how can I make a function in capable to do addition without the use of the sign “+” in the program. These are the steps I take :

First, I make a truth table for basic binary addition in order to know what is needed in the function :
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10

Then I realize that the right hand side of the addition process above must be two bits long instead of only one bit, so I rewrite them in the form below
0 + 0 = 00
0 + 1 = 01
1 + 0 = 01
1 + 1 = 10

Later, I compare the truth table for several logic gates with the result I got above, it turn out that :
- the least significant bit, which I called R, show XOR logical relationship with the input.
R = A xor B .…(E1)

- the most significant bit, which I called C, show AND logical relationship with the input.
C = A and B ….(E2)

Since in its basic form the equation must be in the form of :
A + B = C shl 1 + R ….(E3)

By substituting E1 and E2 to equation E3 we got equation E4, below :
A + B = (A and B) shl 1 + (A xor B) ….(E4)

Then I write a Pascal recursive function capable of doing addition without using the sign “+”.

function AddLogic(const A : integer, B : integer) : integer;
var R,C : integer;
begin
R:=A xor B;
C:=(A and B) shl 1;

if (R=0) then R:=C;
else R:=AddLogic(R,C);

AddLogic:=VN;
end;

I realize later that I can do away with the recursive bit, by using repetition.

function AddLogic(const A : integer, B : integer) : integer;
var A1,B1,R,C : integer;
begin
A1:=A;
B1:=B;
repeat
R:=A1 xor B1;
C:=(A1 and B1) shl 1;
A1:=R;
B1:=C;
until (C=0) or (R=0);
if (R=0) then R:=C;
AddLogic:=VN;
end;

Which later I translate to C.

int AddLogic( int A, int B)
{ int A1,B1,R,C;
A1=A;
B1=B;
do
{ R=A1^B1;
C=(A1&B1)<<1;
A1=R;
B1=C;
} while (C&R);
if C R=C;
return R;
}

These programs didn't run as fast as if I just use the sign "+", which is a proof that something is still missing from my understanding. Later I realize that this level of detail is done in hardware layer instead of software layer. I will tell you what is missing in later posting.

Half Adder, Full Adder and Multiple Bit Adder

2008-01-22T00:13:00.000-08:00

Just like I told before in my previous posting titled “Making Arithmetic function from Logical function ( Pascal, C )”, there is something missing from my knowledge about how arithmetic function is performed by computers using their basic logical function. The missing part as I realized later, is the fact that the things done by programming functions I wrote in my previous posting, is not done at software level, but instead embedded as a firmware inside a computer’s Arithmetic Logic Unit.

Half Adder

I will rewrite Equation E1,E2,E3, and E4 from my previous posting stated above.
R = A xor B .…(E1)
C = A and B ….(E2)
A + B = C shl 1 + R ….(E3)
A + B = (A and B) shl 1 + (A xor B) ….(E4)

One of the basic function of a computer’s Arithmetic Logic Unit is Addition, which most basic part is a Half Adder. A Half Adder is a logic gate structure derived from equation E1 and E2, the C is actually an abbreviation for Carry, which means additional bit carried by the addition function to the More Significant Bit. Here is the structure of a Half Adder.

Several Symbol for Logic IO structure of a Half Adder

Full Adder

There is almost no use for us if computer is only capable of doing one bit addition. The Arithmetic function must be extended to Multiple Bit Addition. In order to add multiple bits, the Carry bit from Less Significant Bit must also be accommodated; this is why we have to make something called a Full Adder. A Full adder unit, have three inputs A,B,CI (Carry In) and two outputs FR (Full Result) and CO(Carry Out).

The relationship in a Full Adder is extended into equation E5 and E6 below :
FR = R xor CI ….(E5)
CO = (R and CI) or C ….(E6)

Several Symbol for Logic IO structure of a Full Adder

Multiple Bit Parallel Full Adder

Once the basic is in place, it is easy to make more advanced logical structure. Multiple Bit Parallel Full Adder is simply a structure made by connecting several Full Adder. The CO from a Less Significant Bit is connected as input for the CI of a More Significant Bit.

The input are vectors of bit, A (A0,A1,A2,A3) and B (B0,B1,B2,B3), with the result of vector R(R0,R1,R2,R3,R4), note that the A0,B0 and R0 are Least Significant Bits, while A3,B3 and R4 are Most Significant Bits.

Several Symbol for Logic IO structure of a 4 bits Parallel Full Adder
(click to view detail)

I realize later that Multiple Bit Full Adder is a basic component for other arithmetic function such as subtraction, multiplication and division. I will present the detail on how subtraction is done logically in the next posting in this blog.

Representation of Negative Number and Subtraction

2008-01-21T23:49:00.000-08:00

Representation of negative number

I was confused the first time I saw a 4 bits Parallel Full Adder, There is also some possibility that you may share the same confusion that I had. My confusion was, “What is that symbol H in a Parallel Full Adder ?”, “What is it for ?”. Later it turned out that Parallel Full Adder can also be used for subtraction, so Parallel Full Adder is somehow equivalent to a Parallel Full Subtractor.
Lets suppose that there is a positive number represented as 4 bits binary or 8 bits binary, the negative binary form of the number, is included in the table below :

Positive	4 bits	8 bits	Negative	4 bits	8 bits
0	0000	00000000	0	0000	00000000
1	0001	00000001	-1	1111	11111111
2	0010	00000010	-2	1110	11111110
3	0011	00000011	-3	1101	11111101
4	0100	00000100	-4	1100	11111100
5	0101	00000101	-5	1011	11111011
6	0110	00000110	-6	1010	11111010
7	0111	00000111	-7	1001	11111001
8	NONE	00001000	-8	1000	11111000

Table of binary representation

From the table above it can be inferred that all negative number’s binary representation have the value of 1 in its Most Significant Bits, which often called Sign Bit. So Sign Bit = 0, means that the number is positive, while Sign Bit = 1, means that the number is negative.

Parallel Full Subtractor

By doing some observation on the relationship between positive and negative number’s binary representation it is not hard, to arrive at equation E7 :
-B = not B +1 ….(E7)

Equation E8, is common arithmetic sense :
A - B = A + (-B) ….(E8)

By substituting equation E7 to equation E8, we can get equation E9 :
A – B = A + not B + 1 ….(E9)

Equation E9 is the basic thought required in order to understand how to use a Parallel Full Adder as a Parallel Full Subtractor, here is the logic in equation E10 and E11 :
{A + B = A + B + H, H = 0} ….(E10)
A – B = A + (-B) = A + not B + 1, which if H =1, is equivalent with equation E11 below
{A – B = A + not B + H, H = 1} ….(E11)

From Equation E0 and E11, it can be inferred that to make a Parallel Full Adder to become a Parallel Full Subtractor, we only need to add (not B+1) with A instead of B.

The input are vectors of bit, A (A0,A1,A2,A3) and B (B0,B1,B2,B3), with the result of vector R(R0,R1,R2,R3,R4), note that the A0,B0 and R0 are Least Significant Bits, while A3,B3 and R4 are Most Significant Bits.

Using 4bit Parallel Full Adder as 4 bit Parallel Full Subtractor.

Full Adder/Subtractor Hybrid

Full Adder/Subtraction Hybrid is a generalized use of a Parallel Full Adder as both Adder or Subtractor, depending on the Sign Bit (H). A Full Adder/Subtraction Hybrid is in fact one of the most simple Arithmetic Logic Unit in existence, with capability of Addition and Subtraction.

The logic construction of a Full Adder/Subtractor Hybrid

This is the most simple part of a Arithmetic Logic Unit

Since H is the Sign Bit, If H is true(1) the system output will be R = A - B, while if H is false(0) the system output will be R = A + B. This is done by placing XOR gates between (B0,B1,B2,B3), and the Sign Bit H, which work due to the fact that :
B xor H = B, if H=0
B xor H = not B, if H =1

More explanation on why this result in a Full Adder/Subtractor Hybrid is given in Equation E1 and E11
{A + B = A + B + H, H = 0} ….(E10)
{A – B = A + not B + H, H = 1} ….(E11)

In my later study it turn out that Full Adder is the basic part of many arithmetic logic application, including basic arithmetic like Parallel Multiplication, Parallel Division, or more advanced application (with Multiplexer and Demultiplexer included) like Float Adder, Float Subtractor, Float Multiplication and Float Division.

I will add these applications in my later posting.

Plan 1 for Parameterized Post Newtonian Collision less Gravity Simulator

2008-01-14T20:13:00.000-08:00

During the experiment “The effect of black hole passing by our solar” using NCGS, I was advised to include relativistic effect into the simulator, to see if something can be different. Therefore this blog is intended as a starting plan to make a new simulator called PPNCGS. Just to make sure I get the meaning of equation [8-1] from http://iau-comm4.jpl.nasa.gov/XSChap8.pdf right.

Parameterized Post Newtonian Collision less Gravity Simulator (PPNCGS), is an upgrade planned for simple Newtonian Collision less Gravity Simulator. By including the Parameterized Post Newtonian into the equation, the relativistic effect can be included into the n-body interaction in an NCGS. So, instead of only the value of G like in NCGS, the other cosmological constant, c will also be included in the simulator.

The original equation [8-1] from http://iau-comm4.jpl.nasa.gov/XSChap8.pdf is this :

Equation 8.1 from

Then we remove the asteroid calculation,

Equation A1. Asteroid removed

From here on this equation will be called equation A1

First we will need to make the equation, more computer friendly. Even if mathematically a*b+a*c = a*(b+c) , these two are not the same computationally. Multiplication need more time to process than addition, so a*b+a*c will need more time to process than a(b+c). Therefore, we simplify this equation to become equation A2, by collecting c from equation A1.

Equation A2

Then we by using the law of distribution, we simplify the red boxed part of equation A2, to become equation A3.

Equation A3

Equation A3 can further be simplified to become Equation A4.

Equation A4

In order to find the derivative of the function, we might need to use software called, Maple. In order to make the equation Maple readable, we must turn Equation A4 into Equation A5. Since Equation A5, is really complex (but Maple readable), I put some color on it to denote relationships between equation A4 and A5. (click image for detail)

Equation A5

After equation A5 have been checked for their compatibility with Equation A1, we will go further to the next step of making calculation network design (required to minimize the number of calculation required).

The other thing that must be done is to find the derivative of acceleration, as the numerical method used in the PPNCGS is Taylor Second Order.

Download NCGS Program and Source Code here

The Wobble of Star caused by Hot Jupiter class planets

2008-01-14T20:07:00.000-08:00

Hot Jupiters are planets with mass of several Jupiter orbiting as close as Mercury or Venus to their primary star. Planets with such mass orbiting the primary at close distance, may disrupt the movement of the star, causing it to wobble relative to the star’s proper motion.

To show this effect in detail, we will conduct several experiments with a 1.1775 Solar Mass star called Eltera, by placing one or two Hot Jupiters in the system.

Single planet

The first Hot Jupiter we place in this system is a 4.3359 Jupiter Mass planet, called Sivatra. Sivatra is placed in an orbit, 0.3 AU from Eltera, with initial orbital speed of 59.022 km/s (relative to Eltera). The wobble caused by Sivatra is shown below.

The wobble of Eltera caused by single planet orbiting it is relatively simple, by calculating the period of a wobble, we can calculate the period of Sivatra orbit. Then if we know the mass of the star Eltera, we can work out the radius of Sivatra orbit. By analyzing the strength of the wobble and taking the radius of Sivatra orbit, we can derive the mass of Sivatra.

Two planets

Now, how if we add another Hot Jupiter called, Ertina, with mass of 2.7558 Jupiter Mass into the Eltera System ? How the shape of the wobble will be ?

It turns out that depending on the starting position of Ertina relative to Sivatra, the shape of the wobble will be different, but there is a clear clue in the plot result, hinting that there are two planets in the system. The clue is the fact that in all figure above, all plot results shows retrograde movement, with two different period.

By analyzing the time difference per two knots over different time ( with the same method used to examine the plot result of sin(a*t)+sin(b*t) to derive the value of 2*Pi/a and 2*Pi/b ), we can derive the period of each planets. If the mass of Eltera is known, we can later derive the distance of each planets from Eltera, which is the information needed to calculate the mass of each planets.

Download NCGS Program and Source Code here

The movement of planet with eccentric orbit relative to other planet with eccentric orbit

2008-01-14T20:01:00.001-08:00

I had written a blog before about the movement of planets relative to other planets, but later I realized that in that blog, I only explained about planets occupying orbits with low eccentricty. The movement of planets with eccentric orbit relative to other planets with eccentric orbits is as interesting, if not more interesting, than if all planets occupy almost circular orbit.

For this experiment lets have a system consisted of a star, a hot jupiter and 3 earth sized planets. The Star is called Vigan ( yellow ), the Hot Jupiter is called Ephemis ( brown ). The three Earth sized planets are Miula ( magenta ), Sihen ( green ) and Altiva ( red ).

Vigan System

The yellow circle is Vigan, the primary star of Vigan system. The brown path is the orbit of Ephemis, the Hot Jupiter. The magenta math is the orbit of Altiva, and the green path is the orbit of Sihen, and the red path is the orbit of Altiva.

movement of planets in Vigan System relative to Ephemis

movement of planets in Vigan System relative to Altiva

movement of planets in Vigan System relative to Sihen

movement of planets in Vigan System relative to Miula

All plot results above show that the retrograde motion of a planets relative to other planets in the system, is more complex than if all planets occupy almost circular orbit.

The movements of planet relative to other planets are interesting things to experiment with. The plot results always show different and interesting new shapes. Whether we can somehow control the shape of the plot result by some kind of mathematic equation, is something I am interested to study.

Download NCGS Program and Source Code here.

The effect of black hole passing by our solar system ( Experiment 2 )

2008-01-14T19:50:00.000-08:00

Most people think that if a black hole is passing by our solar system, the black hole is going to suck everything in the solar system, into it. This is not entirely true, matter only get sucked by a black hole if it pass too close to it. Once matter enter the event horizon, there will be no way back, but the Schwarzchild Radius of a black hole is far less than the size of our solar system.

For a comparison, the size of the Sun is far smaller than the size of the solar system, and a black hole is something that have far higher density than ordinary star like our Sun. From these facts, we can easily know that a black hole ,with the same size as the Sun, will have smaller Schwarzchild Radius than the size of the Sun, so it must be several order of magnitude smaller than the size of our Solar System.

What we have to worry about if a black hole passing by our solar system is not about getting sucked into it, like most people believe. We have to worry about the effect of its gravity, which may disrupt the orbit of some planets in our solar system. For example, a black hole passing by between Mars and Jupiter, may disrupt the "stability" of asteroid belt, causing it to enter the inner region of solar system. This may increase the probability of meteors hitting the inner planets.

Fifth Case - 1000 Solar Mass Black Hole

In this experiment, a 1000 Solar Mass Black Hole is going to pass the solar system plane, 1.26 AU from the sun, 2.26 AU from earth. All planets are lining up in one side of the solar system, while the 1000 Solar Mass Black Hole "hit" solar system in the opposing side. Initially the black hole is 9.6E12 m ( 64,000 AU ) away from the solar system plane, and closing the solar system with speed of 0.1c. ( click image for more detail )

As seen from the experiment result, the Black Hole had pulled the Sun, and disrupt the orbit of outer planets. The only "surviving" planets are Mercury, Venus and Earth, but Venus and Earth now have orbit with greater eccentricity. This may cause Earth to be baked by the Sun in the closest point, or frozen in the farthest point, which will surely disrupt the biosphere. Sun have been pulled away by the black hole, causing the outer planets to be left behind, becoming rogue planets, planets that don't orbit any star.

There is a feature that interest me in bottom left picture, which is about the movement of other planets as viewed from Earth. The movement of planet lefts behind by the Sun relative to Earth, display something called retrograde movement, caused by the fact that Earth is orbiting the Sun. This movement is in fact, was one of the sign that not all celestial bodies orbit earth, like geocentric theorist believed.

Sixth Case - 1000 Solar Mass Black Hole

In this experiment, a 1000 Solar Mass Black Hole is going to pass solar system plane, 3.3333 AU from the Sun, between the orbit of Mars and Jupiter. Initially the black hole is 9.6E12 m ( 64,000 AU ) away from the solar system plane, and closing the solar system with speed of 0.01c. ( click image for more detail )

The experiment result shows, that most planets orbit was disrupted so badly, that the only "surviving" planets is Mercury and Earth. All the outer planets have at one time pass the Sun in close distance ( top-left ). Jupiter was especially so close to the sun, that we can expect it to become a gigantic comet for several days, before escaping to the interstellar space. Both Mercury and Earth now, occupy orbits with greater eccentricity than originally was.

The other interesting features is the movement of Earth relative to Mercury and Mercury relative to earth, after the black hole leave our solar system plane (mid-right and bottom left). The movement of both Earth relative to Mercury and Mercury relative to Earth are chaotics, and exhibit a shape of "&". This had lead me to plan for the next experiment about "the movement of planet with eccentric orbit relative to other planet with eccentric orbit", which I will upload later.

Seventh Case - 1000 Solar Mass Black Hole

This 7th experiment is the same with the 6th experiment, except that now I use 100 Solar Mass Black Hole. ( click image for more detail )

The experiment result shows, that all inner planets had "survived" but have to exhibit more eccentric orbit. The new orbit of Mercury and Earth have some point where they are so close, that there might be two probability that can happen, Mercury may hit Earth sometimes in the future, or Earth may slingshot Mercury away as they come close enough but didn't hit each other. The disruption caused by the black hole had caused all the outer planet to escape the Solar System.

In all experiment, I realize that there is something general there. It is easier for black hole to disrupt the orbit of outer planets, while it is harder to disrupt the orbit of inner planets. Planets close to the sun, have smaller probability of being thrown away from the solar system, even if they have to occupy orbit with higher eccentricity after the black hole had leave the solar system.

Download NCGS Program and Source Code here

Newtonian Collision less Gravity Simulator

2008-01-12T19:30:00.001-08:00

Newtonian Collision less Gravity Simulator

Newtonian Collision less Gravity Simulator (NCGS) is a program made to simulate the interaction between celestial bodies due to a force called gravity. As the name suggests, the simulator is based on Newtonian Gravity, and it is assumed thatcollisions between objects do not occur. The assumption that collisions never happen is based on the fact that the size of celestial bodies are very small compared to the distance between celestial bodies. The other assumption is that celestial bodies are point-sized.

What information does a NCGS need in order to make a simulation? There are several pieces of information required in order to make a simulation with a gravity simulator, they are :
- Gravity Constant
- The mass of celestial objects
- The position vector of celestial objects
- The velocity vector of celestial objects

Why do I see celestial objects colliding in an NCGS, but act as though they never collide? Since the distance between celestial bodies, even inside a planetary system, is astronomical compared to the size of celestial bodies themselves, the size of the icons representing each celestial bodies are thus not drawn to scale. If we are to make a true scale simulation, with one pixel sized icon representing earth, then we would need 12500 pixels to represent the distance between Earth and the Sun ( I think this is greater than the maximum resolution of most monitors, or the maximum resolution that common Graphic Accelerator can handle ). So objects seemingly collide in NCGS, have a high probability of not actually colliding.

The Math behind NCGS

Download NCGS Program and Source Code here

Preview

Inner Solar System (Plus Jupiter) without Trailing

Inner Solar System (Plus Jupiter) with Trailing

The effect of a black hole passing by our solar system

2008-01-12T19:24:00.001-08:00

The effect of a black hole passing by our solar system

When we discussing about astronomy, there are lots of interesting questions which reflects our interests about the universe, come out from the creative mind of science fiction fans. One of them is about what happen to our solar system if a black hole enter and pass by our solar system. Of course the answer depends on how big the black hole is, and where on the solar system plane, the black hole passes by.

Here I will show the result of my experiment, not using actual stars, planets and black holes, of course, as you can believe me, I am not strong enough to throw a black hole to a solar system, and I am not rich enough to have more than one solar system at my disposal. NCGS is a good tool to use if we want to do some experiments, inexpensive compared to using real solar system and black hole.

As the NCGS that I use doesn’t take relativistic effect into account, I will use black holes, moving at 3E7 m/s or 0.1 c (so the relativistic effect can be neglected), to bombard a model resembling our solar system.

First Case - 100 Solar Mass Black Hole, Opposing Side

The first case here is the one where a 100 Solar Mass black hole is closing by from a place 2E12 m ( 13.333 AU )above the solar system plane, with speed of 3E7 m/s ( 0.1c ). The black hole will spend about two days inside the 2E12 m sphere with sun at the center, and intersect the solar system plane, 189,590,000 km ( 1.2639 AU ) away from the Sun, and 339,590,000 km away from Earth. (click image for more detail)

The result is that the black hole only gives Sun and any other planets inside the solar system, some acceleration, then leave it alone. The Sun is accelerated, along with other planets, but the planets still orbit the Sun as if nothing had happened. This is because the tidal force of the black hole is not enough to break the formation of the solar system.

Second Case - 1000 Solar Mass Black Hole

So the next we will use a bigger black hole, with 1000 Solar Mass. The black hole is closing by from a place 4.8E12 m ( 32 AU ) above the solar system plane, with speed of 3E7 m/s ( 0.1c ). The black hole will spend about two days inside the 2E12 m sphere with sun at the center, and intersect the solar system plane, 189,590,000 km ( 1.2639 AU ) away from the Sun, and 245,262,110 km away from Earth. (click image for more detail)

Now, the black hole disrupts the orbit of Venus, Mars and Earth and throws them out of our Solar System. Mercury, which lies in the innermost orbit, doesn’t suffer as much as other planet, as the energy of the black hole isn’t enough to throw it out of orbit, but now mercury have an orbit with greater eccentricity.

Third Case - 1000 Solar Mass Black Hole

In the previous experiment, the black hole pass the solar system plane, in the middle of the first and second quadrant, in this experiment will pass the solar system plane, in the middle of the third and fourth quadrant, where all planets are headings to. Now, what will happen if a 1000 Solar Mass black hole intersect the solar system plane, 189,590,000 km ( 1.2639 AU ) away from the Sun, and 234,095,984 km away from Earth. (click image for detail)

Surprisingly, the black hole didn’t do as much damage as if the black hole intersects the solar system plane in the other side. Now Mercury, Venus, Earth and Mars have an orbit with higher eccentricity, but none of them escape the solar system.

Fourth Case - Two 1000 Solar Mass Black Hole

Now, lets consider what happen if something like two 1000 Solar Mass black holes pass our beloved astronomical backyard. See the data inside the image for more information, as the condition involved is a bit complicated. (The two white trail is the path of the black hole)

As we can see, now both Earth and Mars are slingshoted away from the solar system. Some outer planets in other hand are closing to the sun. We can see the orbit of Jupiter, Saturn and Uranus, inside the 1E12 m radius from the sun. If big planets are closing by the Sun, then it is also likely that objects like the asteroid belt will also come to the inner part of the solar system, putting the inner planet ( if they are still inner planet ) into the danger of meteor shower. But the giant planets closing by have some probability to offer some protection from this catastrophe.

Black hole passing a planetary system doesn’t always seems to bring too much trouble if the black hole is in the order of 100 Solar Mass, as the tidal force is not enough to disrupt the planetary system. Black hole in the order of 1000 Solar Mass is of course more dangerous, but they are as rare as stars with equal mass, so it is not really something to worry about.

There are still thousands of interesting scenarios to try out, and I am still work out on a Black Hole Catastrophic Probability Simulator, which will be capable of simulating more than one scenario, I will upload them later.

The Orbit of Planets as seen from other Planets

2008-01-12T19:13:00.000-08:00

The plot result of the movement of planets, as seen from other planets is interesting to study. One of the interesting points is the fact that if a planet orbits the sun in circular orbit, the plot of the sun movement relative to that planet will also form a circular "orbit". This is by no means saying that if a planet orbits the sun, then it is equivalent with sun orbit the planet.

The planet is not inside inertial reference frame, since it is accelerated by Sun’s gravity, which is greater than the gravity of any planet. So the planet change reference frame all time, which is why the “movement” of Sun relative to a planet (assuming that the planet is have mass far less than the Sun), is called imaginary movement.

The movement of other planets, as seen from Earth

By putting earth as the centre of the coordinate system used to plot the movement of other planets, we can see an effect usually called retrograde motion. The motion of Mercury for example, resembles a closing and distancing motion, with great knot, caused by the movement of both Mercury and Earth. The “orbit” of Sun, forms a circle with radius equal with the orbit of Earth. The most interesting one for me is the movement of Venus, which have small knot, and the total orbit making a shape resembling a pentagonal flower.

The movement of other planets, as seen from Mercury

By putting Mercury as the centre of the coordinate system used to plot the movement of other planets, we get the picture above. As Mercury is the innermost planet, the knot formed by the movement of other planets relative to Mercury is big. The total plot resembles something like the eye of a lizard.

The movement of other planets, as seen from Venus

The movement of Mars, as seen from Venus is something interesting for me. Instead of forming a circle with lots of knots inside, like the movement of other planets, the movement of Mars relative to Venus forms an 8. This is because the distance of Venus and Mars, when Mars is near the 5’o clock and 11’o clock direction of Venus, is always the same.

The movement of other planets as seen from Mars

The movement of Earth and Venus relative to Mars are the most interesting feature in this plot result for me. As the movement of Mars forms an 8 as seen from Venus, the movement of Venus as seen from Mars is also forming the same shape. This is because the distance of Mars and Venus, when Venus is near the 5’o clock and 11’o clock direction of Mars is always the same. The movement of Earth forms some kind of flower shaped form, with seven sides. This is of course doesn’t have any relationship with the fact that there are flowers in earth. :)

My conclusion about these experiments is that forms, made by the movement plot of an object A relative to another Object B, is always the same with the movement plot of object B, relative to object A.

The movement of other planets as seen from outer planets will be uploaded later.

Multiplexer and Demultiplexer

2008-01-11T01:07:00.000-08:00

Multiplexer and Demultiplexer are simple device made from basic logic gates. The devices are basic parts of Read Only Memory (ROM), Random Access Memory (RAM), and Arithmetic Logic Unit(ALU).

Multiplexer is a device used to select one of several input as the output of the device (Out).
The device works by selecting the input choosen by S1,S2,S3.

Demultiplexer is a device used to select one of several output line, to which it must transfer an input (In) value.
The device works by selecting the output choosen by S1,S2,S3.

Basic Logic Gate

2008-01-11T00:55:00.000-08:00

Logic gates are the basic parts of binary computers. Basically what logic gates do is mapping one, two or more digital signal into a digital output. There are basically 8 kinds of logic gates, they are AND, OR, NOT, NAND, NOR, XOR, NXOR, and BUF.

AND logic gate gives true (1) output, if and only if, all of its input are true (1).
OR logic gate gives true (1) output, if and only if, at least one of its input are true (1).
NOT logic gate is a single input single output logic gate, which output is the negation of its input.
NAND logic gate gives false (0) output, if and only if, all of its input are true(1).
Basically it can be thought as if a NAND logic gate is a combination of an AND and a NOT logic gate.
NOR logic gate gives false (0) output, if and only if, at least one of its input are true (1).
Basically it can be thought as if a NOR logic gate is a combination of an OR and a NOT logic gate.

XOR logic gate gives true (1) output, if and only if, the number of its true (1) input are odd.

NXOR logic gate gives true (1) output, if and only if, the number of its true (1) input are even.
BUF logic gate is a single input single output logic gate, which output is the same as its input.
Probably it doesn't make sense that there is such gate, but actually it have its own application in digital electronics as signal amplifier.

Animal Equation

2008-01-10T19:20:00.000-08:00

The Animal Shaped Equation blog is my blog dedicated to show animal shaped mathematical equation I had made earlier using a software called Maple. My purpose of creating them are :

Showing that mathematic and arts are inseparable, there is a way to use math as a canvas for our creativity.
A part of an algortithm used to tell nano-assembler what kind of structure it must assemble.

This is the link to my Animal Shaped Equation blog.

http://animalshapedequations.blogspot.com/

Have fun,

Fendy.