Tuesday, August 19, 2008

Example of Chaos in Rule 23-3

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.

Saturday, August 2, 2008

My website : www.tmvfood.com

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

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