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Re: 2D cellular automata (non-totalistic)

• To: mathgroup at smc.vnet.net
• Subject: [mg75047] Re: 2D cellular automata (non-totalistic)
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sun, 15 Apr 2007 05:11:09 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <evpnh0$60l$1@smc.vnet.net>

alexxx.magni at gmail.com wrote:
> Greetings,
> I want to re-implement a 2D CA I already wrote time ago in C++.
> Its scope was to read a BW image, then evolve it according to some
> rules. Specifically, by the rules I wrote I am able to "etch" the
> input image obtaining a skeleton or graph of the input image...
> These rules, if I understand correctly the term, are non-totalistic,
> i.e. they don't depend just on the total number of B/W cells in the
> neighborhood.
> 
> Example from my input file:
> ...............
> RuleSEinput
> 0 0 0
> 0 1 1
> 0 1 1
> RuleSEoutput
> 0 0 0
> 0 0 1
> 0 1 1
> .......................
> RuleTreeLeftinput
> 1 1 0
> 1 1 0
> 1 1 0
> RuleTreeLeftoutput
> 1 1 0
> 1 0 0
> 1 1 0
> ........................  etc
> 
> my program scans the image with the *input pattern, substituting the
> *output pattern if a match occurs (scanning with or without overlap,
> i.e. with a step=1 or step=3 along x and y in the case of 3x3 rules) .
> 
> Is this a nontotalistic 2dCA?
> 
> Now, do you have some hint on how to implement it in Mathematica - or
> has something similar already been done?
> 
> thanks for any help...
> 
> 
> Alessandro Magni
> 
> 

Hi Alessandro,

Since version 4.2, Mathematica includes a built-in function called 
CellularAutomaton [1, 2]. Chapter 5 [3] of Stephen Wolfram's _A New Kind 
of Science_ may be worth reading as well as the implementations notes 
starting on page 927 [4].

Overall, I believe that these kind of questions would be better answered 
if asked in the NKS Forum [5].

Regards,
Jean-Marc

[1] "CellularAutomaton", 
http://documents.wolfram.com/mathematica/functions/CellularAutomaton

[2] _The Mathematica Book_, "3.8.6 Cellular Automata".
http://documents.wolfram.com/mathematica/book/section-3.8.6

[3] _A New Kind of Science_, "Chapter 5: Two Dimensions and Beyond",
http://www.wolframscience.com/nksonline/chapter-5

[4] _A New Kind of Science_, "Chapter 5 Notes > Section 2 > Page 927",
http://www.wolframscience.com/nksonline/page-927

[5] _A New Kind of Science Forum_, http://forum.wolframscience.com/