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/