Simple 1-D Cellular Automata

Here's some Matlab code for the particularly simple CA which Wolfram extensively classified and studied. The beauty of this code, and something I haven't seen elsewhere, is that the function takes the Wolfram classification number as an argument (e.g. wolfram(110);), making it simple to investigate each of them.

Couple of hundred updates of rule 182, showing pretty triangles

Example Output from the Code, showing Wolfram's Rule 182

function wolfram(wolfrule, initialstate, nrows)
% WOLFRAM    Displays evolution of a famous 1-D Cellular Automata.
%    Pick a rule from 1-256 (Wolfram's classification),
%    WOLFRAM(110) is the most famous, but many others are interesting:
%    rich=[18 30 45 73 89 101 102 105 109 110 126 129 135 ...
%        137 149 151 153 161 167 169 181 182 183 193 195 225];
%    Some rules die immediately with the default inital state, so
%    you must specify your own to see anything:
%    WOLFRAM(92, [1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0], 100);
%    Displaying all rules is interesting to appreciate the richness of
%    this CA's behaviour: for i=1:256, WOLFRAM(i), pause(0.5); end
%    Or jump to the rich ones: for i=rich, WOLFRAM(i), pause(2); end
%        Iain Haslam, April 2006.
if nargin < 3, nrows=700; end
if nargin < 2 %Use default initial state
    ncols=700; A=zeros(nrows,ncols); A(1,ncols-1)=1;
else
    [unused, ncols]=size(initialstate)
    A=zeros(nrows, ncols); A(1,:)=initialstate;
end
rule=dec2bin(wolfrule,8);
for i=1:8
    ru(i)=str2num(rule(i));
end
for i=2:nrows
    for j=2:ncols-1 
        l=A(i-1,j-1); m=A(i-1,j); r=A(i-1,j+1);
        if(( l & m & r & ru(1)) | ...
           ( l & m &~r & ru(2)) | ...
           ( l &~m & r & ru(3)) | ...
           ( l &~m &~r & ru(4)) | ...
           (~l & m & r & ru(5)) | ...
           (~l & m &~r & ru(6)) | ...
           (~l &~m & r & ru(7)) | ...
           (~l &~m &~r & ru(8)) )
            A(i,j)=1;
        end
    end
end
colormap(gray(2)); image(2-A); axis image; title(wolfrule);

Simple 1-D Cellular Automata

Comments

thanks