Leandro Barajas’ Blog
… and other ponderings in 11th-dimensional space

MATLAB’s version of Conway’s Game of Life in 3D

Jul 28th, 2010 | By | Category: Matlab

My 3D version expansion of Conway’s Game of Life.

 

Conway's game of life in 3D

 
function life3D(action)
%LIFE3D   MATLAB's version of Conway's Game of Life.
%   "Life" is a cellular automaton invented by John
%   Conway that involves live and dead cells in a  
%   rectangular, two-dimensional universe. In      
%   MATLAB, the universe is a sparse matrix that   
%   is initially all zero.                         
%                                                  
%   Whether cells stay alive, die, or generate new 
%   cells depends upon how many of their eight     
%   possible neighbors are alive. By using sparse  
%   matrices, the calculations required become     
%   astonishingly simple. We use periodic (torus)  
%   boundary conditions at the edges of the        
%   universe. Pressing the "Start" button          
%   automatically seeds this universe with several 
%   small random communities. Some will succeed    
%   and some will fail.     
%
%   Expanded to 3D by:
%       Leandro Barajas 06-20-2002 L.G.Barajas@ieee.org
%
%   C. Moler, 7-11-92, 8-7-92.
%   Adapted by Ned Gulley, 6-21-93
%
 
%   Copyright 1984-2001 The MathWorks, Inc. 
%   $Revision: 5.9 $  $Date: 2001/04/15 12:03:02 $
 
% Possible actions:
% initialize
% start
 
% Information regarding the play status will be held in
% the axis user data according to the following table:
play= 1;
stop=-1;
 
if nargin<1,
   action='initialize';
end;
 
if strcmp(action,'initialize'),
   figNumber=figure( ...
      'Name','Life3D: Conway''s Game of Life in 3-Dimesions', ...
      'NumberTitle','off', ...
      'DoubleBuffer','on', ...
      'Visible','off', ...
      'Color','white', ...
      'BackingStore','off');
   axes( ...
      'Units','normalized', ...
      'Position',[0.05 0.05 0.75 0.90], ...
      'Visible','off', ...
      'DrawMode','fast', ...
      'Color','none',...
      'NextPlot','add');
%      'NextPlot','replace' );
 
   text(0,0,{'Press the "Start" button to see the Game of Life demo' 'Use the slider to change the number of initial cells.'}, ...
      'HorizontalAlignment','center');
   axis([-1 1 -1 1]);
 
   %===================================
   % Information for all buttons
   labelColor=[0.8 0.8 0.8];
   yInitPos=0.90;
   xPos=0.85;
   btnLen=0.10;
   btnWid=0.10;
   % Spacing between the button and the next command's label
   spacing=0.05;
 
   %====================================
   % The CONSOLE frame
   frmBorder=0.02;
   yPos=0.05-frmBorder;
   frmPos=[xPos-frmBorder yPos btnLen+2*frmBorder 0.9+2*frmBorder];
   h=uicontrol( ...
      'Style','frame', ...
      'Units','normalized', ...
      'Position',frmPos, ...
      'BackgroundColor',[0.50 0.50 0.50]);
 
   %====================================
   % The START button
   btnNumber=1;
   yPos=0.90-(btnNumber-1)*(btnWid+spacing);
   labelStr='Start';
   cmdStr='start';
   callbackStr='life3D(''start'');';
 
   % Generic button information
   btnPos=[xPos yPos-spacing btnLen btnWid];
   startHndl=uicontrol( ...
      'Style','pushbutton', ...
      'Units','normalized', ...
      'Position',btnPos, ...
      'String',labelStr, ...
      'Interruptible','on', ...
      'Callback',callbackStr);
 
   %====================================
   % The STOP button
   btnNumber=2;
   yPos=0.90-(btnNumber-1)*(btnWid+spacing);
   labelStr='Stop';
   % Setting userdata to -1 (=stop) will stop the demo.
   callbackStr='set(gca,''Userdata'',-1)';
 
 
   % Generic button information
   btnPos=[xPos yPos-spacing btnLen btnWid];
   stopHndl=uicontrol( ...
      'Style','pushbutton', ...
      'Units','normalized', ...
      'Position',btnPos, ...
      'Enable','off', ...
      'String',labelStr, ...
      'Callback',callbackStr);
 
   %====================================
   % The NumberOfCell Slider
   labelStr='# Cells';
 
   callbackStr='h=findobj(gcf,''Tag'',''StartCells'');set(h,''Tooltip'',sprintf(''Initial Cells: %4d'',floor(get(h,''Value''))));';
   infoHndl=uicontrol( ...
      'Style','slider', ...
      'Units','normalized', ...
      'Position',[xPos btnWid+btnWid*2+0.05 btnLen/4 0.10*3], ...
      'String',labelStr, ...
      'SliderStep',[.01 .1], ...
      'Max',100, ...
      'Min',1, ...
      'Value',20, ...
      'Tooltip','Initial Cells:  20',...
      'Tag','StartCells', ...
      'Callback',callbackStr);
 
 
  %====================================
   % The INFO button
   labelStr='Info';
   callbackStr='life3D(''info'')';
   infoHndl=uicontrol( ...
      'Style','push', ...
      'Units','normalized', ...
      'Position',[xPos 0.20 btnLen 0.10], ...
      'String',labelStr, ...
      'Callback',callbackStr);
 
   %====================================
   % The CLOSE button
   labelStr='Close';
   callbackStr='close(gcf)';
   closeHndl=uicontrol( ...
      'Style','push', ...
      'Units','normalized', ...
      'Position',[xPos 0.05 btnLen 0.10], ...
      'String',labelStr, ...
      'Callback',callbackStr);
 
   % Uncover the figure
   hndlList=[startHndl stopHndl infoHndl closeHndl];
   set(figNumber,'Visible','on', ...
      'UserData',hndlList);
 
   view(3);  
   StartCells = 20;
   m = 19;
   colormap(jet(m));
   colorbar;
 
elseif strcmp(action,'start'),
   objh=findobj(gcf,'Tag','StartCells');
   StartCells = get(objh,'Value');
   m = 19;
   cla;
   axHndl=gca;
   figNumber=gcf;
   hndlList=get(figNumber,'Userdata');
   startHndl=hndlList(1);
   stopHndl=hndlList(2);
   infoHndl=hndlList(3);
   closeHndl=hndlList(4);
   set([startHndl closeHndl infoHndl],'Enable','off');
   set(stopHndl,'Enable','on');
 
   % ====== Start of Demo
   set(axHndl, ...
      'UserData',play, ...
      'DrawMode','fast', ...
      'Visible','on');
   box off
 
   X = zeros(m,m,m);
 
   p = -1:1;
   for count=1:StartCells,
      kx=floor(rand*(m-4))+2; 
      ky=floor(rand*(m-4))+2; 
      kz=floor(rand*(m-4))+2; 
      X(kx+p,ky+p,kz+p)=(rand(3,3,3)>0.5);
   end;
 
 
   % The following statements plot the initial configuration.
   % The "find" function returns the indices of the nonzero elements.
   plothandle=[];
   figure(gcf);
   hold on
   colour=jet(m);
   for k=1:m
       [i,j] = find(X(:,:,k));
%       kd = sub2ind(size(X(i,j,k)),i,j)      
       kd = k(ones(size(i)));
       if isempty(i)
           i = 1;
           j = 1;
           kd = NaN;
       end
       plothandle(k) = line(i,j,kd);
       set(plothandle(k),'linestyle','none',...
                      'Marker','.',...
                      'MarkerSize',20*2,...
                      'MarkerFaceColor',colour(k,:),...
                      'MarkerEdgeColor',colour(k,:),...
                      'EraseMode','normal');
 
   end   
   drawnow                  
   axis([0 m+1 0 m+1 0 m+1]);
 
   hold off
 
 
   % Whether cells stay alive, die, or generate new cells depends
   % upon how many of their eight possible neighbors are alive.
   % Here we generate index vectors for four of the eight neighbors.
   % We use periodic (torus) boundary conditions at the edges of the universe.
 
   n = [m 1:m-1];
   e = [2:m 1];
   s = [2:m 1];
   w = [m 1:m-1];
   u = [m 1:m-1];
   d = [2:m 1];
 
   rotate3d on
   while get(axHndl,'UserData')==play,
    % How many of eight+5+5 neighbors are alive. (only the ones that share at least one border
    %      N = X(n,:,:) + X(s,:,:) + X(:,e,:) + X(:,w,:) + ...
    %          X(n,e,:) + X(n,w,:) + X(s,e,:) + X(s,w,:);
 
    % 3D Version
 
    % Use Euclidean distance
    d1 = 1/1;           % Adjacent cells (Share 4 vertix)
    d2 = 1/sqrt(2);     % Diagonal cells (Share 2 vertix)
    d3 = 1/sqrt(3);     % Double Diagonal cells (Share 1 vertix)
 
    % How many of 9+9+8 neighbors are alive. (Only the ones that share at least one vertix)
      N = X(n,:,:)*d1 + X(s,:,:)*d1 + X(:,e,:)*d1 + X(:,w,:)*d1 + ...
          X(n,e,:)*d2 + X(n,w,:)*d2 + X(s,e,:)*d2 + X(s,w,:)*d2 + ...
          X(n,:,u)*d2 + X(s,:,u)*d2 + X(:,e,u)*d2 + X(:,w,u)*d2 + ...
          X(n,:,d)*d2 + X(s,:,d)*d2 + X(:,e,d)*d2 + X(:,w,d)*d2 + ...
          X(n,e,u)*d3 + X(s,e,u)*d3 + X(s,w,u)*d3 + X(n,w,u)*d3 + ...
          X(n,e,d)*d3 + X(s,e,d)*d3 + X(s,w,d)*d3 + X(n,w,d)*d3 + ...
          X(:,:,u)*d1 + X(:,:,d)*d1;
 
 
      % A live cell with two live neighbors, or any cell with three
      % neigbhors, is alive at the next time step.
      Xold = X;
 
      CL = 3.0;             % Minimun # cells to create a new one
      CH = 4.0;             % Maximum # cells to create a new one
      KL = 4.0;             % Minimun # cells to kill one
 
      X = ( (    ((N >= CL) & (N <= CH)) ) &...    % Create cells
         ~(  X & ((N >  KL)           )) ) ;       % Kill cells by overpopulation
 
      Xsum = sum(X(:));
      if (Xsum>prod(size(X))/8);
         X = ( X & (rand(size(X))>0.1) ); % Expontaneous cell annihilation
      end
 
      if Xold==X   % if no change the exit
         break;
      end
 
      % Update plot.
      for k=1:m
          [i,j] = find(X(:,:,k));
          set(plothandle(k),'xdata',i,'ydata',j,'zdata',k(ones(size(i))));
      end   
 
      set(plothandle,'Visible','on');
      box on
      title( sprintf('Total Cells: %d',Xsum))
      xlabel(sprintf('Density: %5.2f%%',mean(X(:))*100))
      ylabel(sprintf('Rate: %5.2f%%',(mean(X(:))-mean(Xold(:)))*100))
 
      drawnow
      pause(0.2)
   end
 
   % ====== End of Demo
 
   set([startHndl closeHndl infoHndl],'Enable','on');
   set(stopHndl,'Enable','off');
 
elseif strcmp(action,'info');
   helpwin(mfilename);
 
end;    % if strcmp(action, ...

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