Problem Statement

Implement the Drossel and Schwabl definition of the forest-fire model.

It is basically a 2D   cellular automaton   where each cell can be in three distinct states (empty, tree and burning) and evolves according to the following rules (as given by Wikipedia) Neighborhood is the   Moore neighborhood;   boundary conditions are so that on the boundary the cells are always empty ("fixed" boundary condition). At the beginning, populate the lattice with empty and tree cells according to a specific probability (e.g. a cell has the probability 0.5 to be a tree). Then, let the system evolve. Task's requirements do not include graphical display or the ability to change parameters (probabilities   p   and   f )   through a graphical or command line interface.

Let's start with the solution:

function forest_fire(f,p,N,M)
% Forest fire
if nargin<4;
	M=200; 
end
if nargin<3;
	N=200; 
end
if nargin<2;
	p=.03; 
end
if nargin<1;
	f=p*.0001; 
end

% initialize;
F = (rand(M,N) < p)+1;  % tree with probability p 
S = ones(3); S(2,2)=0;  % surrounding

textmap = ' T#';
colormap([.5,.5,.5;0,1,0;1,0,0]);
while(1)
	image(F); pause(.1)    % uncomment for graphical output 
	% disp(textmap(F));	pause;		  % uncomment for textual output 		
	G = ((F==1).*((rand(M,N)<p)+1));  % grow tree 
	G = G + (F==2) .* ((filter2(S,F==3)>0) + (rand(M,N)<f) + 2);  % burn tree if neighbor is burning or by chance f
	G = G + (F==3);						 % empty after burn
	F = G;
end;