%
% Turing instability
%
% Math Bio 472, Jae-Hun Jung, March, 2007

clear all, close all
N=50;
x = linspace(-pi,pi,N);
y = x;

h = 2*pi/(N-1);
k = h^2/10;

c1 = 0+0.01*cos(2*x); c2 = 0+0.01*cos(2*y);

D1 = 0.1; D2 = 0.01;
%D1 = 0.1; D2=2;

for i = 1:10000
    tmp1 = c1(2:N-1); tmp2 = c2(2:N-1);
    d1(2:N-1) = tmp1 +k*tmp2+k*D1*(c1(3:N)-2*tmp1+c1(1:N-2))/(h^2);
    d1(N) = c1(N)+k*c2(N)+k*D1*(c1(2)-2*c1(N)+c1(N-1))/(h^2);
    d1(1)=d1(N);
    d2(2:N-1) = tmp2 +k*tmp1+k*D2*(c2(3:N)-2*tmp2+c2(1:N-2))/(h^2);
    d2(N) = c2(N)+k*c1(N)+k*D2*(c2(2)-2*c2(N)+c2(N-1))/(h^2);
    d2(1)=d2(N);
    imagesc(d1,[0 1]);
    pause(0.001);
    c1=d1; c2=d2;
end