Beauty of Discrete-Time Attractors

on 15 Oct 2022

% Inspired by the work of Paul Bourke

% see http://paulbourke.net/fractals/clifford/

N = 1e8;

x = single(zeros(N,1)); % required for speed up

y = x;

F = @(x,y) [,];

% Clifford Attractor - discrete system

for k=1:N-1

x(k+1)=sin(-2*y(k))+cos(-2*x(k));

y(k+1)=sin(2*x(k))-cos(2*y(k));

end

I = zeros(900);

E = 1;

D = size(I,1) - 2*E;

for k=1:N

W=ceil(D*(x(k)+2)/4)+E;

U=ceil(D*(y(k)+2)/4)+E;

I(W,U)=I(W,U)+.002;

end

imshow(I);

set(gcf,'Color','k');

axis tight;

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