animated fractal

animated_fractal.m

[X,Y] = meshgrid(-2:.008:2);
Z = ones(size(X));

h = figure;
for frame = -2:.01:2
    for x_ = 1: size(X,1)
        for y_ = 1: size(X,2)
            u = [X(x_,y_),Y(x_,y_)];
            for i = 1:100
    %             julian set
    %             v = [u(1) * u(1) - u(2) * u(2) +  -0.550, u(2) * u(1) + u(2) * u(1)+ -0.550];

    %           mandelbrot set
    %             v = [(u(1) * u(1) - u(2) * u(2)) +  X(x_,y_), (u(2) * u(1) + u(2) * u(1)) + Y(x_,y_)];
                  v = [(u(1) * u(1) - u(2) * u(2)) + frame, (u(2) * u(1) + u(2) * u(1)) ];


                if((v(1) * v(1) + v(2) * v(2)) > 4)
                    break
                end
                u = v;
                Z(x_,y_) = i;
            end
        end
    end
    fx = X(:);
    fy = Y(:);
    imagesc(fx,fy,Z)
    drawnow
    
      result = getframe(h); 
      im = frame2im(result); 
      [imind,cm] = rgb2ind(im,256); 
    
    if frame == -2
        imwrite(imind,cm,'final.gif','gif', 'Loopcount',inf); 
    else 
         imwrite(imind,cm,'final.gif','gif','DelayTime',0.1,'WriteMode','append'); 
    end
    
end