spiral_zoom_1.m

h = figure;
set(h, 'Position', [0 0 (1280+100) (720 + 100)])

WIDTH = 1280;
HEIGHT = 720;

center = [-.73659007459575,-.69270903692418];
[XX,YY] = meshgrid(linspace(0,1,720),linspace(0,1,1280));
Z = ones(size(XX));

%frame = 1;
for frame = 1:.05:43
     scale = (1/2^frame);
     %[X,Y] = meshgrid(linspace(center(1)  - scale,center(1) + scale,1280),linspace(center(2) - scale,center(2) + scale,720));
     X = linspace(center(1)  - scale,center(1) + scale,1280);
     Y = linspace(center(2) - scale,center(2) + scale,720);
    for x_ = 1: 1280
        for y_ = 1: 720
            u = [X(x_),Y(y_)];
            for i = 1:2000
    %             julian set
%                   v = [u(1) * u(1) - u(2) * u(2) +  frame, u(2) * u(1) + u(2) * u(1)+ frame];

    %           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)) + .3, (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
    imagesc(Z)
    ax = gca
    set(ax,'xtick',[])
    set(ax,'ytick',[])
    %set(ax,'Position',[ax.OuterPosition(1),ax.OuterPosition(2),ax.OuterPosition(3),ax.OuterPosition(4)])
    drawnow
   
    
      result = getframe(h); 
      im = frame2im(result); 
      [imind,cm] = rgb2ind(im,256); 
    
    if frame == 1
        imwrite(imind,cm,'final.gif','gif', 'Loopcount',inf); 
    else 
         imwrite(imind,cm,'final.gif','gif','DelayTime',0.1,'WriteMode','append'); 
    end
    
end