zooming into a spiral fractal

spiral_zoom.m

h = figure;
set(h, 'Position', [0 0 700 700])

left = linspace(-.75, -.7367,100)
right = linspace(-.72, -.7364,100)

top = linspace(-.7, -.6928,100)
bottom = linspace(-.684, -.6926,100)

 for frame = 1:1:100
     [X,Y] = meshgrid(linspace(left(frame),right(frame),800),linspace(top(frame),bottom(frame),800));
     Z = ones(size(X));

    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) +  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
    fx = X(:);
    fy = Y(:);
    imagesc(fx,fy,Z)
    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