I was playing around with the Mandlebrot set yesterday in Matlab, and eventually after iterating on my implementation of it, decided to take a few photos and screencaps of deep zooms on particular points. I have been having a bit of a hard time identifying the right points to zoom in on but was still able to arrive at a few pretty nice ones. At the end of this gallery I will also provide my very short code that can generate these.

Finally, I decided to try and see how far I could zoom in on the images. I created a function that would be supplied by a point to zoom on and a number of zooming operations, and it then runs the set generator and appends each image to a video file. Below are the results of four points I pseudorandomly selected to zoom in on.

Finally, my MATLAB implementation that I used to generate the set. Feel free to use and test this function out as you please, but give me a link if you redistribute it.

`function mset_layers = proceduralMandlebrot(dim,iters,bnds)`

`% proceduralMandlebrot(dim,iters,seeds,bnds)`

`%`

`% a function for visualizing the mandlebrot set`

`%`

`% dim: the delta_x we discretize by, default 1000`

`% iters: number of iterations, default 30`

`% bnds: [x1 x2 y1 y2] limits in the complex plane, default [-2 2 -1 1]`

`%`

`% by Majed Samad 2016`

`t0 = tic;`

`if ~exist('dim','var')||isempty(dim), dim = 1000; end`

`if ~exist('iters','var')||isempty(iters), iters = 30; end`

`if ~exist('bnds','var')||isempty(bnds), bnds = [-2 2 -1 1]; end`

`[a,b] = meshgrid(linspace(bnds(1),bnds(2),dim),linspace(bnds(3),bnds(4),dim));`

`x = 0;`

`c = complex(a,b);`

`for i = 1:iters`

` x = x.^2 + c;`

` mset = abs(x)>2;`

` if i==1,mset_layers = mset;else mset_layers = mset_layers + mset/i;end`

`end`

`imagesc(mset_layers)%,colormap(autumn)`

`fprintf('it took %f minutes to execute\n',toc(t0)/60);`