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