Animated Mandelbrot

This is a seemingly difficult question I think. I am (or at least will be) writing a dissertation of Fractal Geometry which is to be submitted electronically. For obvious reasons, I will be hoping to include an illustration of the Mandelbrot Fractal.

There are answers available for a 'simple' image of the fractal but I was hoping there would be a way to animate this image to zoom in (in theory endlessly) – a little like this

but not as detailed. Does anybody know how to do this?

My preamble is currently empty so I full list of necessary packages would be great. Thank you in advance.

If you really want to burn your rader's/reviewer's CPU, here you are:

\documentclass[tikz]{standalone}

\def\pspreparation#1#2#3{
20 div exch 20 div % y x
#3 div exch #3 div % x y
#2 add exch #1 add 2 copy true % y x y x true
}
\def\psiteration{ % y x Y X in?
{dup dup mul 2 index dup mul sub 3 index sub 3 1 roll 2 mul mul 3 index sub exch 2 copy dup mul exch dup mul add 3 le}{false}ifelse
}
\def\psdecoration{
5 1 roll pop pop pop pop % in?
{0 0 0}{1 1 1}ifelse % R G B
}
\def\pgfdeclaremandelbrot#1#2#3{
\pspreparation{#1}{#2}{#3}
\psiteration\psiteration\psiteration\psiteration\psiteration\psiteration\psiteration\psiteration
\psiteration\psiteration\psiteration\psiteration\psiteration\psiteration\psiteration\psiteration
\psdecoration
}
}
\def\pgfprintmandelbrot#1#2#3{
\pgfdeclaremandelbrot{#1}{#2}{#3}
}

\begin{document}
% x-shift, y-shift, scale
\pgfprintmandelbrot{ .6}{ 0}{1}
\pgfprintmandelbrot{ .4}{ 0}{1.2}
\pgfprintmandelbrot{ .2}{ 0}{1.44}
\pgfprintmandelbrot{ .0}{ 0}{1.728}
\pgfprintmandelbrot{-.2}{ 0}{2.0736}
\pgfprintmandelbrot{-.4}{ 0}{2.48832}
\pgfprintmandelbrot{-.4}{.1}{2.985984}
\pgfprintmandelbrot{-.4}{.2}{3.5831808}
\pgfprintmandelbrot{-.4}{.3}{4.29981696}
\pgfprintmandelbrot{-.4}{.4}{5.159780352}
\end{document}


GIF version: (Due to the ImageMagick fails to convert PDF files containing functional shading, it is going to be glitchy)

Fixed GIF version (using Preview on Mac)

• That... is... amazing! You are a genius! Thank you. – PercyF2519 Mar 12 '17 at 20:15
• It seems like my plot heading the opposite direction. That is in fact my prefered direction. See my profile picture. (Yes, it is done by TeX.) – Symbol 1 Mar 12 '17 at 20:22
• Why is it your favourite direction? I suppose it makes no real difference for visual displays. – PercyF2519 Mar 12 '17 at 20:24
• @PercyF2519 Because it makes me unique! But computationally, as you said, I am not :( – Symbol 1 Mar 12 '17 at 20:27