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:


    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
    5 1 roll pop pop pop pop % in?
    {0 0 0}{1 1 1}ifelse % R G B

    % 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}

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

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