Read [Indra’s Pearls][1] by Mumford, Series, and Wright.

Related programs include the following: 

 - [KBMAG][2] by Derek Holt
 - [MAF][3] by Alun Williams
 - [Kleinian][4] by David Wright
 - [Honeycombs][5] by Roice Nelson

You may also be interested in some of the on0line communities that discuss fractals.  Here is one of the older ones:

 - [Fractal Forum][6]

  [1]: https://en.wikipedia.org/wiki/Indra's_Pearls_(book)
  [2]: https://www.gap-system.org/Packages/kbmag.html
  [3]: https://maffsa.sourceforge.net/manpages/MAF.html
  [4]: https://web.archive.org/web/20210417130946/http://klein.math.okstate.edu/kleinian/src/
  [5]: http://hyperbolichoneycombs.org/
  [6]: https://fractalforums.org/