An Introduction to the Apollony Fractal

Written by Paul Bourke
Computers and Graphics, Vol 30, Issue 1, January 2006, pages 134-136.


This paper provides an introduction to the Apollonian fractal, also known by some as the curvilinear Sierpinski gasket. This fractal is not particularly well known, perhaps because it is not as straightforward to construct as many other fractals such as the related Sierpinski gasket or the Menger sponge. The brief history and a general description of the fractal will be given, including the geometric construction in two dimensions and an IFS (Iterated Function System) formulation.