Here is a very simple fractal formula
q = abs(q) / dot(q, q)
or
x = abs(x)
y = abs(y)
m = x*x + y*y
x = x/m+cx
y = y/m+cy
with very cool result image
taken from here:
https://computergraphics.stackexchange.com/questions/8164/how-does-this-small-fractal-shader-work/
http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/