PocketIFS is a nice piece of software for the amateur applied mathematician. It allows you to create fractals based on mathematical functions. So you can imitate nature and create some incredible geometric fractals that go on and on. I made one crazy spiral.
Just select the type of fractal and program and off you go, IFS will generate the corresponding image. The software lacks options and additional functions but as a fun starter package it's fine. Maths has never been so fun.