The first section contains the famous Mandelbrot fractal and a variant thereof, the Burning Ship fractal. The rotating circles enable you to learn how rotating movement can be transferred to lineair movement, and makes for some pretty animations using all the controls available. Then there's a few visualisations about prime numbers and Fibonacci sequences.

In this sections you will mainly find fractals and curves based on problems that are visualised using lines. The Barnsley fractal ('the leaf') however is built up using points, but gives the impression it is built using lines. The Gosper, Peano and Hilbert curves are so called "space filling curves": given enough iterations they fill create a perfect filled plane, without any lines ever crossing each other.
Again, a lot of these visualisations can be changed using different controls in order to study them or create stunning images.
Some scripts make use of the L-rewrite system (see Wikipedia). To experiment with an L-system yourself see my other site.