Langton's Ant 
Here you can explore the patterns produced by the ant. You can set your own rule of up to 13 commands I first read about Langton's ant when I was wandering around in Wikipedia. The simulation uses javascript and requires HTML5. 

Two little tutorials 
Here you can learn about complex numbers, and about some mappings of the complex plane. There are examples for you to try yourself and opportunities for you to create computer generated patterns, some of which might even count as ”art”.  
The Ant Hill 
Here you can explore the patterns produced when several ants interact in the same field.. You can have up to 5 ants each with its own rule and starting location I thought it might be interesting to see what would happen if ants were allowed to get together. There is so much to explore, and I have hardly started. The simulation uses javascript and requires HTML5. 

Turmites 
Here you can explore the patterns produced by a turmite. You can set your own rule using up to 13 states and 13 colours The turmite in this implementation is a generalisation of Langton's Ant. The simulation uses javascript and requires HTML5. 

Driven Pendulum Simulation. 
Here you can explore the various behaviours exibited by a pendulum that is subject to a driving force. This simulation was inspired by "Chaotic Dynamics, an introduction" by G.L.Baker and J.P.Gollub. The simulation uses javascript and requires HTML5. 

VolterraLotka Fractal. 
By changing the parameters, you can find a number of different "strange attractors" including one which has the form of a wiggly loop. The fractal explorer is based on a description given by Peitgen and Richter in their book "The Beauty of Fractals" 

Iterated Function Systems. 
Here you can view some standard examples, or enter your own coefficients. In his book "Fractals, a very short introduction", Kenneth Falconer describes how to draw the fractal defined by an iterated function system (IFS). This method was introduced by Michael Barnsley, and is a kind of random walk. 

Loxodromic paths. 
Loxodromic paths are mentioned in "Indra's Pearls" by Mumford, Series and Wright. The word "loxodromic" was new to me, so here is a little exploration. 