Animal coat are naturally decorated with beautiful
patterns. There has been
several effort to understand mechanism behind the
patterns. Alan Turing, in 1950
proposed
a simple reaction-diffusion system which can generate these patterns.
Let's say that there are two co
lours/chemicals, for example red
and blue which
diffuse in a media (say in 2 dimension). If there is no interaction
between them,
then in steady
state we will have homogeneous distribution of red + blue (= pink).
Any instability of this homogeneous state would generate patterns.
In recent day studies could produce
several patterns with different
symmetry, static and oscillatory and many more.
Your task would be to provide an overview :
1) What is turing pattern
2) What are the basic mechanism (Linear stability)
3) A simple Algorithm
4) CA as an competing candidate ?
5) Summary
Some papers are here : 
[Turing
Complex] [Turing
Review]:(Oscillatory
)
==================
Other References :
==================
Oscillatory Turing patterns:
http://hopf.chem.brandeis.edu/yanglingfa/pattern/oscTu/
====================================================
Bull Sperm:
http://www.sciencemag.org/cgi/content/full/309/5732/300
====================================================
Some movies (and review of turing pattern)
http://www.lce.hut.fi/research/polymer/turing.shtml