Paul Fuller wrote:

>> Does anybody know how either of these simulations actually work?
> 
> Cellula Automata - Each cell (pixel) follows some simple rules based on 
> its current state and that of its neighbours to determine its state in 
> the next generation.

I thought a cellula automaton is where each cell has a *finite* number 
of possible states? In this example, we have (conceptually) continuous 
rather than discrete states.

> This particular example looks like it implements some equations that 
> model the reaction of chemicals in 2D.  There are real mixtures that 
> exhibit the pulsating and alternating patterns that some settings 
> reproduce.

Indeed. That's how I found the link. ;-) I saw a TV program mention that 
the patterns of animal skins can be described by a single mathematical 
formula. Searching for this formula, I came across a document claiming 
it's due to reaction diffusion - and hence the second link, which is a 
simulation of the reaction diffusion differential equation.

Now, if I could figure out what the equation is and how it works, I 
might be able to simulate it...

> Fiddling around with the parameters gives some behaviours that are 
> interesting and some that quickly lead to all dead, all alive or 
> something else.
> 
> The number of possible combinations of the parameters is huge but there 
> are typically a small number of interesting classes of behaviour on the 
> boundaries between boring and chaotic.

Indeed, this is the case with a lot of fractals. A simple set of rules, 
iterated a sufficient number of times, gives rise to complicated and 
unpredictable behaviour, which is often quite pretty to look at. :-)

> Fun stuff.  Thanks for the link.

It's not quite as much fun, but do a search for "boids" to see some 
interesting flocking behaviour...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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