>> 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.

I don't see anything in this case to say that the number of states of a 
cell is infinite :)

OK - this is more properly called a 'continuous automata' or a 
'continuous spatial automata' than a CA.  Very similar except that the 
future state is determined by functions rather than a state table. 
Still if you had a large enough state table...

Still the states here seem to converge to certain preferred values and 
patterns.  Like 'attractors' in a fractal.

> 
>> 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...

Don't the references provided by the site give details ?

"It is based on the Gray-Scott model, and was taken from John E. 
Pearson's Complex Patterns in a Simple System - Science, 261, 189, 9 
July 1993.

More details about the type of system used can be found at the [Xmorphia 
web site].

> 
>> 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. :-)
> 

True.

>> 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...
> 

Been there.  Done that.  We have similar interests.

I first saw Chris Langton's work on Boids described in Scientific 
American.  Maybe 20 years ago (?).  Back then I wrote a version (in 2D) 
on the Apple ][ and it worked but very slowly.  There are many 
simulators out there to play around with now and machine performance is 
so much better that it is just ridiculous.

Ditto with fractals BTW.  I still have the August 1985 Scientific 
American with the Mandelbrot Set cover and article by AK Dewdney in his 
Computer Recreations column.  Talk about a bombshell !  Unfortunately at 
1MHz the old Apple was a little slow and the graphics a bit primitive. 
It wasn't until I wrote a multi-tasking version in assembler on a 
mainframe with output rendered to a laser printer that I was happy.

'Artificial Life' by Steven Levy is a good popular science book on the 
A-Life field including CAs, Boids and Genetic Algorithms.  It was 
published in 1992 so things have progressed a bit and there is a lot of 
more recent work available on the Web.  Still a good read though.

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