>> 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.

Indeed, yes.

>> 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].

The Xmorphia web site apparently no longer exists. (Firefox tells me the 
server cannot be found.)

As for "Science, 261, 189, 9 July 1993", what does that actually *mean*?

>> 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.

I could have chosen this for my final year project in my degree. 
(Actually I chose distributed MVC, because I figured OpenGL would be 
*way* too hard. You have to use C for a start...)

> 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.

I first came across the M set in an edition of the Guinness Book of 
Records. It held the record for "most complicated mathematical object". 
Not entirely sure how they arrived at that conclusion... ;-) The text 
accompanying it mumbled something about real and imaginary numbers, 
fluid dynamics and the stock market. It didn't make a lot of sense.

Later I found books such as The Beauty of Fractals and so on in the 
local library. Most of these consisted of miles of very advanced 
mathematics, most of it concerning the statistical properties of the 
coastline or something, and almost none of it to do with drawing these 
fantastic images that I longed for. The tiny selection of actual 
*pictures* present usually included only the vaguest suggestion of what 
the image *is*, and absolutely no suggestion about HOW TO MAKE IT. It 
was an extremely frustrating time...

Eventually, by dint of wading through many, many textbooks on advanced 
mathematical techniques, I was eventually able to grok the concept of 
complex numbers, and eventually to comprehend *why* the apparently 
unrelated formulas Z = Z^2 + C and (X,Y) = (X^2 - Y^2 + A, 2XY + B) are 
actually the same thing. This happened while I was at college, where 
they actually *had* math books on the shelves. Progress was much more 
rapid after that...

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

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