[Classes of CA] - A New Kind of Science: The NKS Forum

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Classes of CA

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Posted by: Guy Israeli

Hi again,

can someone please provide an explanation or direct me to where I can find an explanation and maybe comparison of the classes of CA (constant, periodic, chaotic and complex)?

Thanks,
Guy


Posted by: Jason Cawley

Start on page 231. If you have questions, post again here and I'll explain any of the trickier bits.


Posted by: Guy Israeli

Hello again,

I have some trouble with the difference between class 1 and 2. Class 1 is said to have some constant behavior after a certain amount of steps. Would rule number 37 (with a {{1},0} as initial step) would be classified as 1 or as 2?

It does have constant behavior but of width of 2 rows. It could also be periodic.

which one is it?

Thanks a lot,

Guy


Posted by: Jason Cawley

That would be considered periodic, class 2. It continues to show some variation with time. But sure, it is about as close to a "fixed point" as something periodic can get.

The original idea of the classes stems from dynamical systems theory and the categorization of "attractors" in continuous math systems. Systems that evolve to a fixed point or equilibrium are class 1 in the strict sense. f[t+x] = f[t] for all x>0, once t is greater than something.

Those that evolve to limit cycles, class 2 (a class that expanded somewhat in the scope of its definition, later). Apparently chaotic or random - when started from random initials, mind - class 3. Local structure - class 4 - Wolfram regarded as something new that he hadn't seen before in continuous dynamical systems, at least the simple ones usually studied.




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