Re: [math-fun] "life" generalized CAs classified ala Wolfram?
The most interesting aspect of this project, it seems to me, is the isInteresting() predicate.
--it occurs to me that you could get a hell of a long way toward making a good IsInteresting predicate by simply computing discrete fourier transforms. I.e. if a cell is periodic in time, a temporal FFT would detect that. Wolfram's "4 (vague) types" of 1D CAs were: 1.Evolution leads to a homogeneous state. 2.Evolution leads to a set of separated simple stable or periodic structures. 3.Evolution leads to a chaotic pattern. 4.Evolution leads to complex localized structures, sometimes long-lived. Note 1 and 2 seem trivial to detect using FFT. Distinguishing types 3 & 4 may be a little bit tougher, but I bet it would be easy to make an automated classifier comparable in ability to Wolfram himself.
Alternatively we might start with the simpler 4 cell neighborhood, thus only 2^10 cases.
--the checkerboard neighborhood graph is bipartite, so this probably not a good idea. Using the equilateral triangle lattice, 6 neighbors, might be better, though.
You might be able to distinguish them all by looking at compression rates; I'd guess the compression would be 1,2,4,3 from best to worst. On Mon, Dec 16, 2013 at 6:05 PM, Warren D Smith <warren.wds@gmail.com> wrote:
The most interesting aspect of this project, it seems to me, is the isInteresting() predicate.
--it occurs to me that you could get a hell of a long way toward making a good IsInteresting predicate by simply computing discrete fourier transforms. I.e. if a cell is periodic in time, a temporal FFT would detect that. Wolfram's "4 (vague) types" of 1D CAs were: 1.Evolution leads to a homogeneous state. 2.Evolution leads to a set of separated simple stable or periodic structures. 3.Evolution leads to a chaotic pattern. 4.Evolution leads to complex localized structures, sometimes long-lived. Note 1 and 2 seem trivial to detect using FFT. Distinguishing types 3 & 4 may be a little bit tougher, but I bet it would be easy to make an automated classifier comparable in ability to Wolfram himself.
Alternatively we might start with the simpler 4 cell neighborhood, thus only 2^10 cases.
--the checkerboard neighborhood graph is bipartite, so this probably not a good idea. Using the equilateral triangle lattice, 6 neighbors, might be better, though.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
participants (2)
-
Mike Stay -
Warren D Smith