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Wuensche idea on entropy classifying CAs
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Posted by: Jason Cawley
At ICCS 2004 in Boston, Andrew Wuensche ( http://www.ddlab.com/ ) showed an interesting graph during his talk, classifying a rule space by entropies. The inuition is that low entropy rules and class 1-2 behavior will line up, class 3 rules ("chaos" in Wuensche's terms) show high entropy, while the 4s show a fluctuating entropy measure.
So he looked at some rule spaces with various sizes of neighbors allowed, and plotted a point for each rule on two axes - entropy and the variance of entropy. He gets a big spike at high but steady entropy, a wavy line along the "order axes" with low variance, and a scatter region away from the origin on both axes, well populated but nothing like the height of the maximal entropy spike. I thought it was quite an interesting graph.
The rest of his talk was mostly showing his program, DDLab, for investigating discrete networks. With a focus on analyzing basins of attraction in relatively small number of nodes cases. Some of this was interesting, and he notes differences in the way basins of attraction analysis looks for class 3 rules compared to simple ones (long slowly branching transients, vs. short bushes e.g.). But I found the entropy graph more striking, because it gives a sense of how many rules fall where in the class categories - or at least a certain measure related to them.
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