Posted by Joe Bolte
After the Q&A, Stephen Wolfram performed a live computer experiment from scratch. He chose to search for complex behavior in a class of systems called step registers. Starting from a blank Mathematica notebook, Wolfram generated a ruleset and combed through it for examples of complex behavior, first using a two-neighbor rule and then a three-nighbor rule. You can see that in the two-neighbor case rules 6 and 9 yielded complex behavior and in the three-nieghbor case, rules 90 and 165 were the interesting results. Wolfram had an intuition that rules 90 displayed additive behavior, but he was not able to demonstrate anything before time ran out. Please take a look at the Mathematica notebook of the experiment.
Update: Christopher Haydock noted a problem with the notebook and submitted a corrected version, with the code extensively refactored to be clearer for those following along at home. Thanks Chris!
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