[Paper on doing computations with rule 54] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Paper on doing computations with rule 54
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Posted by: Paul-Jean L.
This paper may be of interest:
Chaos, Solitons and Fractals 28 (2006) 100–111
I have not gone through the paper in great detail, but it looked interesting from the perspective of the so-called "Class 3 problem" (doing computations with class 3 rules).
Abstract:
Rule 54, a two state, three neighbor cellular automaton in Wolfram's systems of nomenclature, is less complex that Rule 110, but nevertheless possess a rich and complex dynamics. We provide a systematic and exhaustive analysis of glider behavior and interactions, including a catalog of collisions. Many of them shows promise are computational elements.
Posted by: Jason Cawley
I think most consider rule 54 to be class 4. But proving it is universal would still be a nice result. I've read the paper, and they find a number of elements that would be useful for such a proof. They claim at the end only that they've found enough to implement what they call a "counter machine" in rule 54, meaning a system that can be written to, erased, read and shifted, and checked for emptiness. That is not yet universality, but it is a start. The English could use some polishing in a few places and some of their terms for structures within rule 54 are a bit quirky, but they certainly did some good work on the variety of possible structures and collisions.
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