Particle-like structures have garnered the lion's share of attention in research on cellular automata (CAs). Why this fascination? I'll review some of the (engineering) motivations for this focus, but conclude that it is ultimately subjective in the sense that it is not based on a first-principles demonstration that these objects are the main structures one needs to analyze to understand CA behavior.
Can we put the notion of particles---and, for that matter, other emergent objects---on a firm theoretical grounding? I'll recount some familiar and some recent results on structural decompositions of CA spacetime behavior, with a view to explicating the concepts of object, coherent structure, and boundary. Though they arise in a very simple system, the structures produced by CAs do give basic insights into these general concepts.
Department of Mathematics
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