Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics
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TL;DR
The problem of encoding the state-variables and evolution laws of a physical system into this new setting, and of giving suitable correspondence rules for interpreting the model's behavior, is discussed.
Abstract
Cellular automata are models of distributed dynamical systems whose structure is particularly well suited to ultrafast, exact numerical simulation. On the other hand, they constitute a radical departure from the traditional partial-differential-equation approach to distributed dynamics. Here we discuss the problem of encoding the state-variables and evolution laws of a physical system into this new setting, and of giving suitable correspondence rules for interpreting the model's behavior.