Cellular Automata are Generic

TL;DR

This paper demonstrates that any classical algorithm can be simulated by a dynamic cellular automaton with unconstrained topology and cell creation, making it more physically realistic, despite a quadratic overhead.

Contribution

It introduces a universal simulation framework showing cellular automata can emulate any classical algorithm with dynamic topology and cell creation.

Findings

Simulation overhead is quadratic.

Cellular automata can operate over arbitrary unordered domains.

Dynamic cellular automata are closer to physical reality.

Abstract

Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular automaton with unconstrained topology and with the power to create new cells. The advantage is that the latter is closer to physical reality. The overhead of our simulation is quadratic.