Fast Simulation of Cellular Automata by Self-Composition

Joseph Natal; Oleksiy Al-saadi

doi:10.25088/complexsystems.34.3.259

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arXiv · 2409.07065

Fast Simulation of Cellular Automata by Self-Composition

Joseph Natal·Oleksiy Al-saadi

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Abstract

Computing the configuration of any one-dimensional cellular automaton at generation $n$ can be accelerated by constructing and running a composite rule with a radius proportional to $\log n$. The new automaton is the original one, but with its local rule function composed with itself. Consequently, the asymptotic time complexity to compute the configuration of generation $n$ is reduced from $O(n^2)$-time to $O(n^2 / \log n)$, but with $O(n^2/(\log n)^3)$-space, demonstrating a time-memory tradeoff. Experimental results are given in the case of Rule 30.

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BibTeX RIS

Joseph Natal, Oleksiy Al-saadi. 2024-09-11. Fast Simulation of Cellular Automata by Self-Composition. https://doi.org/10.25088/complexsystems.34.3.259

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