Preprint Short Note Version 1 Preserved in Portico This version is not peer-reviewed

Power law behavior of Elementary Cellular Automata

Version 1 : Received: 26 June 2021 / Approved: 28 June 2021 / Online: 28 June 2021 (13:01:49 CEST)

How to cite: Laval, J. Power law behavior of Elementary Cellular Automata. Preprints 2021, 2021060649 (doi: 10.20944/preprints202106.0649.v1). Laval, J. Power law behavior of Elementary Cellular Automata. Preprints 2021, 2021060649 (doi: 10.20944/preprints202106.0649.v1).

Abstract

This paper shows that the percolation clusters from elementary cellular automata {30, 45, 60, 86, 99, 105, 129, 150, 153, 169, 182, 183, 184, 195 and 225 exhibit strong power law behavior, either under random initial conditions, a single occupied cell, or both. Most of the tail exponents are less than unity, implying diverging means and variances of cluster sizes. The analysis presented here is admittedly coarse in an effort to expedite its dissemination.

Subject Areas

Elementary Cellular automata, Power laws, fractals, criticality

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