Optimal noise in the hodgepodge machine simulation of the Belousov-Zhabotinsky reaction

TL;DR

This study modifies the hodgepodge machine cellular automaton to better simulate the Belousov-Zhabotinsky reaction, identifying optimal noise parameters that produce realistic target patterns matching experimental observations.

Contribution

It introduces specific noise configurations in the hodgepodge machine that accurately replicate the chemical reaction's pattern formation.

Findings

Optimal neighborhood excitation noise between 30% and 34%.

Internal excitation noise at 12% produces target patterns.

Noisy model closely matches experimental chemical patterns.

Abstract

One of the simplest multilevel cellular automata - the hodgepodge machine - was modified to best match the chemical trajectory observed in the Belousov-Zhabotinsky reaction. Noise introduces watersheding of the central regular pattern into the circular target pattern. This article analyzes influences of the neighborhood and internal excitation kinds of noise. We have found that configurations of ignition points, which give circular waves - target patterns, occur only in the interval of the neighborhood excitation noise from 30% to 34% and at the internal excitation noise of 12%. Noisy hodgepodge machine with these parameters is the best approximation to the experimental Belousov-Zhabotinsky reaction.