Noisy hodgepodge machine and the observed mesoscopic behavior in the non-stirred Belousov–Zhabotinsky reaction

Abstract

In this paper, we have modified one of the simplest multi-level cellular automata – a hodgepodge machine, so as to represent the best match for the chemical trajectory observed in the Belousov–Zhabotinsky reaction (BZR) in a thin layered planar setting. By introducing a noise term into the model, we were able to transform the central regular structure into the circular target pattern. We further analyze influences of the neighborhood (diffusion process) and internal excitation type of noise. We find that the configurations of ignition points, which give the target patterns, occur only in the interval of the neighborhood excitation noise from 30% to 34% and at the internal excitation noise of 12%. We argue that the BZR occurs on a semi-regular grid – a chemical analogy to a Bénard cell in the viscous fluid, and we discuss the size of the relevant elementary cell. In this way, the BZR is a quintessential example of mesoscopic process, in particular, it does follow neither the deterministic rules of the microscopic system nor the tenet of Boltzmannian statistic physics that only the most frequent events are observed.