The cellular automaton pulsing model, experiments with DDLab

TL;DR

This paper explores the cellular automaton pulsing model, demonstrating sustained rhythmic oscillations under random wiring, extending analysis methods, and providing a DDLab implementation for further research.

Contribution

It extends the analysis of the CA pulsing model with new measures, rules, and automatic recognition methods, and provides a DDLab implementation for validation and experimentation.

Findings

Pulsing phenomena are observed across various glider rules and neighborhood sizes.

Extended entropy-density and return map analyses reveal underlying mechanisms.

The DDLab implementation facilitates further research and validation.

Abstract

The cellular automaton (CA) pulsing model (arXiv:1806.06416) described the surprising phenomenon of spontaneous, sustained and robust rhythmic oscillations, pulsing dynamics, when random wiring is applied to a 2D `glider' rule running in a 3-value totalistic CA. Case studies, pulsing measures, possible mechanisms, and implications for oscillatory networks in biology were presented. In this paper we summarise the results, extend the entropy-density and density-return map plots to include a linked history, look at totalistic glider rules with neighborhoods of 3, 4 and 5, as well as 6 and 7 studied previously, introduce methods to automatically recognise the wavelength, and extend results for randomly asynchronous updating. We show how the model is implemented in DDLab to validate results, output data, and allow experiments and research by others.