Phenomenology of retained refractoriness: On semi-memristive discrete media

TL;DR

This paper investigates a two-dimensional cellular automaton model simulating semi-memristive media, classifying its behaviors into eleven distinct classes based on excitation and recovery intervals, with implications for understanding complex resistive systems.

Contribution

It introduces a novel automaton model capturing semi-memristive properties and provides a comprehensive phenomenological classification of its diverse behaviors.

Findings

Eleven classes of automata behaviors identified.

Classification based on space-filling, diversity, and localizations.

Model simulates semi-memristive medium dynamics.

Abstract

We study two-dimensional cellular automata, each cell takes three states: resting, excited and refractory. A resting cell excites if number of excited neighbours lies in a certain interval (excitation interval). An excited cell become refractory independently on states of its neighbours. A refractory cell returns to a resting state only if the number of excited neighbours belong to recovery interval. The model is an excitable cellular automaton abstraction of a spatially extended semi-memristive medium where a cell's resting state symbolises low-resistance and refractory state high-resistance. The medium is semi-memristive because only transition from high- to low-resistance is controlled by density of local excitation. We present phenomenological classification of the automata behaviour for all possible excitation intervals and recovery intervals. We describe eleven classes of cellular automata with retained refractoriness based on criteria of space-filling ratio, morphological and generative diversity, and types of travelling localisations.