Self-Organized Criticality in Asynchronously Tuned Elementary Cellular Automata

TL;DR

This paper demonstrates self-organized criticality in asynchronously tuned elementary cellular automata, showing how asynchronous updates and local dual modes lead to critical states without parameter tuning.

Contribution

It introduces a simple, general model of SOC in asynchronous cellular automata based on local dual transition modes and their adjunction.

Findings

SOC coincides with criticality in phase transition of asynchronous ECA

Asynchronous updating coupled with duality demonstrates critical states

Model provides a new perspective on SOC in biological systems

Abstract

Self-organized criticality (SOC) reveals a mechanism by which a system is autonomously evolved to be in a critical state without needing parameter tuning. Whereas various biological systems are found to be in critical states and the significance of SOC is being re-estimated, a simple model in a general platform has not been established. Here, we present SOC in asynchronously tuned elementary cellular automata (ECA), which was based on asynchronously updating and tuning the consistency between local dual modes of transitions. This duality was defined by adjunction, which can be ignored during synchronous updates. Duality coupled with asynchronous updating can demonstrate that SOC coincides with the criticality in a phase transition of asynchronous ECA with respect to density decay.