A simple deterministic self-organized critical system

TL;DR

This paper presents a new one-dimensional deterministic cellular automaton that exhibits self-organized criticality without randomness, aligning with known universality classes like the Oslo rice pile and earthquake models.

Contribution

It introduces a novel deterministic cellular automaton system demonstrating self-organized criticality without any embedded randomness.

Findings

System is in the same universality class as Oslo rice pile

Chaos occurs only microscopically in the thermodynamic limit

System is boundary driven and deterministic

Abstract

We introduce a new continuous cellular automaton that presents self-organized criticality. It is one-dimensional, totally deterministic, without any kind of embedded randomness, not even in the initial conditions. This system is in the same universality class as the Oslo rice pile system, boundary driven interface depinning and the train model for earthquakes. Although the system is chaotic, in the thermodynamic limit chaos occurs only in a microscopic level.