The Kinetic Basis of Self-Organized Pattern Formation

TL;DR

This paper introduces a novel one-component kinetic automaton model demonstrating that both stationary and dynamic patterns can emerge without multiple species, expanding the understanding of pattern formation beyond traditional reaction-diffusion systems.

Contribution

The paper presents a new kinetic automaton model showing pattern formation in single-component networks, challenging the necessity of multiple species in traditional models.

Findings

Stationary patterns can emerge in one-component kinetic automaton networks.

Dynamic patterns are also possible within the proposed model.

The model has potential applications in real-world phenomena modeling.

Abstract

In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that different spatio-temporal patterns can arise due to instability of the homogeneous state in reaction-diffusion systems, but at least two species are necessary to produce even the simplest stationary patterns. This paper is aimed to propose a novel model of the analog (continuous state) kinetic automaton and to show that stationary and dynamic patterns can arise in one-component networks of kinetic automata. Possible applicability of kinetic networks to modeling of real-world phenomena is also discussed.