# Turing-like patterns in an asymmetric dynamic Ising model

## TL;DR

This paper introduces a finite-range, asymmetric multi-spin Ising model that can generate Turing-like patterns with tunable length scales, inspired by reaction-diffusion systems and applicable to complex interacting agent systems.

## Contribution

It presents a novel Ising model with finite-range, asymmetric interactions capable of producing Turing-like patterns, bridging reaction-diffusion phenomena and spin systems.

## Key findings

- Model can generate Turing patterns with tunable length scales
- Asymmetric interactions enable pattern formation without infinite-range interactions
- Applicable to complex systems beyond genetic regulation

## Abstract

To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in Ising models always rely on infinite-range interactions, this mapping allows us to design an finite-range interactions Ising model that can produce patterns observed in reaction diffusion systems including Turing patterns with a tunable typical length scale. This model has asymmetric interactions and several spin types coexisting at a site. While we use the example of genetic regulation during embryo-genesis to build our model, it can be used to study the behavior of other complex systems of interacting agents.