A cellular automaton model of gravitational clustering

TL;DR

This paper presents a one-dimensional cellular automaton model that captures the scale-invariant, hierarchical clustering behavior observed in gravitational systems, reproducing key features of N-body simulations.

Contribution

It introduces a simple cellular automaton framework to model gravitational clustering, highlighting self-similarity and universal scaling exponents.

Findings

Reproduces self-similar clustering features

Displays scale-invariant dynamics with universal exponents

Produces a tree-like space-time structure

Abstract

Gravitational clustering of a random distribution of point masses is dominated by the effective short-range interactions due to large-scale isotropy. We introduce a one-dimensional cellular automaton to reproduce this effect in the most schematic way: at each time particles move towards their nearest neighbours with whom they coalesce on collision. This model shows an extremely rich phenomenology with features of scale-invariant dynamics leading to a tree-like structure in space-time whose topological self-similarity are characterised with universal exponents. Our model suggests a simple interpretation of the non-analytic hierarchical clustering and can reproduce some of the self-similar features of gravitational N-body simulations.