A cellular automaton model of gravitational clustering

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.