  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.
