Fractal distribution of galaxies modeled by a cellular-automaton-type stochastic process

Abstract

A cellular-automaton-type stochastic process is introduced in order to simulate the fractal distribution of galaxies. The rules of the model are constructed to approximate the explosive-galaxy-formation scenario. For a range of the single parameter the model depends on, the fractal dimension corresponding to the power-law density correlation function is found to be D≊1.2, in good agreement with the observations. The multiplicity function n(s) is shown to scale as n(s)∼${\mathrm{s}}^{\mathrm{-}\mathrm{\tau }}$, with τ≊1.9, where s is the cluster size.