Bootstrap Percolation Automaton

Site percolation on a grid means that there is a continuous path of marked nearest-neighbor cells from one side of the grid to its opposite. This can be illustrated by a two-dimensional binary totalistic cellular automaton which processes a von Neumann neighborhood of range 1 by rule number 1018. Thus it has a birth rule that at least 2 of its 4 neighbors are alive, and a survival rule that all cells survive. The plot shows steps of evolution on a grid with random initial conditions. The density of the initial condition is specified by the probability of a cell being occupied. Percolation of sites depends on the size and the density of the initial condition.