An elementary cellular automaton sets each site's new state to the exclusive-or of…
PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Monte Carlo and lattice simulation of physical systems · Monte Carlo and lattice simulation of physical systems
Computational Physics, Ch Rules on a lattice: diffusion, percolation and growth
Problem
An elementary cellular automaton sets each site's new state to the exclusive-or of all three sites of its neighbourhood, its own included, rather than of its two neighbours alone.
((a)) Write out the rule's output for each of the eight neighbourhoods, in the order 111, 110, 101, 100, 011, 010, 001, 000, and read off the number that names the rule.
((b)) Write the update as one line of array arithmetic on a row, in the form used for rule 90, and use it on a row of 21 sites holding a single occupied site at the centre, with both end sites held empty. Give the number of occupied sites in each of the first four rows produced.
((c)) Say what this rule's first four rows share with rule 90's, and what they do not, using only the rows you have produced.