Some Beautiful and Difficult Questions About Cellular Automata

Abstract

One of the most interesting things about cellular automata (CA) is that such simple sets of rules can give rise not only to such strange and unpredictable behavior, but also that it can create seemingly predictable behavior that is nonetheless extremely difficult to actually pin down. One example of this apparently simple behavior comes from the “Life without Death” cellular automaton, which is the exact same as Conway’s Game of Life with the exception that cells never die. Just by playing around with random starting patterns, it immediately becomes “clear” that the majority of sufficiently large patterns explode quadratically in this rule and fill most of the 2D plane. However, it was not even known if there is a single quadraticallygrowing pattern in this rule until Dean Hickerson found one in 2009, over 20 years after this CA was first studied.