Object Synthesis in Conway’s Game of Life and Other Cellular Automata

Abstract

Of the very large number of cellular automata rules in existence, a relatively small number of rules may be considered interesting. Some of the features that make such rules interesting permit patterns to expand, contract, separate into multiple sub-patterns, or combine with other patterns. Such rules generally include still-lifes, oscillators, spaceships, spaceship guns, and puffer trains. Such structures can often be used to construct more complicated computational circuitry, and rules that contain them can often be shown to be computationally universal. Conway’s Game of Life is one rule that has been well-studied for several decades, and has been shown to be very fruitful in this regard.