Conway's Game of Life is Omniperiodic

TL;DR

This paper proves that Conway's Game of Life contains oscillators of all possible periods, establishing its omniperiodicity, by discovering the last two missing oscillator periods, 19 and 41.

Contribution

It provides the final proof that Life is omniperiodic by identifying the last two unknown oscillator periods and reviews the history and strategies used in this discovery.

Findings

Existence of oscillators with periods 19 and 41 confirmed.

Life is now proven to be omniperiodic.

Summarizes decades of research on oscillator periods.

Abstract

In the theory of cellular automata, an oscillator is a pattern that repeats itself after a fixed number of generations; that number is called its period. A cellular automaton is called omniperiodic if there exist oscillators of all periods. At the turn of the millennium, only twelve oscillator periods remained to be found in Conway's Game of Life. The search has finally ended, with the discovery of oscillators having the final two periods, 19 and 41, proving that Life is omniperiodic. Besides filling in the missing periods, we give a detailed history of the omniperiodicity problem and the strategies used to solve it, summarising the work of a large number of people in the decades since the creation of Life.