In this recent submission, the authors discuss the theory of cellular automata, specifically focusing on the concept of oscillators. An oscillator is a pattern that repeats itself after a fixed number of generations, known as its period. The authors highlight the significance of the omniperiodicity of cellular automata, which refers to the existence of oscillators for all possible periods. In the case of Conway’s Game of Life, only twelve oscillator periods were yet to be discovered at the turn of the millennium. However, this search has now concluded with the identification of oscillators that exhibit the final two periods, 19 and 41, thus confirming that Life is indeed omniperiodic. The authors also provide insight into the history of the omniperiodicity problem and the strategies that have been employed to solve it, acknowledging the contributions of numerous individuals over several decades.
https://arxiv.org/abs/2312.02799