An Exploration of Extremal Conway's Game of Life on a 2-Torus
Abstract
Although significant attention has been given to the behavior of Conway’s Game of Life on large and infinite boards, little attention has been paid to the extreme lower limits of this system. This paper introduces the notion of an “extremal” cellular automaton and observations regarding extremal Conway’s Game of Life. In addition, a complete dataset of all possible initial and final extremal Game of Life boards has been included. Finally, Scala programs for reproducing these results are provided.
Fields of Study & Subjects
Cellular Automata and Applications
semigroups and automata theory
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 27 January 2026
- Language
- EN