8 problems

Omniperiodicity conjecture. Oscillators of every period $p\geq 1$ exist in Life; equivalently, Life is omniperiodic.

Let Game of Life on Graphs features, DeepWalk features, and Weisfeiler–Leman kernel features be feature representations of graphs. The feature-comparison conjecture. The features e…

For graphs equipped with the distance $d_{GLG}$ induced by the Euclidean distance between their Game of Life on Graphs feature vectors, consider triples satisfying … The topologica…

Let the Game of Life on Graphs generate patterns from an input graph, and regard the resulting patterns as graph features. The graph-isomorphism conjecture. The highly irregular st…

Let $G(N,M)$ be a random graph with $N$ vertices and $M$ edges, and let $c$ be a constant describing an edge density with $M\sim cN$. The halting-complexity conjecture. The most di…

A doubly periodic configuration in the Game of Life is a configuration with two independent spatial periods, and a Garden of Eden is a configuration with no preimage. Undecidabilit…

For the Game of Life, consider finite-support Gardens of Eden and rectangular orphans, with the encodings specified in the paper and polynomial-time many-one reductions. Co-NP-comp…

For the Game of Life, consider the decision problems of recognizing finite-support Gardens of Eden and rectangular orphans under the encodings used in the paper. Co-NP-hardness con…