A Glider for Every Graph: Exploring the Algorithmic Requirements for Rotationally Invariant, Straight-Line Motion

The primary goal of digital physics research is to provide a description of the physical universe in terms of simple programs. One approach to attaining this goal is creating a toolbox of algorithms that reproduce the behavior of basic quantum phenomena. As a step in this direction, a simple pseudo-particle algorithm has been developed that exhibits rotationally invariant, glider-like motion across graphs in two or more dimensions. This algorithm is applied to a range of lattice and irregular graphs from the sparse to the densely connected, and it is shown that rotationally invariant motion can be easily obtained from irregular graphs that are sufficiently densely connected. Such graphs are also shown to be potentially compatible with spatial curvature and relativistic invariance. This work points the way toward a class of algorithms that can be used to tightly approximate the basic phenomena encountered in particle physics, while maintaining the desired properties of discreteness, determinism, and algorithmic simplicity.