Probabilistic Cellular Automata for Granular Media in Video Games

Abstract

Granular materials are very common in the everyday world. Media such as sand, soil, gravel, food stuffs, pharmaceuticals, etc. all have similar irregular flow since they are composed of numerous small solid particles. In video games, simulating these materials increases immersion and can be used for various game mechanics. Computationally, full scale simulation is not typically feasible except on the most powerful hardware and tends to be reduced in priority to favor other, more integral, gameplay features. Here we study the computational and qualitative aspects of side profile flow of sand-like particles using cellular automata (CA). Our CA uses a standard square lattice that updates via a custom, modified Margolus neighborhood. Each update occurs using a set of probabilistic transitions that can be tuned to simulate friction between particles. We focus on the look of the sandpile structure created from an hourglass shape over time using different transition probabilities and the computational impact of such a simulation. The toppling behavior and final structure of the sandpiles are largely dependent on the chosen probabilities. As the probability to topple decreases, representing greater friction, elongated sandpiles begin to form, leading to longer settling times.