Mining Frequent Patterns in 2D+t Grid Graphs for Cellular Automata Analysis

Abstract

A 2D grid is a particular geometric graph that may be used to represent any 2D regular structure such as, for example, pixel grids, game boards, or cellular automata. Pattern mining techniques may be used to automatically extract interesting substructures from these grids. 2D+t grids are temporal sequences of grids which model the evolution of grids through time. In this paper, we show how to extend a 2D grid mining algorithm to 2D+t grids, thus allowing us to efficiently find frequent patterns in 2D+t grids. We evaluate scale-up properties of this algorithm on 2D+t grids generated by a classical cellular automaton, i.e., the game of life, and we show that the extracted spatio-temporal patterns may be used to analyze this kind of cellular automata.