Statistical Exploration of Distributed Pattern Formation Based on Minimalistic Approach

In this paper, we discuss the pattern formation of objects that can be stacked and transported by distributed autonomous agents. Inspired by the social behavior of termite colonies, which often build elaborate three-dimensional structures (nest towers), this paper explores the mechanism of termite-like agents through a computational and minimalistic approach. We introduce a cellular automata model (i.e., spatially discretized) for the agents and the objects they can transport, where each agent follows a “rule” determined by the assignment of fundamental actions (move/ load/ unload) based on the state of its neighboring cells. To evaluate the resulting patterns from the viewpoint of structural complexity and agent effort, we classify the patterns using the Kolmogorov dimension and higher-order local autocorrelation, two well-known statistical techniques in image processing. We find that the Kolmogorov dimension provides a good metric for the structural complexity of a pattern, whereas the higher-order local autocorrelation is an effective means of identifying particular local patterns.