Clustering free-falling paper motion with complexity and entropy

Abstract Many simple natural phenomena are characterized by complex motion that appears random at first glance, but often displays underlying patterns and behavior can be clustered in groups. The movement of small pieces paper falling through the air is one these systems whose complete mathematical description seems unworkable. Understanding types thus demands automated experimentation capable producing large datasets covering different behaviors —a task has become feasible only recently with advances computer vision machine learning methods. Here we use related to free-falling shapes propose an information-theoretical approach automatically clusters behavior. We evaluate permutation entropy statistical complexity from time series observable area captured a video camera. find chaotic tumbling motions have distinct average degree complexity, allowing us accurately discriminate between two unsupervised algorithm. Our method performance comparable other approaches based on physical quantities does not depend reconstructing three-dimensional trajectory.