This article deals with individuals moving in procession in real and artificial societies. A procession is a minimal form of society in which individual behavior is to go in a given direction and the organization is structured by the knowledge of the one ahead. This simple form of grouping is common in the living world, and, among humans, procession is a very circumscribed social activity whose origins are certainly very remote. This type of organization falls under microsociology, where the focus is on the study of direct interactions between individuals within small groups. In this article, we focus on the particular case of pine tree processionary caterpillars (Thaumetopoea pityocampa). In the first part, we propose a formal definition of the concept of procession and compare field experiments conducted by entomologists with agent-based simulations to study real caterpillars’ processionaries as they are. In the second part, we explore the life of caterpillars as they could be. First, by extending the model beyond reality, we can explain why real processionary caterpillars behave as they do. Then we report on field experiments on the behavior of real caterpillars artificially forced to follow a circular procession; these experiments confirm that each caterpillar can either be the leader of the procession or follow the one in front of it. In the third part, by allowing variations in the speed of movement on an artificial circular procession, computational simulations allow us to observe the emergence of unexpected mobile spatial structures built from regular polygonal shapes where chaotic movements and well-ordered forms are intimately linked. This confirms once again that simple rules can have complex consequences.