Environmental memory boosts group formation of clueless individuals

The formation of groups is a widespread phenomenon observed across diverse systems, from microorganisms to social insects, and even in artificial systems like robotic swarms and AI algorithms. Group formation offers numerous advantages, including improved resource utilization, enhanced fitness, and more efficient consensus-building. Many such systems exhibit high-level coordination emerging from individuals with limited information processing abilities, relying on simple communication rules. Stigmergy, a form of indirect communication mediated by environmental modifications or markers, plays a crucial role in coordinating collective behavior in numerous natural systems. This involves individuals interacting with and modifying their environment, leaving traces that subsequently influence the behavior of others. This research explores a novel mechanism of group formation where the environment itself acts as a shared memory, coordinating the behavior of individuals even in the absence of any direct communication or information processing capabilities.

Existing research extensively explores stigmergy as a key mechanism for collective behavior in decentralized systems. Studies have shown how environmental modifications or marker deposition can facilitate indirect communication, enabling coordinated actions in systems ranging from microorganisms to social insects. For example, ants utilize pheromone trails to navigate efficiently, while bacteria employ chemical signaling for biofilm formation. In artificial systems, stigmergy principles have been implemented in robotic swarms and AI algorithms to achieve collective tasks. However, these studies often assume a minimal level of communication or signal processing by individuals. This paper investigates the possibility of collective behavior emerging solely through environmental memory, without any explicit communication among individuals.

The researchers employed Janus silica colloids, half-coated with carbon, as a model system for self-motile individuals. These particles exhibit self-propulsion when exposed to laser light in a critical binary mixture of water and 2,6-lutidine. The experiments were conducted in a quasi-two-dimensional environment containing both the active Janus particles and passive silica colloids at varying densities. The densities of active (ρₐ) and passive (ρₚ) particles were systematically varied to observe their effect on group formation. The motion of the particles was tracked using digital video microscopy. The formation of groups was defined as clusters of at least three particles separated by at most 0.1d (particle diameter) and persisting for at least one frame. To quantify path reuse, a path revival function was introduced, measuring the probability of a region traversed by one particle being traversed by another within a specified time lag. Simulations using a particle-based model were performed to gain a deeper understanding of the underlying mechanism. The model incorporated an aligning torque reflecting the interaction of active particles with passive obstacles. A kinetic model based on mean-field rate equations was used to analyze the aggregation dynamics, considering monomer-monomer, monomer-group, and group-group aggregation events.

The experiments revealed a non-monotonic relationship between the density of passive particles (ρₚ) and group formation. At intermediate densities of passive particles, the largest groups were observed. This non-monotonic behavior was attributed to the emergence of a shared environmental memory through path reuse. Active particles tend to reuse pre-existing paths created by other particles, rather than creating new ones, resulting in enhanced aggregation. This path reuse is quantified by the path revival function, which exhibits a faster decay at intermediate ρₚ values, indicating faster path reuse. The microscopic mechanism behind path reuse was elucidated by examining the motion of individual Janus particles navigating the obstacles. An aligning torque, caused by asymmetric demixing around the particle's self-propulsion mechanism in the presence of obstacles, guides the particles away from clusters of passive particles and towards open paths. Simulations confirmed the importance of this aligning torque in reproducing the experimental observations. The kinetic model demonstrated that at intermediate ρₚ, the kinetics of group formation are dominated by monomer-group and group-group aggregation events, suggesting that the shared environmental memory significantly accelerates the group growth. The simulations showed that in the absence of the aligning torque, the aggregation rates monotonically decrease with increasing ρₚ.

The findings demonstrate that a dynamic environment can act as a shared memory, coordinating group formation even in a system of clueless individuals with no direct communication. The aligning torque induced by the interaction with passive particles is the key mechanism enabling path reuse and stigmergy. The non-monotonic dependence of group formation on passive particle density highlights the complex interplay between individual motility and environmental structure. This mechanism of indirect coordination could have broad implications for understanding collective behavior in various biological and artificial systems. The environmental memory effect could potentially lower the threshold for quorum sensing in microbial communities or for reaching consensus in decision-making processes.

This research presents a novel mechanism of group formation driven by environmental memory. Even in the absence of communication or information processing, a dynamic environment can coordinate collective behavior through transient storage of individual movements. The aligning torque plays a key role in this process. Future research could explore the generality of this mechanism in other active matter systems and its implications for designing self-organizing artificial systems.

The study focuses on a specific model system (Janus particles in a critical mixture). The generalizability of the findings to other types of active matter systems requires further investigation. The simulations use a simplified model, neglecting potential complexities such as hydrodynamic interactions and detailed particle-particle interactions. The quasi-two-dimensional experimental setup might not perfectly capture the dynamics in three-dimensional systems.