Environmental memory boosts group formation of clueless individuals

Many living and artificial decentralised systems form groups to increase fitness, optimise resources, and reach consensus. Examples span bacterial quorum sensing, biofilms, social insects, animal groups, human crowds, active colloids, and robotic swarms. Prior work has demonstrated motility-induced phase separation and living crystals in active colloids, as well as complex collective patterns via designed interactions, confinement, or feedback. Stigmergy—indirect coordination via environmental modification or markers—underlies collective behaviours in many natural systems. The authors address whether explicit signalling or information processing is necessary: they hypothesise that even “clueless” self-motile individuals, incapable of sensing or communicating, can form groups if a dynamic environment transiently stores and shares memory of their passage. They propose that obstacle-induced environmental modifications can create reusable paths that bias subsequent motion, coordinating aggregation and group formation.

The paper situates its contribution within research on active matter and swarm systems: (i) group benefits and consensus formation across biological and artificial systems; (ii) active colloids showing motility-induced phase separation and living crystals; (iii) engineered collective behaviours via particle design, confinement, and feedback; (iv) the role of crowding and active–passive mixtures in modulating energy landscapes and assembly; and (v) stigmergy as a general coordination mechanism in biology, social insects, crowds, robotics, AI, and active colloids. Typically, individuals are assumed to have minimal signalling/processing capabilities, enabling shared environmental memory. This work departs by removing explicit signalling entirely, focusing on environmental dynamics as the primary memory and coordination mechanism.

Experiments:

• Active particles: Janus SiO2 colloids (d = 4.77 ± 0.20 µm) half-coated with 60 nm carbon. Suspended in a near-critical water–2,6-lutidine mixture (0.286 mass fraction lutidine) below Tc (T ≈ 307 K). Under uniform green CW laser illumination (λ = 532 nm, I = 2.5 µW µm−2), particles self-propel at v ≈ 1.9 µm s−1 due to local demixing around the cap. Motion occurs in the Stokes regime (Re ≪ 1). Active particles interact via steric and short-range attractions; boundaries can induce aligning interactions.
• Environment: Quasi-2D chambers with freely diffusing passive SiO2 colloids (same size) as obstacles. Passive density ρp varied from 0% to 75% (fractional surface coverage). Active density ρa from 0.5% to 1.6%. Janus particles represent a small fraction of total particles.
• Group definition: Clusters of ≥3 active particles, with interparticle separation ≤0.1 d, persisting for at least one frame.
• Measurements: Digital video microscopy (10 fps) on an inverted microscope with thermal control at 30 °C; trajectories of active and passive particles tracked. Mean-square displacements (MSDs) quantify motility. Path reuse quantified by the path revival function 1 − Caa(t), where Caa(t) is the cumulative probability that a region crossed by one active particle is crossed by another within lag time t. Assuming Poisson-distributed velocities for path choice, 1 − Caa(t) ≈ exp(−t/τρ), with effective path revival lifetime τρ fit from data.
• Mechanism probing: High-resolution observations of Janus particles interacting with local clusters of passive obstacles reveal reorientation events consistent with an aligning torque arising from asymmetry in demixing near obstacles; particles steer away from obstacles and align with open paths.

Simulations:

• Particle-based model in 2D periodic box (L = 60 d) with na active and np passive spheres (diameter d, mass m) matching experimental ρa and ρp. Dynamics integrated via velocity Verlet (LAMMPS). Translational and rotational motion obey Langevin equations; thermal noise included. Parameters mapped to experiments via Péclet number Pe = dv/Dt, with d = 4.77 µm, v = 1.9 µm s−1, Dt = 0.0249 µm2 s−1. Dt and Dr computed including near-wall drag corrections.
• Interactions: Passive–passive via truncated repulsive Lennard-Jones (r_cut = d); active–active via attractive LJ with r_cut = 5 d; well depths εij from experiment.
• Aligning torque: Effective torque Ωi = −Ω0 (vi × Σj eij κij / rij), steering active particles away from nearby passive obstacles and aligning to path boundaries. Torque strength Ω0 fit to experiments.
• Analyses: Simulated path revival function and group statistics (largest cluster size Cmax, number of groups Ng). Rate coefficients for aggregation computed from simulations (αmm, αmg, αgg) to parameterise a mean-field kinetic model.

Kinetic model:

• Mean-field rate equations for number density of monomers c1 (free active particles) and number density of groups cg: • dc1/dt = −αmm c1^2 − αmg c1 cg • dcg/dt = (1/2) αmm c1^2 − αgg cg^2
• Rates αmm, αmg, αgg encapsulate encounter frequencies and effective cross-sections; without shared memory they scale with effective diffusion. Here, shared environmental memory (reusable paths) modifies encounters, enhancing αmg and αgg at intermediate ρp.

• Environmental memory via transient, reusable paths: Active Janus particles carve open paths through crowded passive colloids; before Brownian closure, other actives preferentially reuse these paths from either end, establishing sematectonic stigmergy. This feedback accelerates encounters and aggregation into groups.
• Non-monotonic dependence on environmental crowding: For fixed ρa, the largest group size Cmax and the average particles per group peak at intermediate ρp. At low ρp, encounters are too sparse (especially at ρa = 0.5%); at intermediate ρp, reusable paths and shared memory boost aggregation; at high ρp, motility is strongly hindered, reducing group growth and cohesion.
• Number of groups vs. size: Ng increases roughly monotonically with ρp, but group sizes become smaller and more homogeneous at high ρp. At the peak, a single large cluster can comprise up to about two-thirds of the active particles in groups.
• Path revival function reveals enhanced path reuse: 1 − Caa(t) follows an exponential with lifetime τρ. Compared to low ρp, τρ is reduced by approximately a factor of two at intermediate ρp, indicating faster path reuse and stronger shared memory than expected from decreased velocities alone.
• Aligning torque as mechanism: Microscopy shows obstacle-induced reorientation steering particles toward open paths. Simulations require an effective aligning torque to reproduce experimental trends: fitting yields Ω0 ≈ 72 ± 16 kBT. Without the torque, τρ increases with ρp (as expected from reduced velocities), and the non-monotonic peak in Cmax disappears.
• Density of actives shifts optimal crowding: Increasing ρa shifts the peak in group size to lower ρp and broadens/increases the peak: more actives more effectively create and reuse environmental correlations, lowering the passive density needed to promote group formation.
• Kinetic pathways: From simulations, αmg (monomer–group) and αgg (group–group) exhibit maxima at intermediate ρp and dominate kinetics once initial groups exist; αmm is comparatively flat. When torque is off, all aggregation rates decay monotonically with ρp, consistent with diffusion hindered by obstacles.

The study addresses whether explicit signalling is necessary for group formation in decentralised systems of individuals lacking sensing and information processing. Findings show that dynamic environmental changes created by motion through crowded passive media generate a shared memory (transient paths) that biases subsequent trajectories, coordinating aggregation and group growth. An obstacle-induced aligning torque provides the physical mechanism linking environmental structure to particle orientation, enabling stigmergy without communication. This environmental feedback explains the non-monotonic dependence of group formation on crowding and the dominance of monomer–group and group–group aggregation at intermediate ρp. The results generalise to other systems where environmental features (e.g., electrostatic, phoretic, hydrodynamic fields or sensing) can produce effective aligning interactions, suggesting that environmental memory can synergise with or even replace explicit signalling to lower thresholds for quorum formation and consensus in biological and artificial collectives.

This work uncovers a pathway to coordinated group formation in systems of clueless active particles via shared environmental memory created by crowding. Transient paths carved in a dynamic obstacle field are reused, enhancing encounters and producing large groups at intermediate obstacle densities. The key enabling mechanism is an obstacle-induced aligning torque; incorporating this effect in simulations reproduces experimental path reuse, non-monotonic group sizes, and the kinetics dominated by monomer–group and group–group aggregation. Beyond active colloids, environmental-memory mechanisms could be exploited to steer self-organisation in decentralised systems, potentially informing the design of antimicrobial surfaces, crowd management strategies, neuromorphic computing architectures, and artificial swarm intelligence. Future research could explore different environmental couplings (e.g., phoretic/hydrodynamic fields), robustness across particle properties and geometries, and control protocols to program desired collective states.