More Like this

1. A visual model of collective motion in human crowds

   Warren, W.H.; Dachner, G. (February 2020, Perception)

   null (Ed.)

   Collective motion in human crowds emerges from local interactions between individual pedestrians. Previously, we found that an individual in a crowd aligns their velocity vector with a weighted average of their neighbors’ velocities, where the weight decays with distance (Rio, Dachner, & Warren, PRSB, 2018; Warren, CDPS, 2018). Here, we explain this “alignment rule” based solely on visual information. When following behind a neighbor, the follower controls speed by canceling the neighbor’s optical expansion (Bai & Warren, VSS, 2018) and heading by canceling the neighbor’s angular velocity. When walking beside a neighbor, these relations reverse: Speed is controlled by canceling angular velocity and heading by canceling optical expansion. These two variables trade off as sinusoidal functions of eccentricity (Dachner & Warren, VSS, 2018). We use this visual model to simulate the trajectories of participants walking in virtual (12 neighbors) and real (20 neighbors) crowds. The model accounts for the data with root mean square errors (.04–.05 m/s, 1.5°–2.0°) the distance decay as a consequence of comparable to those of our previous velocity-alignment model. Moreover, the model explains Euclid’s law of perspective, without an explicit distance term. The visual model thus provides a better explanation of collective motion. 

   more » « less
2. Local interactions underlying collective motion in human crowds

   https://doi.org/10.1098/rspb.2018.0611  

   Rio, Kevin W.; Dachner, Gregory C.; Warren, William H. (May 2018, Proceedings of the Royal Society B: Biological Sciences)

   null (Ed.)

   It is commonly believed that global patterns of motion in flocks, schools and crowds emerge from local interactions between individuals, through a process of self-organization. The key to explaining such collective behaviour thus lies in deciphering these local interactions. We take an experiment-driven approach to modelling collective motion in human crowds. Previously, we observed that a pedestrian aligns their velocity vector (speed and heading direction) with that of a neighbour. Here we investigate the neighbourhood of interaction in a crowd: which neighbours influence a pedestrian's behaviour, how this depends on neighbour position, and how the influences of multiple neighbours are combined. In three experiments, a participant walked in a virtual crowd whose speed and heading were manipulated. We find that neighbour influence is linearly combined and decreases with distance, but not with lateral position (eccentricity). We model the neighbourhood as (i) a circularly symmetric region with (ii) a weighted average of neighbours, (iii) a uni-directional influence, and (iv) weights that decay exponentially to zero by 5 m. The model reproduces the experimental data and predicts individual trajectories in observational data on a human ‘swarm’. The results yield the first bottom-up model of collective crowd motion. 

   more » « less
3. Visual Influence Networks in Walking Crowds

   https://doi.org/10.1101/2025.01.29.635594  

   Yoshida, Kei; di_Bernardo, Mario; Warren, William H (January 2025, bioRxiv)

   Collective motion in human crowds has been understood as a self-organizing phenomenon that is generated from local visual interactions between neighboring pedestrians. To analyze these interactions, we introduce an approach that estimates local influences in observational data on moving human crowds and represents them as spatially-embedded dynamic networks (visual influence networks). We analyzed data from a human “swarm” experiment (N= 10, 16, 20) in which participants were instructed to walk about the tracking area while staying together as a group. We reconstructed the network every 0.5 seconds using Time-Dependent Delayed Correlation (TDDC). Using novel network measures of local and global leadership ('direct influence' and 'branching influence'), we find that both measures strongly depend on an individual’s spatial position within the group, yielding similar but distinctive leadership gradients from the front to the back. There was also a strong linear relationship between individual influence and front-back position in the crowd. The results reveal that influence is concentrated in specific positions in a crowd, a fact that could be exploited by individuals seeking to lead collective crowd motion. 

   more » « less
4. Is the neighborhood of interaction in human crowds metric, topological, or visual?

   https://doi.org/10.1093/pnasnexus/pgad118  

   Wirth, Trenton D; Dachner, Gregory C; Rio, Kevin W; Warren, William H (May 2023, PNAS Nexus)

   Borge-Holthoefer, Javier (Ed.)

   Abstract Global patterns of collective motion in bird flocks, fish schools, and human crowds are thought to emerge from local interactions within a neighborhood of interaction, the zone in which an individual is influenced by their neighbors. Both metric and topological neighborhoods have been reported in animal groups, but this question has not been addressed for human crowds. The answer has important implications for modeling crowd behavior and predicting crowd disasters such as jams, crushes, and stampedes. In a metric neighborhood, an individual is influenced by all neighbors within a fixed radius, whereas in a topological neighborhood, an individual is influenced by a fixed number of nearest neighbors, regardless of their physical distance. A recently proposed alternative is a visual neighborhood, in which an individual is influenced by the optical motions of all visible neighbors. We test these hypotheses experimentally by asking participants to walk in real and virtual crowds and manipulating the crowd's density. Our results rule out a topological neighborhood, are approximated by a metric neighborhood, but are best explained by a visual neighborhood that has elements of both. We conclude that the neighborhood of interaction in human crowds follows naturally from the laws of optics and suggest that previously observed “topological” and “metric” interactions might be a consequence of the visual neighborhood. 

   more » « less
5. Behavioral dynamics of pedestrians and crowds. International handbook of ecological psychology.

   Warren, WH (December 2025, Routledge)

   Romero, V; Segundo-Ortin, M; Wagman, J; Nonaka, T (Ed.)

   Where does the organization in behavior come from? Ecological psychology seeks to explain adaptive behavior as self-organized, emerging from the dynamics of agent-environment interactions, without assuming such organization a priori. This chapter offers an accessible introduction to the behavioral dynamics approach to modeling perception and action, applied to the case of human locomotion and crowd behavior. Most models of such behavior are ‘omniscient’, presuming accurate knowledge of the environmental state, but we find that information-based ‘visual’ models more closely capture human data. At the individual level, a locomotor trajectory emerges from an agent’s interactions with goals and obstacles, as attractors and repellers appear, shift, and bifurcate. At the dyad level, pedestrian interactions governed by visual control laws yield coordinated movements such as interception, collision avoidance, and following. At the collective level, these local interactions generate human ‘flocking’, crowd bifurcations, and patterns of lanes and stripes in crossing flows of pedestrians. By adopting an empirical, bottom-up, information-based approach, behavioral dynamics helps explain individual and collective behavior as resulting from a process of self-organized pattern formation, without appealing to internal plans or external commands. 

   more » « less