Hidden order in chaotic crowds

One of my best learning-photojournalism photos was at a crowded large street fair, and the scene involved unusual crowd dynamics.

I'm short, but I had a lot of practice moving through crowds to shoot political demonstrations while carrying gear (cameras, and a bulky backpack), and could usually just know how to move quickly through a crowd. (Not quite gliding through the Matrix, since it's not a straight line, but constantly moving and thinking very focused "situated action", and it somehow working better than I would've thought it would.)

That day at the street fair, when it suddenly felt like the crowd dynamics were changing, I couldn't see why, so I moved to find out. Then I saw part of the crowd had turned into a wall of people who were kinda being led forward in one direction, and a clearing starting in front of them. So I ran to just ahead of them, and got the shot, before getting out of the way.

It was a celebrity (Zach Braff), and someone unidentified but with a kind of gravitas strong presence -- one or both de facto leading this crowd of 20-somethings. Somehow this formed a flood of people, but with a wide flat front. I'd guess that no one wanted to move ahead of the leaders.

Fortunately, I had my usual kit (Canon prosumer DSLR hanging on each shoulder, for my beloved long zoom, and an especially sharp ultrawide), and operating it was all "muscle memory", so the ultrawide captured expressions in the crowd well. At least half the people in the front line were looking towards the leaders, generally smiling/happy, one of them absolutely giddy, as the crowd was moving in this emergent formation.

having been to many many festivals, where you pass through many crowds some static (eg people standing still) or dynamic (eg like the paper - everyone moving)

I found that people will just follow the nearest person moving roughly in the same direction as you want, if you can't see no one doing that, you then muddle your way through people but then find that theres a train of people behind you.

if you cant't find anyone to folow and you're the front person, then simple rules seem to come into action eg angles of how people are stood also seem to play a part, you prefer to go around the back of people rather than in front of them. and if there's two people together you try not to go through them. etc..

this knowledge is based in the UK where people are somtimes too polite

Actual paper is here: https://www.science.org/doi/10.1126/science.add8091. Very cool result. This is the gist:

> We introduce a theoretical approach that uses temporal coarse-graining akin to Einstein’s kinetic theory of Brownian motion (34). Our averaging scheme is valid in the case of nonjamming mixtures of hard particles, where the dynamics is dominated by pairwise interactions, which is a good approximation for typical pedestrian flows as well as dilute colloids. We recover and unify in a systematic manner the fundamental insights of Helbing and Vicsek (22) as well as Vissers et al. (11) and Klymko et al. (23) by showing that undulation-induced drift and diffusion can both contribute to lane nucleation. We also demonstrate that diffusive processes suppress the formation of very narrow lanes, thereby providing a dynamical selection mechanism that favors the nucleation of lanes of a particular width. We provide explicit formulas for the propensity of a given system to nucleate lanes, and we present a simple approximate rule that lanes emerge at a rate proportional to the product of agent speed, density, and an effective parameter related to the average magnitude of lateral displacement in agent-agent collisions.

So, there are 2 main mechanisms proposed in the literature on lane formation: "drift" and "diffusion". Drift arises from the tendency of people to have a preferred direction to turn to avoid a collision (i.e. right- or left-bias). When facing an opposing flow, repeated conflicts will cause you to slowly drift sideways in your preferred direction. Diffusion is the random Brownian Motion-like jostling that arises from conflicts with opposing pedestrians, which has no directional bias.

In both cases, you're getting jostled around more when there's an opposing flow in front of you than when you're in a lane of people going in the same direction, so there will be a tendency for lanes to form spontaneously ("nucleate"), even from a completely homogeneous initial configuration.

The point of the paper is that they derive, with minimal assumptions, a quantitative relationship that incorporates both mechanisms, and makes specific non-obvious predictions about the shapes and widths of lanes. It also predicts that the rate of lane formation has a simple form (density * speed * average jostle displacement from conflicts with other pedestrians). They do some real-world experiments to validate some of their predictions.

As someone who works on pedestrian simulation software, I don't see how to use this to write the simulation code, but it could be an interesting way to validate the software (i.e. verify that lane formation obeys the predicted relationship).

Something that bothers me about a lot of these papers though is they often perform simulations with periodic boundary conditions. I get why they do that, but it seems to me that that will cause spatial correlations to show up that wouldn't happen in real life. Would the rate of lane formation be different in a system with different boundary conditions?

Another limitation mentioned in the paper that makes this model difficult to apply to crowds of pedestrians is that they assume the interaction between 2 pedestrians depends only on their relative displacement. However, it's known that they key parameter in pedestrian interactions is actually the Time To Collision--i.e., pedestrian collision avoidance is fundamentally anticipatory [1]. Presumably this would complicate the model too much though (now you have to take into account displacement and relative velocity).

[1] http://motion.cs.umn.edu/PowerLaw/

Would be cool, as a follow-up study, to repeat the experiment but with the curves painted onto the ground, and participants are advised to loosely follow the lines of their color (or avoid lines of the opposite color). Could also do a variation where only a couple people towards the front know of the paths and implicitly guide the rest of the group's trajectory.

Simple flocking behavior :)