New styles of moshing

In my recent Modeling Complex Systems course, the final project involved implementing a model from an article from the exisiting literature. Most of the models the students could choose from were complex systems 'classics'. For example, Nowak & May's spatial games; Albert, Jeong & Barabasi networks; Couzin et al. leadership of flocks were all included. But for fun I added one of my favourite papers of last year, by Silverberg et al., on mosh pits.

Silverberg and colleagues first analyzed online videos to identify how rock fans behaved when moshing. An example of a 'circle pit' is shown to the left. To explain how these pits are formed, the researchers built a model which assumed two types of concertgoers, those that want to bounce around and those that want to stand still. The active, bouncing moshers were subject to three types of forces. The first force was a tendency to follow in the same direction as those around them, the second was a tendency to mosh around at random and the third was the inevitable force caused by bumping in to others. The passive moshers were subject only to the last force. When active moshers bumped in to passive bystanders they bounced off them. This model was able to reproduce both the circle pit shown in the picture and the traditional random mosh pit.

Two groups of students in my class worked through a complete re-implementation of the model. Both groups were able to reproduce the original results, but they also found that getting a mosh pit going involved quite specific initial conditions. Only if the moshers started in a pit would the pit remain stable. To address this issue they modified the model a bit. Kristoffer Jonsson and Jonas Mirza added a  force that repulsed the passive concertgoers from the centre. The idea here is that the passive individuals want to avoid the centre of the pit. The active moshers then formed a stable mosh circle. This is shown in the video below.

Another group of students, John Svensson and Andreas Gådin, solved the issue by confining the moshers to a fixed area. This is a pretty realistic assumption. Heavy metal concerts do not take place on an infinite donut as is commonly assumed in this type of simulation.  The change led to some new and interesting mosh patterns. The video below shows how these build up, culminating in a collective rush backwards and forwards (see around 2:30 in the video). This is reminiscent of the Wall of Death, where the crowd run at each other like crazy. The striking thing here is that these walls can move backwards and forwards without the band initiating them.

Another pattern to look out for next time you are at a rock concert is the double vortex pit. This is pictured on the right and arises for specific parameter value combinations. The moshers move outwards in two ways, crash in the middle and then move out again.

The striking aspect of all these patterns is the lack of intelligence needed to produce them. Moshers can be as stupid as they like and they will still make pretty patterns! Thinking more broadly, the rules of the model are not unlike those which might govern cells during developmental processes. These models show how simple movements, combined with the right boundary conditions, can produce many different and robust patterns.

Thank you to John, Andreas, Kristoffer and Jonas for working so hard on your projects. It makes teaching more fun when I also learn something new.