This explorable illustrates beautiful dynamical patterns that can be generated by a simple game theoretic model on a lattice. The core of the model is the Prisoner’s Dilemma, a legendary game analyzed in game theory. In the game, two players can choose to cooperate or defect. Depending on their choice, they receive a pre-specified payoffs. The payoffs are chosen such that it seems difficult to make the right strategy choice.

This explorable illustrates one of the most famous and most fundamental models for the emergence of flocking, swarming and synchronized behavior in animal groups. The model was originally published in a 1995 paper by Tamás Vicsek and co-workers and is therefore called the Vicsek-Model. The model can explain why transitions to flocking behavior in groups of animals are often not gradual. Instead, one can expect a sudden emergence of flocking and synchronized movements if a critical density is crossed.

This explorable illustrates how a remarkably simple mathematical model for pedestrian dynamics can capture a number of features that are observed in actual pedestrian flows on walkways for example. In the model individual pedestrians move with an individual anticipated speed and direction. When obstacles get in their way, either physical obstacles or other pedestrians, walkers experience a repulsive social force, that alters their velocity and current direction to avoid collision. This alone is sufficient to produce a variety of patterns that are reminiscent of actual pedestrian dynamics. The explorable is a simplified variant of a series of beautiful models introduced by Dirk Helbing that have found a wide range of application, e.g. panic dynamics, crowd turbulence, traffic jams and more.

This explorable is about pattern formation in a model system for the growth of a bacterial population in a petri dish in which the bacterial population is made up of a mix of two or three mutant strains that have identical fitness and reproduction properties. In the model system, an initially well mixed drop of bacteria with an equal amounts of every mutant strain is positioned in the center of the petri dish. After that, the bacteria start replicating, the population expands radially and a pattern will emerge.