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 a dynamic model for pattern formation in a growing community of microbes. Many microbial organisms exhibit collective behavior when a community of them expands say on a surface with nutrients. These patterns are often very beautiful and rich in structure.

This explorable illustrates one of the most basic mechanisms for spontaneous pattern formation: Local excitation and long range inhibition. This mechanism or similar ones are responsible for patterns observed in many natural systems, such as neural tissue, animal fur and spatial heterogeneity in social systems.