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 the dynamics of the famous hypercycle model. It was originally conceived by Peter Schuster and Nobel laureate Manfred Eigen (1927-2019) in 1979 to investigate the chemical basis of the origin of life. Because living things make copies of themselves, in the beginning complex chemicals like polymer chains, including small RNA molecules (see e.g. RNA-world), had to acquire the ability to catalyse their own synthesis from smaller parts, e.g. single nucleotides.

This explorable illustrates how simple, single-cell organisms can manage to aggregate into multi-cellular structures by emitting and responding to chemical signals. Individual cells respond by orienting towards a chemical signal and moving up its gradient, a process known as chemotaxis. The combination of synchronized signal emission and chemotaxis yields collective behavior with beautiful spatial branching patterns during the aggregation process.

This explorable illustrates how a school of fish can collectively find an optimal location, e.g. a dark, unexposed region in their environment simply by light-dependent speed control. The explorable is based on the model discussed in Flock’n Roll, which you may want to explore first.