Complexity Packages

This explorable illustrates the dynamics of a simple neural network model that is able to self-organize a one- or two-dimensional representation of a complicate input space.

The explorable illustrates spatio-temporal pattern formation in a system of pulse-coupled oscillators. The model is a generic model that yields spiral waves and target patterns depending on the parameter choices.

This explorable illustrates a dynamic network that explains the emergence of groups of uniform opinion. Nodes can change their opinion based on their open-mindedness and can rewire their connections to other nodes that are like them.

This is a model for collective behavior in animals, e.g. flocks of birds or schools of fish based on simple rules of interaction.

A collection of regular fractals that illustrates the nature of self-similarity

This explorable illustrates a simple and beautiful model for swarms, flocks and collective motion in animal populations.

This explorable illustrates the dynamics and properties of the famous Ising Model of statistical mechanics. It's a lattice of spins / magnets arranged on a lattice. Each spin interacts with its neighbors and tried to align its direction with the neighborh

The XY model is a key model of statistical mechanics. Among other things, it describes self-organization of spatially arranged magnets but also concepts like opinion dynamics in social systems.

This explorable illustrates the emergence of collective intelligence in a model for a school of fish. The combination of speed differences in the light and the dark and cohesive swarm forces helps the swarm find the safe regions.

This explorable illustrates spontaneous pattern formation in a spatial model in which points on a lattice interact by local positive feedback and negative long-range feedback.

This explorable illustrates a stockastic cellular automaton, a simple model that is able to generate fractal growth structures and a diverse set of patterns.

This explorable illustrates the chaotic sea of the famous two-dimensional map known as the kicked rotator or standard map. It's a very important system in nonlinear dynamics.

This explorable illustrates oscillatory dynamics and spatio-temporal patterns in the most famous predator prey model on a lattice.

This explorable is an implementation of Conway's Game of Life, one of the most famous cellular automata models for the emergence of structure, replication and complex behavior generated by simple rules.

This explorable illustrates a model for fractal growth patterns in natural systems based on the aggregation of randomly moving particles.

This explorable illustrates a famous game theoretic model, known as the prisoner's dilemma. On a lattice it can yield beautiful patterns and chaos.

This explorable illustrates the basic mechanism of evolution. In a population of replicating species, species with the highest fitness dominate until mutations yield yet more fit species. The fitness of the entire population increases steadily.

This explorable illustrates a model for pattern formation in microbial communities. Depending on parameters like food concentration, medium resistance and others, the emerging pattern exhibit different characteristics.

This explorable is a spatial implementation of the Kuramoto Model for phase coupled oscillators. It illustrates spatial synchronization and the dynamics of phase singularities.

This explorable illustrates the beauty of strange attractors of selected two-dimensional chaotic maps. The attractors change shape as a function of their parameters.