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 explorables is a combination of two models, one that explains the emergence of dynamic patterns and collective behavior in schools of fish or flocks of birds, the second, the Schelling model, captures the geographic segregation of populations of different kinds of individuals. When these two models are combined, a great variety of beautiful dynamic swarming patterns can be generated. These patterns show traces of the generic swarming states like “milling” and segregation effects within these dynamic states.

This explorable illustrates how variation and selection in a population of replicating organisms naturally leads to a gradual increase in the population’s overall fitness. The explorable simulates a system that is captured (to some extent) by the Replicator-Mutator Equation which is both, a generalization of the famous Replicator Equation and the Quasispecies Equation.

This explorable illustrates the dynamics of the Schelling model named after economist and Nobel laureate Thomas Schelling (1921-2016). Although this model has been applied in different contexts, it is best known for its ability to capture geographical ethnic segregation of human populations and cities based on very simple principles.

This explorable features an agent based model for road traffic and congestion. The model captures a phenomenon that most of us have witnessed on highways: phantom traffic jams, also known as traffic shocks or ghost jams. These are spontaneously emergent congested segments that move slowly and oppositely to the traffic. The explorable illustrates that phantom jams are more likely to occur if the variability in car speeds is higher:

This explorable illustrates the mechanism of herd immunity. When an infectious disease spreads in a population, an individual can be protected by a vaccine that delivers immunity. But there’s a greater good. Immunization not only projects the individual directly. The immunized person will also never transmit the disease to others, effectively reducing the likelihood that the disease can proliferate in the population. Because of this, a disease can be eradicated even if not the entire population is immunized. This population wide effect is known as herd immunity.

This explorable illustrates an evolutionary process in an “ecosystem” of interacting species (cartoon maggots, in this case). Individuals move around in their enviroment, replicate and eat each other. Optionally, mutations can generate new species. The system is similar to the Explorable A Patchwork Darwinge, only a bit more animalistc and dynamically slightly different. However, for this one here, you need a bit more patience in order to observe interesting effects.

This explorable illustrates of an intuitive dynamic model for collective motion (swarming) in animal groups. The model can be used to describe collective behavior observed in schooling fish or flocking birds, for example. The details of the model are described in a 2002 paper by Iain Couzin and colleagues.

This explorable illustrates the dynamics of the SIRS epidemic model, a generic model that captures disease dynamics in a populations or related contagion phenomena.