Most recent Explorables:
“The Prisoner's Kaleidoscope”
The prisoner's dilemma game on a lattice
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.
“Horde of the Flies”
The Vicsek-Model
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.
Featured Explorables:
“Stranger Things”
Strange attractors
This explorable illustrates the structure and beauty of strange attractors of two-dimensional discrete maps. These maps generate sequences of pairs of number $(x_n,y_n)$ where the index $n=0,1,2,…$ denotes the step of the iteration process that starts at the point $(x_0,y_0)$. The map is defined by two functions $f(x,y)$ and $g(x,y)$ that determine the point $(x_{n+1},y_{n+1})$ given $(x_{n},y_{n})$:
“Lotka Martini”
The Lotka-Volterra model
This explorable illustrates the dynamics of a predator-prey model on a hexagonal lattice. In the model a prey species reproduces spontaneously but is also food to the predator species. The predator requires the prey for reproduction. The system is an example of an activator-inhibitor system, in which two dynamical entities interact in such a way that the activator (in this case the prey) activates the inhibitor (the predator) that in turn down-regulates the activator in a feedback loop. Activator-inhibitor systems often exhibit oscillatory behavior, like the famous Lotka-Volterra System, a paradigmatic model for predator prey dynamics.