## 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

*. 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.*

**defect**# “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:

# “Knitworks”

## Growing complex networks

This explorable illustrates network growth based on * preferential attachment*, a variant of the

**Barabasi-Albert model**that was introduced to capture strong heterogeneities observed in many natural and technological networks. It has become a popular model for scale-free networks in nature.

Preferential attachment means that nodes that enter the network during a growth process preferentially connect to nodes with specific properties. In the original system, they preferentially connect to existing nodes that are already well connected, increasing their connectivity even further. This *rich get richer* effect generates networks in which a few nodes are very strongly connected and very many nodes poorly.

# “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

*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*

**activator-inhibitor***, a paradigmatic model for predator prey dynamics.*

**Lotka-Volterra System**