# “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**# “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 $(x_{n},y_{n})$:

# “Double Trouble”

## The double pendulum

This explorable illustrates the beautiful dynamical features of the **double pendulum**, a famous idealized nonlinear mechanical system that exhibits deterministic chaos.
The double pendulum is essentially two simple pendula joined by a bearing. It’s a classic complex system in which a simple setup generates rich and seemingly unpredictable behavior. The only force that is acting on it is gravity. There’s no friction.

# “Kick it like Chirikov”

## The kicked rotator (standard map)

In this explorable you can investigate the dynamics of a famous two-dimensional, time discrete map, known as the standard or * Chirikovâ€“Taylor map*, one of the most famous dynamical systems that exhibits deterministic chaos. It is almost identical to the

*, an idealized physical system in which a rotating rod is periodically kicked by an external force.*

**“Kicked Rotator”**