# “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 simple systems that exhibits determinstic chaos.