# Tinkerbell Map

Submitted by michael on Sat, 01/19/2019 - 14:29

The Tinkerbell map is a chaotic dynamical system with an interesting strange attractor. The iterated function is

$$x_{n+1} = x_n^2 - y_n^2 + a x_n + b y_n$$

$$y_{n+1} = 2 x_n y_n + c x_n + d x_n$$

In this example, the parameters are $a=0.9$, $b=-0.6013$, and $c=2.0$. $d$ is randomly chosen on $(0.35, 0.55)$, and the colour is based on $d$.

See also Wikipedia.

## Controls

The buttons below the image control the generation. The step button will stop the generation and compute and draw the next point in the iteration. Restart sets a new random colour and $d$ parameter. The save button will download the image to your computer.