Description
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.