Sand Attractor

Sand particles are dropped onto the canvas, with each subsequent position governed by this fascinating and elegant strange attractor:

x_n+1 = a₁ + a₂x_n + a₃x_n² + a₄x_ny_n + a₅y_n + a₆y_n²
y_n+1 = a₇ + a₈x_n + a₉x_n² + a₁₀x_ny_n + a₁₁y_n + a₁₂y_n2

Coefficients a1 - a12 are chosen from a dozen sets known to produce stable patterns*. Even a small change in just one of the coefficients can profoundly influence the results.

Colour palettes are created by sampling one of several photographs taken by the programmer**. Colours are chosen from the palette according to the distance the particle has had to jump to reach its current position from its last.

At each refresh, the coefficients are adjusted slightly and a new palette chosen, leading to slightly different results*** on every new iteration.
* see also here. And here. Oh, and here.
** the sampling method is adapted from some code by Jared Tarbell, whose fascinating artworks can be viewed here.
*** which may or may not be stable!

Have a go: