Strange attractors are fractals that arise from relatively simple math: they're generated by iterative systems, in which a formula applied to its own results over and over. The results, instead of forming a simple shape as you might expect from simple equations, skip around forever, slowly filling in a lacy pattern.

Quaternion Julia sets have much in common with the familiar 2D Julia sets, and indeed each contains a Julia set as its central cross-section. More about the math is here, and of course there are many more online.

This particular one was generated by Nicolas Desprez using his excellent freeware, Chaoscope.