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.
 

Quaternion Julia, 80mm glass cube – $72

Without illumination the crystal works best on a dark background.  It comes with clear rubber feet to avoid scratching your desk or mantel. On the left, this base lights up your fractal!  With a gloss black finish and white LEDs that are cool and energy-efficient, it's bright enough for the office by day, or a brilliant nightlight. Light base, 3½ x 3½ x 1" – $20

 

This attractor was generated by Nicolas Desprez using his excellent freeware: