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

Quaternion Julia sets have much in common with the more 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 light base is a great way to light up your fractal! It's made of black Formica and has white LEDs that are cool, long-lasting and energy-efficient.  Bright enough for the office by day, or a brilliant nightlight. Light base – $20

 

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