Image produced by R.R. Hogan, University of Cambridge.

This pretty picture looks like something you'd see through a kaleidoscope, but it's more than a bit of fun. It's an image of a two-dimensional crystal — but not as you would see it if you looked at it. Instead, it shows the Brillouin zones of the crystal, which give important information about how waves, such as light or X-rays, pass through it.

The picture, created by R.R. Hogan, is one of the images that appear in the book 50 visions of mathematics, which celebrates the 50th anniversary of the Institute of Mathematics and its Applications.

To find out more about crystals and what can happen when you bombard them with waves, read Shattering crystal symmetries.