A Mobius-like object with holes by Tom Longtin and Rinus Roelofs.

The interactions between sub-atomic particles at the particle accelerator at CERN in Geneva.

Circle packings

Circle packing is a study of arranging a maximal number of different sized circles (or spheres) so that none overlap. In the picture above, circles of the same size have the same color. See more here.

A beautiful spot in the 3-d Mandelbrot set. To see more check out this gallery.

Conchoids of a 5 cusped epicycloid with pole at center.

Boundary formed by trochoids of different parameters.

Parallels of the Witch of Agnesi by Xah Lee

A fractal dodecahedral subdivision of the sphere

The colors represent the amplitude of the ground's horizontal motion 6 seconds into a 4.4-magnitude earthquake. This image produced on a supercomputer in Pittsburgh is one of several such simulations whose accuracy provides architects with localized information on the kind of intensity buildings may have to withstand.
This is one of many beautiful supercomputer simulations compiled by Discover.

An Apollonian gasket

A cube 6-compound shows 6 overlapping cubes.

A cross-section of a structure generated by n-dimensional cubes by Haresh Lalvani/Patrick Hanrahan with an early 80s computer graphics program. I'd like to see this program adjusted to a modern computer to incorporate color.

This image by Stephen Schiller has been one of my favorites for years. It shows the distribution of fractions of Gaussian integers with a restriction on the denominator. Explicitly, this is the set of complex numbers (a + bi)/(c + di) where a,b,c, and d are integers, and √(c² + d²) < 25. Source: The Pattern Book, by Clifford Pickover.