An image from an awesome demo by Ed Pegg Jr. that's part of the Wolfram Demonstrations Project. This image corresponds to Gaussian integers raised to the 11th power. The demo allows one to view Gaussian integers raised to any fractional power. The user can choose a numerator and denominator less than 20.

Gaussian integers raised to the 17/6 th power

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.

Irreducible fractions come up all the time in math problems, but who knew they looked so beautiful all together?
This picture, from Wolfram, is of irreducible fractions in the Complex plane.