When we say we want to create an "interesting" texture, we usually don't care exactly what it looks like -- we're only concerned with the overall appearance. We want to add random variations to our texture, but in a controlled way. Noise and turbulence are very useful tools for doing just that.

A noise function is a continuous funtions that varies throughout space at a uniform frequency. To create a simple noise function, consider a 3D lattice, with a random value assigned to each triple of integer coordinates: