Procedural texturing is commonly used to increase visual complexity and realism
in rendered scenes. Procedural texture basis functions, such as Perlin’s noise
function, are often built on hash functions defined over the integer lattice.
These hash functions are usually based on permutation tables and have a short
period. This causes procedural textures to repeat. In this paper, we present a
method for constructing hash functions with long periods. Our method is based on
techniques for constructing long-period pseudo-random number generators. The
hash functions we propose are almost as efficient as the traditional ones, but
allow to generate procedural textures with very large periods. This increases
the visual complexity and realism of procedural textures, and enables robust
implementationsof texture basis functions.