Non-periodic Tiling of Procedural Noise Functions

Procedural noise functions have many applications in computer graphics, ranging from texture synthesis to atmospheric effect simulation or to landscape geometry specification. Noise can either be precomputed and stored into a texture, or evaluated directly at application runtime. This choice offers a tradeoff between image variance, memory consumption and performance. Advanced tiling algorithms can be used to decrease visual repetition. Wang tiles allow a plane to be tiled in a non-periodic way, using a relatively small set of textures. Tiles can be arranged in a single texture map to enable the GPU to use hardware filtering. In this paper, we present modifications to several popular procedural noise functions that directly produce texture maps containing the smallest complete Wang tile set. The findings presented in this paper enable non-periodic tiling of these noise functions and textures based on them, both at runtime and as a preprocessing step. These findings also allow decreasing repetition of noise-based effects in computer-generated images at a small performance cost, while maintaining or even reducing the memory consumption.