Wavelet noise is an alternative to Perlin noise which reduces the problems of aliasing and detail loss that are encountered when Perlin noise is summed into a fractal.
Algorithm detail The basic algorithm for 2-dimensional wavelet noise is as follows: Create an image, , filled with uniform white noise. Downsample to half-size to create , then upsample it back up to full size to create . Subtract from to create the end result, . This results in an image that contains all the information that cannot be represented at half-scale. From here, can be used similarly to Perlin noise to create fractal patterns.
External links Wavelet Noise Paper at pixar.com.