The basic algorithm for 2-dimensional wavelet noise is as follows:

• Create an image, ${\displaystyle R}$ , filled with uniform white noise.
• Downsample ${\displaystyle R}$  to half-size to create ${\displaystyle R^{\downarrow }}$ , then upsample it back up to full size to create ${\displaystyle R^{\downarrow \uparrow }}$ .
• Subtract ${\displaystyle R^{\downarrow \uparrow }}$  from ${\displaystyle R}$  to create the end result, ${\displaystyle N}$ .

This results in an image that contains all the information that cannot be represented at half-scale. From here, ${\displaystyle N}$  can be used similarly to Perlin noise to create fractal patterns.

• Wavelet Noise Paper at pixar.com.