Wavelet noise

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.

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.

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