MedicalVisualization

## 3D Perlin Noise

Perlin Noise is a procedural description of a noise-function.

Simple noise volume:

$f(x,y,z) = random(x,y,z) \in [-1,1]$

Interpolation of the noise volume yields a noise function with a carrier frequency of half the voxel distance.

Perlin Noise is the sum of noise-function with increasing carrier frequency and decreasing amplitude. Typically the frequency is doubled and the amplitude is halved. This is also known as turbulence function.

graphs by Hugo Elias
graphs by Hugo Elias

3D Perlin Noise:
blender.org

$f(x,y,z) = \sum \frac1f noise_f(x,y,z)$