Fractal Perlin Noise

Sum over mutliple instance with increasing frequencies

\(f\) : Smooth Perlin Noise function
\(\displaystyle g(x) = \sum_{k=0}^{N} \alpha^k f(\omega^k\;x)\)
- - \(N\) number of Octave
- - \(\alpha\) persistency (\(1/\alpha\) attenuation)
- - \(\omega\) frequency gain

\(\;\;\;\;\;\;\;f(x)\)

\(0.8\,\,\,f(2\,x)\)

\(0.8^2\,f(4\,x)\)

\(0.8^3\,f(8\,x)\)

\(0.8^4\,f(16\,x)\)