Fractal noise
Purpose
Description
Tips
Macro Synopsis
Modules
Related Functions
References
Purpose
Generate a fractal noise signal
Description
"Fractal noise" generates a noise sequence y as a one-dimensional realization of a fractal Brownian Motion process Y. Fractal Brownian Motion is a non-stationary stochastic process with growths that obey a normal distribution and a variance
with H ranging from 0 to 1.
For H=0.5, the growths are stochastically self-similar in a sense that 
and 
are statistically indistinguishable for all 
and 
.
Parameters of "Fractal noise" are
- Length N (in samples)
- Hurst exponent H
Tips
The fractal dimension D is determined by H via 
. Coast lines, e.g. are best modelled by D = 1.2, leading to a Hurst exponent H = 0.8.
Macro Synopsis
y = FractalNoise(N,H);
signal y;
int N;
float H;
Modules
Student, Professional
Related Functions
Gaussian noise, Grey noise,
Poisson noise, Uniform noise, Long term correlation analysis (LTCA), R/S statistics.
There is also a Dataplore ® macro 'Brownian Noise' (BrownNoise.dpm).
References
Mandelbrot [30], Peitgen et al. [31]