## 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]