TOPICS
Search

Fractal Process


A one-dimensional map whose increments are distributed according to a normal distribution. Let y(t-Deltat) and y(t+Deltat) be values, then their correlation is given by the Brown function

 r=2^(2H-1)-1.

When H=1/2, r=0 and the fractal process corresponds to one-dimensional Brownian motion. If H>1/2, then r>0 and the process is called a persistent process. If H<1/2, then r<0 and the process is called an antipersistent process.


See also

Antipersistent Process, Persistent Process

Explore with Wolfram|Alpha

References

von Seggern, D. CRC Standard Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 2007.

Referenced on Wolfram|Alpha

Fractal Process

Cite this as:

Weisstein, Eric W. "Fractal Process." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FractalProcess.html

Subject classifications