Two-Dimensional Fractional Brownian Motion

Two methods for generating a fractional Brownian motion to simulate a natural surface are demonstrated here. The Hurst exponent describes the raggedness, with higher exponents leading to smoother surfaces. Fractional Brownian motion is a generalization of ordinary Brownian motion that has been used successfully to model a variety of natural phenomena, such as terrains, coastlines, and clouds. It has the scaling property . Ordinary Brownian motion has .

(29 lines omitted)

Random addition refines the list of points by interpolation and adding random offsets.
Fourier synthesis generates a random spectrum such that the resulting data has the correct scaling property.
The surfaces are colored by height using the "Topography" gradient mapping and level curves.
The code for generating the data is from Roman E. Maeder, The Mathematica Programmer II, New York: Academic Press, 1996.
comments
 
Powered by Wolfram Mathematica
Give us your feedback
Give us your feedback

Source page:




 often  occasionally  never

Note: Please do not include anything you consider confidential or proprietary. Your message and contact information may be shared with the author of any specific Demonstration for which you give feedback, but will not otherwise be published or distributed.
Privacy Policy »

Note: To run this Demonstration you need the free
Mathematica Player
or Mathematica 7+
Download or upgrade to Mathematica Player 7
I already have Mathematica Player or Mathematica 7+