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Fractional Brownian field or surface generator

version (3.24 KB) by Zdravko Botev
Fast simulation of fractional Brownian surface on unit disk, with Hurst parameter 'H'.


Updated 03 Feb 2016

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Simulates Fractional Brownian field on unit disk, with Hurst parameter 'H';
Note that the covariance function is isotropic, see reference below.
- 'H' is the Hurst parameter of the Gaussian process
- 'n' is the number of grid points, where 'n' is a power of 2;
if the 'n' supplied is not a power of two,
then we set n=2^ceil(log2(n)); default is n=2^8;
- two statistically independent fields 'field1' and 'field2'
over unit disk; if not output requested, then function
outputs a figure of one of the fields
- vectors 'tx' and 'ty' so that the field is plotted via
[field1,field2,tx,ty]=Brownian_field(.9,2^10);surf(tx,ty,field2,'EdgeColor','none'),colormap bone
Kroese, D. P., & Botev, Z. I. (2015). Spatial Process Simulation.
In Stochastic Geometry, Spatial Statistics and Random Fields(pp. 369-404)
Springer International Publishing, DOI: 10.1007/978-3-319-10064-7_12

Comments and Ratings (2)


Hi Botev,

How can we measure these fractals using box counting dimension method.



Dear Botev,

Thanks for sharing this file. I am trying to run the file, but Matlab says that is necessary to have a function rho. Could you provide a rho function as an example? You have done it in your other code (stationary_Gaussian_process) and it was great to have a start point.



- updated reference
- introduced error control

MATLAB Release Compatibility
Created with R2015b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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