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Fractional Brownian field or surface generator

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Fractional Brownian field or surface generator

by

Zdravko Botev (view profile)

 

07 Nov 2012 (Updated )

Fast simulation of fractional Brownian surface on unit disk, with Hurst parameter 'H'.

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Description

Simulates Fractional Brownian field on unit disk, with Hurst parameter 'H';
Note that the covariance function is isotropic, see reference below.
 INPUTS:
        - '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;
 OUTPUT:
          - 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
            surf(tx,ty,field1,'EdgeColor','none')
 Example:
  [field1,field2,tx,ty]=Brownian_field(.9,2^10);surf(tx,ty,field2,'EdgeColor','none'),colormap bone
Reference:
 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

Acknowledgements

Circulant Embedding Method For Generating Stationary Gaussian Field and Fractional Brownian Motion Generator inspired this file.

Required Products MATLAB
MATLAB release MATLAB 8.6 (R2015b)
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Comments and Ratings (2)
16 Mar 2014 Damodara

Hi Botev,

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

Regards
dams

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24 Sep 2013 Luiz

Luiz (view profile)

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.

Thanks!

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Updates
03 Feb 2016 1.1

- updated reference
- introduced error control

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