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FRACTAL SURFACE ALGORITHM


Detrending Moving Average (DMA) Algorithm for FRACTAL SURFACES



The DMA_2D algorithm allows the calculation of the:

(c) Hurst exponent of fractal surfaces according to the method proposed in :
Algorithm to estimate the Hurst exponent of high-dimensional fractals
Phys. Rev. E 76, 056703 (2007)


Click here to download the package "surfaces.zip" including executables and configuration files


The folder "surfaces.zip" contains:

(1) DMA_2D ----This is the executable program for the DMA algorithm for d=2.

(2) Configuration.txt (this is the configuration file with the parameters used by the executable program (1).) The parameters must be changed according to the surface to be analysed. Now the parameters are those working for the signal included in the folder(5)

(3) the folders Fraclab Surfaces 1024 and Fraclab Surfaces 256. These folders contain:

(3a) files (e.g. Surface_1024_05) with samples of Fractal Surfaces with size 1024X1024 and 256 X 256. The Hurst exponent of the fractal surfaces is 0.5. The generated by the Cholesky-Levinson factorization method (FRACLAB).
(3b) files (e.g. Surface_1024_05.dat.out ) output of the DMA_2D algorithm. The 1st column is "s"; the 2nd column "sigma_DMA".

(4) progression.txt (this file defines the sizes of the sub-arrays (squares) where the 2d moving avaerage is calculated)

(5) the folder with the soiurce files (C++) is also provided.


To implement the DMA_2D calculation:

a) run the program DMA_2D.exe:
b) load the file Configuration.txt by clicking on the "...." button
c) check that all the parameters are ok (especially the input and output file paths! )
d) press the "calculate" button.
e) the program will calculate the size of the fractal surface (e.g. 1024 rows and 1024 columns) and will ask to continue. Click yes!
f) the ouput file described at the (3b) e.g. Surface_1024_05.dat.out will be obtained.
g) plot the data of the output file in log-log scales