Multifractal estimation using a standard box-counting algorithm

Software used to determine multifractal spectra: Generalized dimensions Dq and spectrum of singularities f(alfa), the software is described in the paper:

1. Saravia LA (2014) mfSBA: Multifractal analysis of spatial patterns in ecological communities [v2; ref status: indexed, http://f1000r.es/347]. F1000Research 3: 14. doi:10.12688/f1000research.3-14.v2.

mfSBA estimate both spectra and outputs data to evaluate the fits. A more detailed description is in the file mfSBA_README.

mfSBArnz estimate the Dq spectrun and randomize the original image N times to calculate a confidence interval to test the hipothesis that the original distribution was random.

multiSpeciesSBA estimates the multifractal spectra of a 2D species distribution assuming that each position is one individual and that each value represents a different specie. The species can be analyzed as a spatial rank surface (SRS) or as a generalization of species area distribution which I call multifractal SAD (species abundance distribution).

sed2grad transforms a sed file using a discrete gradient transformation.

R Functions and scripts

There are two scripts to test and demonstrate the software:

testMFA.r: Test and demostration of functions for standard, SRS and SAD multifractal analysis

Fun_MFA.r: R Functions for multifractal analysis,

The output should be compared with the same files in folder testOut

Other files

Several ".sed" files ".tif" are used as examples

The q21.sed is a file with q values used to estimate spectra.

These programs were used in the following papers:

1. Saravia LA. (2105) A new method to analyse species abundances in space using generalized dimensionss. Methods in Ecology and Evolution. doi: 10.1111/2041-210X.12417

2. Saravia LA, Giorgi A, Momo FR (2012) Multifractal Spatial Patterns and Diversity in an Ecological Succession. PLoS One 7: e34096. 

3. Saravia LA, Giorgi A, Momo F (2012) Multifractal growth in periphyton communities. Oikos 121: 1810–1820.

Please leave an Issue on github if you have some trouble.

License

Copyright 2011 Leonardo A. Saravia

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.