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Multifractal Analysis Functions
Here you will find MATLAB and Mathematica functions and examples of how to use them. Enjoy!
For comparisons between different techniques, see Lovejoy and Schertzer 2012.
For software in R.With comparisons between different techniques (Hébert et al 2021).
These examples give a brief description of the function, its inputs, outputs, and possible errors
To download all functions at once, click here
To download all analysis functions in Mathematica, click here
To download the multifractal simulation functions in Mathematica, click here
A document evaluating their performance is here.
| Documentation/Examples | Functions | Data |
|---|---|---|
| Structure Functions | Difference or Tendency | EPICA ice core data (includes explanation) |
| Haar (uniform resolution) | Haar (includes Smooth1D) | Rain gauge data (in 0.1mm) |
| Haar (nonuniform, no interpolation) | HaarNoInterpolate (Mathematica) | |
| Trace Moment | TraceMoment (includes Flux+Flux2nd+Fluxall) | Streamflow data (in ft3/s) |
| Outerscale | Outerscale (includes reslinpairsfilter+reslinpairsfilererr+FitFx) | Global temperature data (four series) |
| Interpolate Table | InterpolateTable (includes Degrade+Flux) | ECMWF atmospheric multifractal field |
| Spectrum Average 1D | SpecAverage1D (includes Window1D) | Lander temperature data (hourly) |
| ProbDistribution Delta | PDdelta (includes Tally+SortTally) | |
| Detrend Drop | DetrendDrop (includes Spectrum1D) | |
| Multifractal Simulation | Multifractal simulation (1-D and 2-D) (New more rapid versions, 18.6.14) | |
| Haar correlations and unceratinties with examples | Haar correlations |