compute multifractal spectrum of 2D HDR images
https://mathr.co.uk/multifractal
https://code.mathr.co.uk/multifractal
https://en.wikipedia.org/wiki/Multifractal_system
A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead, a continuous spectrum of exponents (the so-called singularity spectrum) is needed.
“Direct determination of the f(α) singularity spectrum”
by Ashvin Chhabra and Roderick V. Jensen
in Phys. Rev. Lett. 62, 1327 – Published 20 March 1989
https://doi.org/10.1103/PhysRevLett.62.1327
The direct determination of the f(α) singularity spectrum from experimental data is a difficult problem. This Letter introduces a simple method for computing f(α) based on the theorems of Shannon, Eggelston, and Billingsley which is markedly superior to other recently proposed methods, especially when dealing with experimental data from low-dimensional chaotic systems where the underlying dynamics are unknown.
git clone https://code.mathr.co.uk/multifractal.git
cd multifractal
make./multifractal platform resolution input.exr output.dat
gnuplot -c ../multifractal.gnuplot "output.dat" \
"q-dq.png" "q-dq-excerpt.png" "a-fa.png"platform is OpenCL platform index (eg 0)
resultion is number of data points to compute (eg 1280)
input.exr is input EXR image file (RGBA)
output.dat is output data text
multifractal -- compute multifractal spectrum of 2D HDR images
Copyright (C) 2020 Claude Heiland-Allen
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