The Barycentric Fixed-Mass method for estimating fractal dimensions

A method for estimating (multi) fractal properties of 2D/3D point distributions

Multifractal dimension estimation with the Barycentric Fixed Mass method. Covers a given 2D/3D point distribution with equal mass circles/spheres centered at each point and then applies two additional criteria:
1) Barycentric: A circle/sphere is considered only if its center point is the closest point to its barycenter.
2) Non-Overlapping: Barycentric circles/spheres are randomly chosen such that the overlap is minimized while maximizing the overall coverage

For detailed information check the following publication:
Y. Kamer, G. Ouillon and D. Sornette (2013) Barycentric fixed-mass method for multifractal analysis http://arxiv.org/abs/1305.7384

% EXAMPLE:
% Generate a 3D monofractal with D=1.58...
mat_p1 = [0 1; 0 0];
mat_p1(:,:,2) = [1 0; 1 0];
pts_mat = recursiveFrac(mat_p1,7);
% ...and estimate D(q) vs q using BFM
[q_vec, Dq_vec] = call_BFM(pts_mat);
plot(q_vec, Dq_vec, '.-k');