A multifractal scale-free lattice

We study the distribution of number of neighbors, ζ, of a multifractal self-affine lattice, Qmf, defined by a single parameter ρ. ζ is neither a constant like in regular lattices nor follows a Gaussian distribution as in the Voronoi lattice. The histogram of ζ show exponential behavior for low ζ and power-law for high ζ. There is no trivial correlation between the distribution of ζ and the critical exponent related to the correlation length, ν, for percolation in the Qmf. The analysis of maximal ζ versus ρ makes evident the relationship between Qmf and the square lattice.