Critical points of generalized scaling

It is shown, using data of laboratory and numerical simulations obtained by different authors, that for generalized scaling Fq∼Fpτ(q)/τ(p) (where Fq is a moment of qth order) the index-function τ(q) can be represented by the ‘critical’ form τ(q)∼(q−qc)γ for a wide class of multifractal processes (including, in particular: random walks on linear fractals and on percolation clusters, turbulence, 2D active DLA zone, diffusion in the presence of an absorbing polymer, and multiparticle production at high energies).