The classification of fractal objects on nanometer scale in the tree-dimensional space is well developed on the base of small-angle neutron and X-ray scattering. Using the power law of the scattering intensity vs momentum transfer (I ⁓ q-Δ) one can distinguish between the surface fractals (3 < Δ < 4) and mass fractals (2 < Δ < 3) as well as the logarithmic fractals (Δ = 3) [1, 2]. The exponent Δ close to 3 was until recently interpreted as an intermediate case of the transition from mass to surface fractal. We showed that the cubic dependence in the SANS cross-section corresponds to the pair correlation function (r) ⁓ ln(/r) in the limit r/ << 1, where  is the size of the scattering object [2]. It has the specific scaling property γ (r/a) = γ (r) + ln(a), when the scaling down by a gives an additive constant to the correlation function, in contrast to the mass fractal, which is characterized by multiplicative constant. We found that the logarithmic correlation function is not a rare case for the structural organization of the life forms. In nature the structures are often-times generated by multiple repetition of the same morphogenetic mechanism, for example the branching. Tree is the most illustrative example of its realization. It grows in a way that on each next level of branching, the sum of squares of radii of the branches equals the square of the radius of the branch that was divided: the property which was noticed long ago by Leonardo da Vinci [3].