  Starting from the morphological-functional assumption of the fractal brain, a
mathematical model is given by activating brain non-differentiable dynamics
through the determinism-nondeterminism inference of the responsible mechanisms.
The postulation of a scale covariance principle in Schrodinger type
representation of the brain geodesics implies the spectral functionality of the
brain dynamics through mechanisms of tunelling, percolation etc., while in the
hydrodynamical type representation, it implies their structural functionality
through mechanisms of wave schock, solitons type etc. For external constraints
proportional with the states density, the fluctuations of the brain stationary
dynamics activate both the spectral neuronal networks and the structural ones
through a mapping principle of two distinct classes of cnoidal oscillation
modes. The spectral-structural compatibility of the neuronal networks generates
the communication codes of algebraic type, while the same compatibility on the
solitonic component induces a strange topology (the direct product of the
spectral topology and the structural one) that is responsible of the quadruple
law(for instance, the nucleotide base from the human DNA structure).
Implications in the elucidation of some neuropsychological mechanisms (memory
location and functioning, dementia etc.) are also presented.
