We shall show that the oscillations observed by Strichartz JRS92, Str90] in the Fourier transforms of self-similar measures have a large-scale renormali-sation given by a Riesz-measure. Vice versa the Riesz measure itself will be shown to be self-similar around every triadic point.

It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil’s staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations.

The evolution of codification within the increasing complexity and diversity of relations is examined within a triadic architectural frame of filiated hierarchical levels of both material organization and consciousness. Inertia and entropy are understood as basic forces within codal organization, and evolution is examined as a force of mediation between these two forces, operating to move energ...