ABSTRACT
The complexity of geosciences has inspired the development of many innovative concepts and techniques. Multifractals are indeed very broad generalizations of the geometrical fractals whose field is a set indicator function with a binary codomain, therefore a kind of degenerate case for multifractal fields. Multifractals are in fact invariant with respect to multiple scale symmetry and therefore correspond once again to a broad generalization of properties that were once perceived in a more restrictive framework. Scale symmetry is in fact an element of the extended Galilean invariance. Scale symmetry has been widely used under the denomination of self-similarity, but with unnecessary limitations. The direct and inverse Mellin transforms correspond to the Laplace and inverse Laplace transforms for Log. The Legendre duality was first pointed out by Parisi and Frisch in a different context and with restrictive geometric hypotheses. The already large class of Lévy-Clifford algebra of multifractal generators is a particularly important contribution in privileged direction.
