Comment on the equivalence between fracton/spectral dimensionality, and the dimensionality of recurrence

Abstract

The "fracton/spectral dimensionality"Dfracton is an important characteristic of fractal processes. Until now, it has not been interpreted as the fractal dimensionality of any well-defined fractal set, and it has been claimed thatDfracton is more "intrinsic" than "the" fractal dimensionality. In fact,Dfractol, is best understood as an original dynamical reinterpretation of a well-defined previously known kinetic dimensionality:Dfracton 's twice the fractal codimensionality of the time instants when a fractal process returns to a point it had previously visited. © 1984 Plenum Publishing Corporation.