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

The fracton/spectral dimensionality ^D fracton 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 that ^D fracton is more intrinsic than the fractal dimensionality. In fact, ^D fractol, is best understood as an originaldynamical reinterpretation of a well-defined previously knownkinetic dimensionality: ^D fracton 's twice the fractal codimensionality of the time instants when a fractal process returns to a point it had previously visited.Presented at theThird Conference on Fractals: Fractals in the Physical Sciences, held at the National Bureau of Standards, Gaithersburg, Maryland, on November 20–23, 1983.While this talk has been widely discussed, its text was not available for inclusion in these proceedings.