EACH FRACTAL SET HAS A UNIQUE FRACTAL DIMENSION.

Abstract

Fractals and the fractal dimension D find many roles in the sciences, especially in physics, first due to my work since 1963 and now due to the work of many scholars. My work either states or implies that the sets that involve genuine disagreement between different definitions of fractal dimension are of interest in mathematics, but are not, at present, of interest in physics. However, many authors' reexamination of different definitions seems to yield conflicting dimensions. To those unacquainted with this discrepancy has become irritating, but I propose to show it is not serious. Typically, it reveals that it is now necessary to go beyond simple strictly self-similar fractal sets, and to inject (among others) fractal measures and fractal graphs.