CATRAKIS, H. J., and DIMOTAKIS, P. E. 1997 "Scale-dependent fractal geometry," NATO Advanced Studies Institute series, Mixing: Chaos and Turbulence (7--20 July 1996, Corsica, France), GALCIT Report FM97-2.


A generalization of fractal geometry that allows for a scale-development behavior is described. The resulting framework, termed "scale-dependent fractal" (SDF) geometry, can be used quantify and model various phenomena whose geometric complexity may depend on scale. Relations are derived between scale distributions and coverage dimensions in the SDF framework, for one- as well as multi-dimensional sets, and applied to level sets arising in turbulence and mixing.