18:24
@user334732 Fractal geometry is the study of the geometry of fractals. :)
And tautologies are tautological. :P
Basically, "fractals" are sets in metric spaces which have somewhat pathological properties.
There is no one agreed upon definition, but Mandelbrot suggested that sets with "interesting" dimensional properties should be considered fractal---his own first attempt at a definition was a set with Hausdorff dimension strictly exceeding topological dimension.
Some folk attempt to do analysis on fractals (Kigami and Strichartz, for example). They are interested in differential (or pseudo-differential) operators on fractals, and employ some ideas which look similar to those employed by differential geometers.
I am more interested in the actual geometry of such sets, as described by the interplay between measure and metric. My primary tools are zeta functions associated to fractal sets (or metric spaces), which can be used to recover some geometric properties.
