Fractal domain

Fractal domain is a function domain <math>D<math>, where <math>D<math> is a fractal set. As there is no clear definition of a fractal, except for the ones most "popular" (such as that the fractal set is any set that has the non-integer Hausdorff dimension), not much more can be said here.

A function with a fractal domain is, for example, Hausdorff dimension itself. We lay <math>\dim_H(D)=d<math>, where <math>d\in (0,\infty).<math>

Therefore we have <math>d\colon D \mapsto (0,\infty)<math>.