Hausdorff-Besicovic dimension

A fractal object such as a C curve may have some unusual properties. The properties are that it has a fractal dimension but this fractal dimension is not a fraction. In the case of the C curve it is equal to two. The reason this object is still a fractal relates to a definition of fractal dimension. First, one defines two concepts of dimensions the topological dimension, which corresponds to our usual concept of a dimension, and a so-called Hausdorff-Besicovic dimension. If for a given object the two dimensions defined are different, the object is said to have a fractal dimension. In the case of the... 

C curve, the topological dimension is equal to one and the Hausdorff-Besicovic dimension is equal to two and that is why it is considered fractal, despite the fact that neither of these dimensions is itself fractional. In most cases, however, a fractal has a fractional dimension. 

---

See also in sourсe #XX -- [ , ]

See also in sourсe #XX -- [ ]

---