Fractals of rational dimension and fractals of integral powers

[Loren Booda]

What generalizations can be made concerning fractals of nonzero rational dimensions M/N (where M and N are nonzero integers)?

How does a fractal of non-integral dimension F compare geometrically to a fractal of dimension GF, where G is a nonzero integer?

 

[Loren Booda]

In the first paragraph, I was concerned with a fractal space that could be raised to the integer Nth power to obtain a whole number dimensional space.

Similarly, in the second paragraph, I wondered about the geometry of an "axis" of fractal dimension F extended to G axes to produce a GF fractal dimensional space, or moreso, comparing the geometry of int[GF] dimensional spaces of int[GF] axes for G=1, 2, 3... .

 

[Ben-CS]

Believe the Serpinski gasket has a fractal dimension of exactly two.

 

[rdt2]

Originally posted by Ben-CS
Believe the Serpinski gasket has a fractal dimension of exactly two.

no - triangle has a dimension of 1.58. Carpet has a dimension of 1.89.

If its dimension was 2 it wouln't be a fractal.

Cheers,

ron.

Can't help with the earlier Q.