Fractional Dimensions

[Asymptote]

I have in the past read a bit about fractal geometry, and I'm familiar with the idea of fractal dimensions that are non-integers (i.e., the dimension of the Sierpinski Triangle is - log(3)/log(1/2) = 1.585...).

In view of this, I was wondering if anybody happened to know if the fractional part actually represents some sort of unusual dimension, or if it's just a mathematical byproduct of the fractal geometry.

[pat]

AFAIK, the fractional part of the dimension doesn't have any direct geometric significance except for comparison. Something with dimensions 1.585... is more like a two-dimensionsal thing that something with dimension 1.321...

I'm pretty sure they don't map nicely either across different integer parts... something with dimensions 1.585... isn't to 1-D and 2-D what something 2.585... is to 2-D and 3-D.

[wendy]

The fractal dimension has little to do with the real euclidean space.

The concept is to do with 'dimensional analysis' of metrology, where one associates L, M, T with unit length, mass, time. One derives, eg charge as (LM)^2, and resistance as L/T etc.

In fractal things, the linear property increases exponentially as the length is decreased: a measure in inches is not 12 times that in feet, but say 16 times. and so forth.

[Asymptote]

All right, thanks. That's about what I'd expected.