
(1) 
where

(2) 
is the box size, and is the Natural Measure. If , then

(3) 
The Capacity Dimension (a.k.a. Box Counting Dimension) is given by ,

(4) 
If all s are equal, then the Capacity Dimension is obtained for any . The Information Dimension
is defined by
But

(6) 
so use L'Hospital's Rule

(7) 
Therefore,

(8) 
is called the Correlation Dimension. The dimensions satisfy

(9) 
See also Fractal Dimension
© 19969 Eric W. Weisstein
19990525