释义 |
q-Dimension
| (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 Dimensionis 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
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