Fractal dimension
From Encyclopedia of Mathematics
A, possibly non-integer valued, dimension concept. Let be a metric space and a bounded subset. For each let be the minimal number of balls of radius necessary to cover . Then
is the fractal dimension of . It has also been called the capacity, the Mandelbrot dimension or the Shnirel'man–Kolmogorov dimension of .
One has
If denotes the Hausdorff dimension of , then .
References
[a1] | B.B. Mandelbrot, "Form, chance and dimension" , Freeman (1977) |
How to Cite This Entry:
Fractal dimension. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fractal_dimension&oldid=11902
Fractal dimension. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fractal_dimension&oldid=11902