21 Fractal Analysis and Programming of Elastic Systems …
313
Fig. 21.3 CCM pattern in the first iteration step, n = 1: a 1/r = 3, N = 2, b 1/r = 5, N = 3, c 1/r =
4, N = 2
Fig. 21.4 Integration of CCM with a box-counting method
1. Determine curve via boxes covered it.
2. Cover the element of a curve along one of the axe by boxes.
3. Define the sizes of maximal and minimal boxes.
4. The repeatable boxes on one axe do not take part in counting: They are skipped
and marked by cross.
Definition 3 Let N be the number of boxes calculated by function n: (δ, max ) → N,
where ε max is a maximal box size, and ε min is a minimal box size that contains at
least one element of the curve δ and ordered along axes. If
d u = lim
ε max →ε min
log(n(δ, ε max ))
log(1/ε max )
(21.4)
exists, then the limit is called the box-counting dimension of δ and is denoted by d u .
313
Fig. 21.3 CCM pattern in the first iteration step, n = 1: a 1/r = 3, N = 2, b 1/r = 5, N = 3, c 1/r =
4, N = 2
Fig. 21.4 Integration of CCM with a box-counting method
1. Determine curve via boxes covered it.
2. Cover the element of a curve along one of the axe by boxes.
3. Define the sizes of maximal and minimal boxes.
4. The repeatable boxes on one axe do not take part in counting: They are skipped
and marked by cross.
Definition 3 Let N be the number of boxes calculated by function n: (δ, max ) → N,
where ε max is a maximal box size, and ε min is a minimal box size that contains at
least one element of the curve δ and ordered along axes. If
d u = lim
ε max →ε min
log(n(δ, ε max ))
log(1/ε max )
(21.4)
exists, then the limit is called the box-counting dimension of δ and is denoted by d u .