| For self-similar fractals such as the Koch curve and the
Sierpinski gasket, the box-counting dimension is easiest to compute if the
box sizes are taken to be powers of the scaling factor, 1/3 for the Koch
curve and 1/2 for the Sierpinski gasket. |
| For example, we observed the gasket can be
covered with 3n boxes of side length 1/2n,
so the box-counting dimension computation is |
| db |
= limn → ∞Log(3n)/Log((2n)) |
| = limn → ∞(nLog(3))/(nLog(2)) |
|
= Log(3)/Log(2). |
|
| Note n cancels out of the computation. This is not an accident, but a
consequence of the self-similar scaling. |
| This observation can be exploited to simplify the computation
of the dimension, in the case of self-similar fractals. |