Hausdorff dimension is easy to calculate for simple objects like the Sierpinski gasket or a Koch curve. Each of these may be covered with a collection of scaled-down copies of itself. In fact, in the case of the Sierpinski gasket, one can take the individual triangles in each approximation as balls in the covering. At stage , there are triangles of radius , and so the Hausdorff dimension of the Sierpinski triangle is at most , and it can be shown that it is equal to .
From some notes from Koro
Define the diameter of a bounded subset of to be .
We also define the function
When is a subset of with any norm-induced metric, then this definition reduces to that given above.
|Date of creation||2013-05-18 23:14:26|
|Last modified on||2013-05-18 23:14:26|
|Last modified by||unlord (1)|