Measuring Fractal Dimension ?
Tue Jun 16 14:22:46 EDT 2009
Lawrence D'Oliveiro <ldo at geek-central.gen.new_zealand> writes:
> I don't think any countable set, even a countably-infinite set, can have a
> fractal dimension. It's got to be uncountably infinite, and therefore
I think the idea is you assume uniform continuity of the set (as
expressed by a parametrized curve). That should let you approximate
the fractal dimension.
As for countability, remember that the reals are a separable metric
space, so the value of a continuous function any dense subset of the
reals (e.g. on the rationals, which are countable) completely
determines the function, iirc.
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