Measuring Fractal Dimension ?

David C. Ullrich ullrich at
Thu Jun 18 14:16:06 EDT 2009

On Wed, 17 Jun 2009 14:50:28 +1200, Lawrence D'Oliveiro
<ldo at geek-central.gen.new_zealand> wrote:

>In message <7x63ew3uo9.fsf at>,  wrote:
>> 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
>>> uncomputable.
>> 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.
>Fractals are, by definition, not uniform in that sense.

Sorry if I've already posted half of this - having troubles hitting
the toushpad on this little machine by accident.

The fractal in question is a curve in R^2. By definition that
means it is a continuous function from [a,b] to R^2 (with
the same value at the two endpoints). Hence it's
uniformly continuous.

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