Measuring Fractal Dimension ?

[David C. Ullrich]

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 ruckus.brouhaha.com>,  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.

I won't ask where I can find this definition. That Koch thing is a
closed curve in R^2. That means _by definition_ that it is a
continuous function from [0,1] to R^2 (with the same value
at the endpoints). And any continuous fu