Measuring Fractal Dimension ?
charles at declareSub.com
Sat Jun 20 19:36:01 EDT 2009
On Jun 18, 2009, at 2:21 PM, David C. Ullrich wrote:
> On Wed, 17 Jun 2009 05:46:22 -0700 (PDT), Mark Dickinson
> <dickinsm at gmail.com> wrote:
>> On Jun 17, 1:26 pm, Jaime Fernandez del Rio <jaime.f... at gmail.com>
>>> On Wed, Jun 17, 2009 at 1:52 PM, Mark
>>> Dickinson<dicki... at gmail.com> wrote:
>>>> Maybe James is thinking of the standard theorem
>>>> that says that if a sequence of continuous functions
>>>> on an interval converges uniformly then its limit
>>>> is continuous?
>> s/James/Jaime. Apologies.
>>> P.S. The snowflake curve, on the other hand, is uniformly
>>> continuous, right?
>> Yes, at least in the sense that it can be parametrized
>> by a uniformly continuous function from [0, 1] to the
>> Euclidean plane. I'm not sure that it makes a priori
>> sense to describe the curve itself (thought of simply
>> as a subset of the plane) as uniformly continuous.
> As long as people are throwing around all this math stuff:
> Officially, by definition a curve _is_ a parametrization.
> Ie, a curve in the plane _is_ a continuous function from
> an interval to the plane, and a subset of the plane is
> not a curve.
> Officially, anyway.
This simply isn't true.
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