Measuring Fractal Dimension ?

[Charles Yeomans]

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>
>> wrote:
>>> 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.

Charles Yeomans