Measuring Fractal Dimension ?

[David C. Ullrich]

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.


>Mark