Measuring Fractal Dimension ?

Mark Dickinson dickinsm at gmail.com
Wed Jun 17 14:46:22 CEST 2009


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.

Mark



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