On Mon, Aug 4, 2008 at 3:01 PM, James Propp <jpropp@cs.uml.edu> wrote:
Is there any reason to think that this sequence of orientations of the ball should converge to some particular orientation in the configuration space of the ball (where we mod out by translation --- all we care about is rotation --- so we're really looking at the configuration space of a sphere)?
This seems easy - since the limit of the length is infinite, you could only get a fixed point as you go from level n to n+1 if there's some very nice (rational) relationship between the size of the ball and the length of the level n snowflake. In other words, I think the answer to all your questions are "no, it doesn't make sense to talk about rolling a ball on a fractal". Am I missing something obvious? --Joshua Zucker