From: utzoo!decvax!yale-com!leichter
Newsgroups: net.physics
Title: Re: A Mathematical Question
Article-I.D.: yale-com.1059
Posted: Sat Mar 12 13:32:33 1983
Received: Sun Mar 13 08:34:14 1983
References: tekecs.612

The Question was:  What's the maximum shoreline a lake, all of whose water is
inside a 1/pi radius circle, can have?  (I paraphrased, but I think this is
the intent.)

The answer is:  Unless you put some restrictions on what the shoreline can be,
there is NO maximum; you can get as large a shoreline as you like.  Any space-
filling curve, in fact, will give you an infinite shoreline, I think - although
I'm not sure (space-filling curves may not have definable arclengths, in which
case the "length of the shoreline" is meaningless.)  You can probably build
shorelines of any finite lengths using the constructions in fractal geometry.

A couple of years back, there was an article giving the algorithms in "Software-
Practice and Experience".  For their first year or so, they had a column of
"Computations Recreations" (or something like that) by "Aleph 0".  One of their
articles gave programs that would plot (approximations to) space-filling
curves.  (If you are interested, it should be pretty easy to find - S-P&E was
a quarterly then, and the column only ran for about 2 years or so.)
							-- Jerry
						decvax!yale-comix!leichter