Mandelbrot, Mobius, Mirth

Image via Wikipedia

In their tributes to the Father of Fractals, Benoit Mandelbroit (recently deceased), several sites have done posts on "infinite coastlines." One of the related notions that I've always found mind-blowing is that of a closed border or perimeter having INFINITE length, yet enclosing a region of FINITE area (very counter-intuitive!). The Koch Snowflake is probably the most oft-used example of this (though there are any number of other possible cases).
Most of you are likely well-familiar with it, but if not, or if you need a refresher, a couple of the many sites expounding on it:

http://www.cut-the-knot.org/WhatIs/Infinity/Length-Area.shtml

http://en.wikipedia.org/wiki/Koch_snowflake

p.s... here's another one of those video zooms of the Mandelbrot Set, magnified 10^214 e.214. The poster himself calls it "mathematical porn"!:

http://vimeo.com/1908224

Further memorializing the recently-deceased, Ivars Peterson reports on yet another oddball Mobius-band trick passed along to him by Martin Gardner some years ago:

http://tinyurl.com/3484lyg

And to end the week with some chuckles, re-visit this old caption-writing contest from WildAboutMath blog, if you missed it the first time:

http://tinyurl.com/2atzumj