
The graphic should be doing its best to bear to you a gift of
a mathematical snowflake.
The snowflake, or rather increasingly accurate
approximations to it - was born (or invented or discovered
by Niels von Koch) around 1904. It's birth was announced in 1906
(i.e., publication
date). And, quite appropriate for a snowflake, it's
Swedish.
I can't help it - (very) short math lesson
Also wishing you infinity
this season
(perhaps in the form of a real snowflake in your hand?):
To see a world in a grain of sand
William Blake, from Auguries of innocence
The
lettering was created using Bezier curves (lots
and lots and lots of piece-wise cubic polynomials).
The lettering and Koch snowflake were created using
Mathematica. The graphic is copyleft Kreminski, 2003. Press
reload, and the graphic should load
much more quickly.
Previous year's cards:
2002
and
2001
Start first with a triangle; then, on each side, add a smaller
triangle - one that's 1/9th the area or the original.
Then, on each side of the new figure (...there are now 12 sides...),
add a still
smaller triangle one ninth the area of the smaller triangles;
i.e., 1/81th (or is that 1/81st??)
the area of the original. And so on.
Ad infinitum.
In the limit, the Koch snowflake has infinite length
(infinte perimeter).
It also isn't one-dimensional, like an ordinary
hexagon or a circle ... or like I tend to be...
it's a bit more interesting: it's
1.261859-dimensional (more precisely,
that's
log4/log3)
And a heaven in a wild flower,
Hold infinity in the palm of your hand
And eternity in an hour.

--Anne, Amelia, Ben, and Chris - and Rick - the blame is mine
(and the cats
and hamsters and birds and fish and hermit crabs)
--December, 2003