Wishing you mathemagical holidays

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
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)

                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
                And a heaven in a wild flower,
                Hold infinity in the palm of your hand
                And eternity in an hour.

                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.

--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