I call this shape the careenium. I borrowed this name from Douglas Hofstadter, who wrote a wonderful book called Metamagical Themas in which there is an essay on the possible ‘appearance’ of consciousness on the neuron level of the brain entitled “Who Shoves Whom Around in the Careenium?” Hofstadter loves his words: ‘careenium’ is a play on ‘cranium’.

I designed this shape to serve as the basis for a piece of music called Careenium, which is an unfinished work for percussion quartet. Turned 90? clockwise and slightly modified, it also serves as the background for this site.

Imagine, if you will, a ball bouncing around inside this shape. It always bounces at a 45 degree angle to any wall. Every time it hits a wall, a note is sounded. Every time it hits a corner, however, it ’slips through’ into another part of the careenium while simultaneously, it is reflected back and reverses its original course, almost like a quantum particle splitting. Got it? No? Don’t worry about it. That’s the basis of the piece, and even if you don’t get it on reading, you may get it on hearing a bit of it here:

The shape also reflects my general obsession with number series and geometry, in this case the series of primes. In one corner you’ll see a rectangle 1×2, in the next a 2×3 rectangle, and so on. Continue this pattern out to 17×19, and you get the overall pattern. (There is, in fact, one error in the series which yields a 17×17 square, but that is a result of the orientation of the shape, or rather, what corner I started out with. It’s unimportant anyway, since the result (i.e. the music) is promising.) One can be too much a slave to order, even in circumstances like this!