Archive for April 24th, 2008

Two dimensions and beyond (or at least between)

April 24, 2008

I fear that this will be a shaggy dog post. One of my students posed an interesting question the other day, and I found myself surprised by the answer. So here’s the quick version of today’s post: What’s the dimension of a tetrix? A tetrix is also known as a Sierpinski tetrahedron, and indeed it is like a three-dimensional version of the Sierpinski triangle, except that, being a fractal, its dimension is less than three. There’s a picture below (which I think of as upside-down), and also a cool java applet version here which you can spin around. Click for cool pictures of a tetrix and other fractals, as well as an explanation for what fractal dimension means.

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