Sierpinski carpet

This is a test post to see what’s involved in uploading images.

This is of course the Sierpinski carpet. What’s interesting to me is that many objects that, in a previous age dominated by a picture of the physical world as a continuum, seemed deeply pathological, have straightforward computer-language descriptions. For example, you can check whether or not a point in the plane is on the Sierpinksi plane by looking at the ternary expansion of its coordinates, which is a couple of lines of computer code. From the point of view of the computer, the Sierpinksi carpet is not much more complicated than a parabola. I suspect that the popularity of fractals marks a change in the popular imagination of the dominant metaphor for mathematics, from mathematics as mechanics to mathematics as computer program.