
Sierpinski Gasket

formulas: sierpinski


Another pre-Mandelbrot classic, this one found by W. Sierpinski around
World War I. It is generated by dividing a triangle into four congruent
smaller triangles, doing the same to each of them, and so on, yea, even
unto infinity. (Notice how hard we try to avoid reiterating "iterating"?)

If you think of the interior triangles as "holes", they occupy more and
more of the total area, while the "solid" portion becomes as hopelessly
fragile as that gasket you HAD to remove without damaging it -- you
remember, that Sunday afternoon when all the parts stores were closed?
There's a three-dimensional equivalent using nested tetrahedrons instead
of triangles, but it generates too much pyramid power to be safely
unleashed yet.

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