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| Jerusalem Cube |
The Jerusalem Cube fractal is a little odd. Although it
seems simple enough — it's just a cube repeatedly penetrated by crosses — for it to work
properly, the ratios of the cube and sub-cubes don't have whole-number integer, or even
fractional integer ratios. We're talking irrational numbers, here, and while you might expect irrationals to show up when you're assembling shapes at funny angles, in this case, they appear when we connect simple cubey blocks together, face-to-face.
It can't be built using a simple integer grid, and that's probably why you probably haven't come across it before. Where the
Menger Sponge can be visualised as the result of applying discrete logic within a simple "base three" number system, the
Jerusalem Square and
Jerusalem Cube correspond to the same sorts of orderly processes being performed on number systems that aren't based on integers.
