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.

Very beautiful !

ReplyDeleteI tred to do the 2D version and I wiould name it the swiss carpet.

see : http://www.mathcurve.com/fractals/sierpinski/suisse3.gif

Do the numbers 5,364,480 in ratio to 144 have anything to do with the Jerusalem cube model that you created?

ReplyDeleteReally cool piece, thanks for posting it.