Thursday, 18 August 2011

The Jerusalem Cube

jerusalem Cube
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.

Friday, 5 August 2011

Tony Bomford's Hyperbolic Rugs

Tony Bomford (1927-2003) made a series of hooked rugs based on the Coxeter/M.C. Escher hyperbolic tiling patterns. He started the series in 1981.

You can find a useful biography and listing of the rugs (and further discussion) on Doug Dunham's pages as a series of PDF files (e.g. ).