Jerusalem Menger CubeInspired by Robert Dickau
Graphics by Paul Bourke
Unlike the traditional Menger sponge this variation had irrational scaling on each iteration. If the zero'th iteration, a cube, is of unit 1 then the 8 corners of the Jerusalem Cube are cubes of side length sqrt(2)-1. The 12 smaller units are cubes of side length (sqrt(2)-1)2. This is the general scaling law to iterate from the n-1 iteration to the n'th iteration, noting (sqrt(2)-1) + (sqrt(2)-1)2 + (sqrt(2)-1) = 1.
Another way to imagine the construction is to repeatedly remove (negative extrusion) Greek crosses from the faces of a cube. Note the Greek crosses at each scale pass right through the final Jerusalem cube.
On each iteration the number of geometric primitives increases by a factor of 20, the same as the traditional Menger sponge. The compression ratio is sqrt(2)-1, the fractal dimension is 2.529 ...
Level 7 (Click for higher resolution)
Sample PovRay file: scene.pov
Interactive virtual model.