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My friend Tamiko Thiel did the brilliant "nested cubes" packaging and design of Thinking Machine's Connection Machine II supercomputer (left). Her design visually reflects that computer's bit-connected fractal architecture. I wondered what such a design would look like if it used a nested-tetrahedral arrangement, rather than nested-cubes.
The applet at right shows a sketch. Each level has four elements, shown in red, green, blue and magenta, respectively. Each element contains four sub-elements, recursively. Each top level element is shown as transparent; the children that surround it are shown as opaque. In this way, every level produces four times as many processors. I've only shown the top two levels (16 processors).
Notice that half the volume at each level is unused. We can use the central region for memory and connectors. Also, to pack the space more efficiently, we could use star-shaped processors. Click here to see how that would look.