Date: Fri, 26 Apr 2013 13:17:04 -0400 From: Warren D Smith <warren.wds@gmail.com>
This way of doing things focuses attention on the "critical exponents" which in 3D and 2D (we have shown nonrigorously) are <=2 and <=1.585 respectively; improvements versus Euler/Clausen/Keller's 7/3=2.3333 and 2 respectively. Can these exponents be shrunk by using better fractals? Can they be justified rigorously?
I don't know but Bucky Fuller's notion of "tensegrity" is structures built out of members that are only being used purely for tension or purely for compression, on the theory that otherwise, the material isn't being used efficiently. He described tensegrity "masts" which are columns built in this way. The basic design looks like tetrahedra in stacked cubical cells... with none of the compression members touching. In some of the designs the struts have balls at their ends. Of course, solid or even tubular compression struts have the same inefficiency, so... "The concept that tensegrity is fractal, at different orders of magnitude, was often discussed by Fuller in his lectures." http://tensegrity.wikispaces.com/Mast Nice examples given there: the interior structure of bone, and the way the spine is held straight by muscle tension between projections from the vertebrae. This piece http://www.unisa.it/uploads/4760/course.pdf has some math about minimizing weight for a given strength and number of parts. Those two urls were the first two google hits for "fractal tensegrity column"; googling "tensegrity mast" gives pics and videos near the top. --Steve