The following graphic is of a 3-D Fractal based on the Mean Proportional Geodesic. These forms, although they have the recursive self similiarity of conventional fractals, do not appear on first observation to have any chaos factor. Any randomness of pattern seems to be based on the energy level at creation. The molecular architecture of living matter seems to follows such a radial propagation as shown. The molecular architecture of non living matter seems to follows the architecture of the closer packed planar octet type of arrangement. The Mean proportional Geodesic consist of 12 molecules surrounding a mother molecule of a proportional larger size of Tau. The mother molecule is not included in this graphic. This graphic was first posted on 6/5/97 by rlc.
The following graphic is of a 3D Fractal octet truss arrangement with a golden section packing inset which has a u(n+1)=u(n) +1 unidirectional size progression if the outer chord of the octahedron is considered as 1. The inset "golden section" packing can be again fractalized in a 1:Tau(squared) progression as shown in the preceeding graphic. The graphic can be expanded to become a fractal image of a tetrahedron but was not done so in this case. All 12 basic Platonic elements along with the 5 Platonic solids can be presented as 3D fractals by using a combination of the elements.
Hypothesis I: My hypothesis is that the fundamental elements of Plato; earth, water, air & fire refer to the internal geometrical structure of what we now refer to as quarks and leptons. Not that Plato understood his teachings which he obtained from the Egypians, but the Egyptians priest themselves probably didn't understand what had been passed down to them. I feel that by understanding the underlaying structure of matter which is mirrored in a macromolecular way, one can do such things as disassociate water molecules with a minimum of energy expended by simply knowing the internodal distances and determining the harmonic frequencies required to break the bonds. This in the future could be a cheap source of energy.
Hypothesis II: I propose that the molecule C-60 is not based on the architecture of the Bucky Ball as is now the commonly thought, but that it is based on the mean proportional geodesic. The difference between the two, being that the Bucky Ball is an Icosahedron truncated at the 1/3 distances from the vertices, while the mean proportion is a truncated at the 1/Tau(squared) mark.