My name is Michael Thudén and I'm an inventor (not a real mathematican or
biologist) but I think I have stumbled across something that might be of
interest. It's a simple symmetrical geometrical binary model that can do
arithmetic, (the division and multiplication are clumsy, but I wanted to
show that it works), represent Boolean functions (corresponding to subsets
in binary-trees), and express some sort of memory.
I think you can skip these parts about Boolean functions, arithmetic and
memory (or read it later) if you want to save some time.
The system also has the ability to be used as a binary coordinate system,
meaning that arithmetic, Boolean function and memory can be used in a plane
or space context regarding different positions. The system can be expanded
into a three dimensional binary-sphere that have some remarkable symmetrical
properties (beside those described above) corresponding to biological cells.
For example: the binary-sphere can only be divided symmetrically into two
binary-spheres starting from an equatorial-plane perpendicular to the two
poles. A biological cell alsodivides starting from the equatorial plane
perpendicular to its poles (see
metaphase plate in mitosis). The two "new" binary-spheres will consist of
one half from the "old" binary-sphere and a new constructed half, exactly as
in a biological cell where one half of the "new" cell is from the "old" cell
and the second half is "new".
Further more: the binary-sphere can use the "binary-coordinate" system in
assembling divided binary-spheres to each other (can it be used in DLA
simulations?). It's easy to make a
"genetic" binary code that generates radial, spherical and bilateral
symmetries (the binary sphere is by itself bilateral). To make bilateral
symmetries it's even possible to use the same code for the left and right
side (there's no need to have a separate code for each side).
The interior of the binary-sphere also have a compartments that can be
binary described (and perhaps be used as a simulated cytoskeleton?).
So if you think this sounds interesting go to my site
http://members01.chello.se/rocker/telia/bin/eindex.htm and check it out.
This is a pure mathematical approach and though it's been a while since I
studied math at university the math is stable according to some "real"
mathematicians that's been checking it out.
I hope that you find the reading interesting, in spite of my poor English.
I'm grateful for all constructive criticism, which also include the