# a mathematical attempt to simulate some of the properties that cells have

Michael Thudén michael.thuden at chello.se
Tue Feb 10 23:11:50 EST 2004

```I sent a post for some years ago to this group. From time to time I get e-mails from people that want to access the broken  link to my site (they have apparently searched for "binary sphere" or something similar on google groups and this group appear). In any case : here is the new link http://members.chello.se/rocker/bin/eindex.htm

And here is an excerpt from the introduction:

This is an attempt to simulate some of the properties that cells have. That is NOT to say that this is the way cells work. Cells are extremely complexed and can not be reduced into something as simple as this presentation. A human consists of about 100 trillions of cells all originating from one single cell. The cells manage, some how, to adhere to each other and form our bodies. How this coordination is achieved is by most parts unknown. How do the cells organize their interior parts (another construction of complexity that is truly amazing)? How can cells communicate with each other? How can the cell read the code of DNA and know where in the cell the instructions shall be executed ? Is there's perhaps a map in the DNA code pointing out places in the cells coordinate system? If so, how is this coordinate system of the cell formed and how could such a coordinate system evolved? How can cells have a memory?
We want to think that we humans are logical beings (this is really questionable), but how can cells do logical operations? How can cells count (cancer cells seems to have lost part of this ability)? If DNA contain all information for an organism how can this discrete code controll and regulate all these things? The questions are many and the answers few. We are far from understanding even the very basic nature of the cell. The cell is probably the most complicated construction ever built.

The cells complexity must, however, have been evolved from a very simple construction that through evolution got more and more complexed. This presentation can be seen as an attempt to show how very basic "building block" could be fit together and form a "lattice" that could be used in such construction. But I do stress that this by NO means prove that the cell evolved or works in this manner. It is merely a way to show that complexity can evolve from a very simple starting point. This presentation can perhaps contribute to a discussion on how such structures can evolve.

The presentation is a simple geometrical binary model that can do arithmetic, (the division and multiplication are clumsy, but I wanted to show that it works), represent Boolean logical functions (corresponding to subsets in binary-trees), and be used as a memory. The system also has the ability to be used as a binary coordinate system, meaning that arithmetic, Boolean logical functions and memory can be used in a plane or space context regarding different positions. A discrete code (such as DNA) can easily navigate, handle logical expressions, count and/or store memories in this system.
The system can be expanded into a three dimensional binary-sphere that have some remarkable 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 a equatorial-plane perpendicular to the two poles. A biological cell also divides starting from the equatorial-plane perpendicular to its poles. 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 adhering divided binary-spheres to each other. It's easy to make a "genetic" discrete code that generates radial, spherical and/or 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). Bilateral, spherical and radial symmetries are very common in biological structures.
The interior of the binary sphere is also unambiguously binary defined and can serve as a a internal coordinate system (cytoskeleton) .

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