Soft Cell Geometry

On the left are the geometrically correct contours of a nautilus shell simulated on a computer, and on the right is the actual shape of the cell compared to the simulated one. In nature, the cells in a nautilus shell have a more complex shape than the algorithm shows (this is partly due to Darwinian variability), but they still lend themselves to the described tiling.

Soft cells correlate well with polygon tessellations by combinatorial equivalence. If you imagine a paved surface as a flexible and plastic rubber mat, then it is obvious that it will not tear under the influence of various elastic deformations. In this case, the shape and curvature of the lines and the degree measure of the angles will change significantly, but from a topological point of view the surface will not change (adjacent areas will remain adjacent, non-adjacent areas will remain non-adjacent). In accordance with the geometry described by Domokosh’s group, it is combinatorial equivalence that makes it possible to give convexity to the faces and curvature to the edges without disturbing the general arrangement of figures on the plane. Here we find an analogy between the formation of living cells and the formation of vesicles – generally unsurprising, since coacervatesprobable cell precursors, were stable droplets of a biochemical solution. Notice what samples of frozen foam structures look like:

Apparently, it is soft cells that are the first building blocks of biological forms and show that the geometry of living forms must be fundamentally different from the geometry of nonliving ones. The concept of soft cells makes it possible to explain not only the static shape of biological tissues, but also the growth, healing and ontogenesis of organisms. For example, it is the biology of soft cells that makes it possible to describe the development of plant roots or the formation of biological fractals, for example, Romanesco cabbage.

In conclusion of this article, let me remind you of another of my publications, “TESSERAE – the prehistory of the orbital hive.” In it, I described the project of a gradually expanding space station, the modules of which are built from figures similar in shape to a dodecahedron or fullerenes. Notice how similar the station images from that article are to the structure of the polyhedra modeling the foam bubbles in the illustration above. It can be assumed that the geometry systematized by Domokosh’s group describes the growth of not only living, but also artificial soft cells. Like nautilus chambers, they may have corners in cross-section but not on the surface. If we algorithmize the growth of soft cells on a macro- and world-scale, this can solve the problem of airtightness in space and under water, as well as implement new methods for self-healing of materials and arbitrary changes in shape depending on the available free space.