Evidence for pattern development; hexagons common (Introduction)

by David Turell , Sunday, April 10, 2016, 02:57 (2940 days ago) @ romansh

An article on principles of physics that make hexagons common: - http://nautil.us/issue/35/boundaries/why-nature-prefers-hexagons - "According to William Kirby in 1852, bees are “Heaven-instructed mathematicians.” Charles Darwin wasn't so sure, and he conducted experiments to establish whether bees are able to build perfect honeycombs using nothing but evolved and inherited instincts, as his theory of evolution would imply. - "Why hexagons, though? It's a simple matter of geometry. If you want to pack together cells that are identical in shape and size so that they fill all of a flat plane, only three regular shapes (with all sides and angles identical) will work: equilateral triangles, squares, and hexagons. Of these, hexagonal cells require the least total length of wall, compared with triangles or squares of the same area. So it makes sense that bees would choose hexagons, since making wax costs them energy, and they will want to use up as little as possible—just as builders might want to save on the cost of bricks. This was understood in the 18th century, and Darwin declared that the hexagonal honeycomb is “absolutely perfect in economizing labor and wax.” - *** - "If you blow a layer of bubbles on the surface of water—a so-called “bubble raft”—the bubbles become hexagonal, or almost so. You'll never find a raft of square bubbles: If four bubble walls come together, they instantly rearrange into three-wall junctions with more or less equal angles of 120 degrees between them, like the center of the Mercedes-Benz symbol. - "Evidently there are no agents shaping these rafts as bees do with their combs. All that's guiding the pattern are the laws of physics. Those laws evidently have definite preferences, such as the bias toward three-way junctions of bubble walls. The same is true of more complicated foams. - *** - "Nature is even more concerned about economy than the bees are. Bubbles and soap films are made of water (with a skin of soap molecules) and surface tension pulls at the liquid surface to give it as small an area as possible. That's why raindrops are spherical (more or less) as they fall. - *** - "But those who think (as some do) that the honeycomb is just a solidified bubble raft of soft wax might have trouble explaining how the same hexagonal array of cells is found in the nests of paper wasps, who build not with wax but with chewed-up wads of fibrous wood and plant stem, from which they make a kind of paper. Not only can surface tension have little effect here, but it also seems clear that different types of wasp have different inherited instincts for their architectural designs, which can vary significantly from one species to another. - *** - "The rules of cell shapes in foams also control some of the patterns seen in living cells. Not only does a fly's compound eye show the same hexagonal packing of facets as a bubble raft, but the light-sensitive cells within each of the individual lenses are also clustered in groups of four that look just like soap bubbles. - *** - "The rules of cell shapes in foams also control some of the patterns seen in living cells. Not only does a fly's compound eye show the same hexagonal packing of facets as a bubble raft, but the light-sensitive cells within each of the individual lenses are also clustered in groups of four that look just like soap bubbles. In mutant flies with more than four of these cells per cluster, the arrangements are also more or less identical to those that bubbles would adopt." - Comment: The article goes on to describe diatomes and sponges with these patterns. The benzene ring in organic molecules is a hexagon. Another example of patterns at the basis for building life.