There's a fantastic book on the subject http://www.amazon.com/Patterns-Nature-Peter-S-Stevens/product-reviews/0316813311/ref=dp_top_cm_cr_acr_txt?ie=UTF8&showViewpoints=1
Joanna ----- Original Message ----- You have to ask yourself, how does the universe after the Big Bang learn to incorporate this mathematical sequence into so many parts of itself, from the shape of DNA to spiral galaxies? ----------- That is the wrong question. A better question is how is it that matter and energy together with physical forces produce orangized forms through evolution? There is a basic rule in this game. You have to provide a physical explanation. There is a mathematical-physical answer to why the sunflower forms its seed pods into complex spirals. The phenomenon is also seen in the hexagonal array of some insect nests like honey bees. It's called the closest packing theorem. It means if you want to fill a volumn of space without leaving empty places, you tile it in hexagonal polypeds. Hexagons are not only the regular shape that qualifies. Triangles or tetahedrons are another. These shapes and their 3-d analogues produce further symetries on the plane or in space, from which we see patterns such as the sunflower seed pods or the comb of the bee, or the pine cone. You can study these and many more regular patterns in chemistry and crystallography. The carbon molecule for example is a hexagonal ring. Anyway it's a beautiful video. Below is a youtube link with the video. http://www.etereaestudios.com/docs_html/nbyn_htm/movie_index.htm When it is finished a screen will come up with more. Click on the one labeled mobius revealed. It show the mobius transforms are the symmetries of the surface of a half sphere. CG _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l
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