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SNOWFLAKES AND GLACIERS. "In regular ice, like you have in your freezer -- hexagonal type 1, the formation of water molecules is not as open as in snow. It's more tightly packed, as if you folded a flat hexagon in a weird way. And joined those together in a tighter formation. This structure is more dense and stronger than a snowflake structure." http://www.dailykos.com/story/2009/11/15/804812/- View in LinkedIn

CLUSTER FORMATION. "Multicellular C. reinhardtii display a novel two-stage life cycle in which motile unicellular propagules disperse shortly after transfer to fresh medium, then undergo successive rounds of mitosis to form nonmotile, multicellular clusters bound by an extracellular matrix." https://lnkd.in/dU8HRX5 View in LinkedIn

ITERATIVE HEXAGONS. "Different temperatures create different patterns, but they are all based on hexagonal geometry. These many different forms have become named things like: fernlike, dendritic, stellar, plate, columnar." http://thesmarthappyproject.com/hexagon-geometry-snowflake/ View in LinkedIn

SHORT TIME. "Using experimental evolution, we find that simple algal multicellularity can arise in as little as 219 days in a species that has never had a multicellular ancestor." https://lnkd.in/dU8HRX5 View in LinkedIn

"A HEXAGONAL PLATE is the beginning of every snowflake, as it grows the water available becomes less able to fill all the space and so branches and tendrils appear always on a six fold pattern which are what we recognise as traditional looking snowflakes." http://thesmarthappyproject.com/hexagon-geometry-snowflake/ View in LinkedIn

GENERAL ROUTE. "Given the unicellular ancestry of all multicellular organisms, the evolution of a single-cell genetic bottleneck by co-option of the ancestral phenotype may represent a rapid and general route by which this trait can arise." https://lnkd.in/dU8HRX5 View in LinkedIn

THE HEXAGON. "The molecule H2O (water) contains one oxygen and two hydrogen. These two hydrogen atoms sit at an angle in relation to the oxygen which is perfectly the same angle as the corners of a hexagon, so building the lattice structure." http://thesmarthappyproject.com/hexagon-geometry-snowflake/ View in LinkedIn

SO ENDS my homage to Kepler's moment on the Charles Bridge in Prague. The mathematics of tiling tessellations from MC Escher transition through Kepler's snowflake to next weekend's Fragment on the geometry of spider webs. All three captured in a memorable moment on the Charles Bridge on the very anniversary of Kepler's birthday. With a fleck of snow on a black coat. A real treat linking radiant spots in time. View in LinkedIn

"THE KOCH SNOWFLAKE (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described. The progression for the area of the snowflake converges to 8/5 times the area of the original triangle, while the progression for the snowflake's perimeter diverges to infinity. Consequently, the snowflake has a finite area bounded by an infinitely long line." https://en.wikipedia.org/wiki/Koch_snowflake View in LinkedIn

SIMPLICITY BENEATH. "Throughout the natural and artificial world one observes phenomena of great complexity...research in physics and to some extent biology and other fields have shown that the basic components of many systems are quite simple. It is now a crucial problem for many areas of science to elucidate the mathematical mechanisms by which large numbers of such simple components, acting together, can produce behavior of the great complexity observed." https://lnkd.in/dc_82je View in LinkedIn