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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

MAJOR TRANSITIONS. "The major evolutionary transitions in the history of life on Earth include the transition from non-coded to coded information (the origin of the genetic code), the transition from prokaryotes to eukaryotes, the transition from protists to multicellular organisms, and the transition from primate groups to linguistic communities." https://lnkd.in/dTS7dFy View in LinkedIn

DRIVING FORCE OF TRANSITIONS. "Here we propose that a transition from bottom-up to top-down causation – mediated by a reversal in the flow of information from lower to higher levels of organization, to that from higher to lower levels of organization – is a driving force for most major evolutionary transitions." https://lnkd.in/dTS7dFy View in LinkedIn

"TOP-DOWN CAUSATION has been suggested to occur at all scales of biological organization as a mechanism for explaining the hierarchy of structure and causation in living systems." https://lnkd.in/dTS7dFy View in LinkedIn