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THE NOTHING TREATISE ON A SNOWFLAKE. "Lacking the necessary funds to buy an appropriate Christmas gift for a friend, Kepler decided to write the essay on the snowflake. After all, he asked rhetorically, what do astronomers and mathematicians "who have Nothing and receive Nothing" have to give, but Nothing?" http://www.keplersdiscovery.com/SixCornered.html View in LinkedIn

SERIOUS SNOWFLAKE MATHEMATICS. How Kepler's "nothing" could demand such deep thinking to solve. Take a block of ice for this journey. https://lnkd.in/d6pKQyK View in LinkedIn

ON SNOWFLAKES AND VIRUS GEOMETRY, a ride on the wild side. Take a pinch of salt for this journey. https://lnkd.in/deFn7Te View in LinkedIn

TILING SHAPES. "Fibonacci snowflakes are somehow related to the Fibonacci fractals. They also form a subclass of tiles used for tiling the plane." https://lnkd.in/desvnVq View in LinkedIn

COMPLEMENTARY SHAPES. "Very cold? We get columns. Cold and high humidity? Dendrites. Cold and medium humidity? Sectored plates. Still, none of this explains how two separate arms can form complementary patterns." Nice graph of temperature vs form. http://www.itsokaytobesmart.com/post/72704847892/youve-watched-this-weeks-video-on-the-science View in LinkedIn

HALF TRUTH. "Snow crystals usually aren’t completely symmetrical. Instead, they are quite irregular and lumpy, full of conglomerations and corrections. The hexagonal crystal structure holds up in all cases, but the sort of perfect fractal sculpture you’ve been led to believe defines a snowflake? It’s a half-truth, at best." https://lnkd.in/dTbpCSB View in LinkedIn

RARE SYMMETRY. "If you think this is hard to swallow, let me assure you that the vast majority of snow crystals are not very symmetrical. Don't be fooled by the pictures -- irregular crystals (see the Guide to Snowflakes) are by far the most common type. If you don't believe me, just take a look for yourself next time it snows. Near-perfect, symmetrical snow crystals are fun to look at, but they are not common." https://lnkd.in/dhNbMdR View in LinkedIn

DIVERSIFIED OPTIONS. "The reasoning is straightforward: epigenetic factors permit a single cell line with a given genotype to express many different phenotypes on which natural selection might act, thereby providing a competitive advantage through diversification." https://lnkd.in/dTS7dFy View in LinkedIn

CITRATE EXAMPLE. "An excellent example is the evolution of citrate catabolism in E. coli (a highly beneficial trait) in 1 out of 12 experimental populations after 31,500 generations of evolution in citrate-containing medium. No citrate utilization occurred in the other 11 populations, even after 8,000 further generations of selection. Even though E. coli was unlikely to evolve the ability to use citrate, this selection experiment clearly shows that the possibility existed." https://lnkd.in/dU8HRX5 View in LinkedIn

INFORMATION IS SELECTIVE ADVANTAGE. "Such a vast jump in the potential information content of single cells is believed to have led to a dramatic selective advantage in unicellular populations capable of epigenetic regulation and inheritance." https://lnkd.in/dTS7dFy View in LinkedIn