Amazing Snowflakes

"And it was then that all these kinds of things received their shapes from the Ordering One, through the action of Ideas of Numbers" (Plato: in Timaeus). Indeed, Hamilton's 'Principle of Least Action is mathematical discrimination between inorganic and organic systems. The geometrical progression of organic life has the property of producing by simple addition, a succession of numbers or similar shapes making the homothetic (gnomonic) growth-work by 'imbibition' (outwards). Whereas, inorganic matters (crystals, snowflakes, rocks) grow by 'agglutination' (inwards) and final distribution of energy to cause no further motion. While in inorganic growth (hexagonal), the Principle of Least Action tends to save energy, in gnomonic growth (pentagonal) there is a tendency to save the substance. Involving the avid travelers "father jaguar and the cub," this tourbook of the "snow gallery" mathematically and geometrically analyzes the deposition, aggregation, capacitance, and velocity of the snowflake formation, vis a vis the hexagonal (honeycomb) tendency. When the tour is over, the cub classifies his most favorite snowflakes, giving them names.