Snowflake unlikely that any two snowflakes are alike due to the estimated 10 (10 quintillion) water molecules which make up a typical snowflake, which grow at different rates and in different patterns depending on the changing temperature and humidity within the atmosphere that the snowflake falls through on its way to the ground. Snowflakes that look identical, but may vary at the molecular level, have been grown under controlled conditions. Although snowflakes are never completely symmetrical, a non-aggregated snowflake often grows so as to exhibit an approximation of six-fold radial symmetry. The symmetry gets started due to the hexagonal crystalline structure
Koch snowflake snowflake. After each iteration, the number of sides of the Koch snowflake increases by a factor of 4, so the number of sides after iterations is given by: If the original equilateral triangle has sides of length , the length of each side of the snowflake after iterations is: the perimeter of the snowflake after iterations is: The Koch curve has an infinite length because the total length of the curve increases by a factor of four thirds with each iteration. Each iteration creates four times as many line segments as in the previous iteration, with the length of each