Snowflake of ice. At that stage, the snowflake has the shape of a minute hexagon. The six "arms" of the snowflake, or dendrites, then grow independently from each of the corners of the hexagon, while either side of each arm grows independently. The microenvironment in which the snowflake grows changes dynamically as the snowflake falls through the cloud and tiny changes in temperature and humidity affect the way in which water molecules attach to the snowflake. Since the micro-environment (and its changes) are very nearly identical around the snowflake, each arm tends to grow in nearly the same way. However, being
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