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 Koch snowflake 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. It is based on the Koch curve, which appeared in a 1904 paper titled "On a continuous curve without tangents, constructible from elementary geometry" (original French title: "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire") by the Swedish mathematician Helge von Koch. The progression for the area of the snowflake converges to times the area of the original triangle, while the progression for the snowflake's