How it works
Begin with an equilateral triangle. Divide each edge into three equal parts. Replace the middle part with two sides of a new equilateral triangle pointing outward. Apply the same replacement to every new segment.
Where it began
Swedish mathematician Helge von Koch described his curve in 1904. It gave a geometric example of a continuous curve without a tangent anywhere. Joining three copies around an equilateral triangle produces the familiar snowflake.