6 Simple Rules That Build Infinite Shapes

Six famous fractals, built step by step from the simple rule behind each one, then followed into an endless zoom. 0:00 Koch Snowflake 1:09 Sierpiński Triangle 2:22 Dragon Curve 3:28 Barnsley Fern 4:33 Pythagoras Tree 5:28 Menger Sponge 6:22 Outro Koch Snowflake (Helge von Koch, 1904): split each line in 3, add a bump. Sierpiński Triangle (Wacław Sierpiński, 1915): remove the middle, or pick a random corner and jump halfway. Dragon Curve (Heighway, Harter & Banks, 1960s): fold a strip in half again and again, then unfold. Barnsley Fern (Michael Barnsley, 1988): four rules, picked at random. Pythagoras Tree (Albert E. Bosman, 1942): two smaller squares at a right angle, and in 3D, two cubes turned a quarter. Menger Sponge (Karl Menger, 1926): cut a cube into 27 and remove the 7 middles. No narration. Every picture is computed, not drawn by hand.