I Let 20 Fractals Draw Themselves (And It's Hypnotising)

One simple rule, repeated over and over. Every line is replaced by a smaller copy of the whole pattern, and step by step you get snowflakes, dragons, space-filling curves and trees. It ends with a fern made of 300,000 dots, drawn by pure chance. The pen plays notes as it draws (the higher it is, the higher the note), every new step rings a bell, and each fractal finishes with a chord. No talking, no sudden sounds: put it on to relax, study, focus or fall asleep. CHAPTERS 0:00 The Koch Curve 0:19 The Koch Snowflake 0:39 The Cesaro Fractal 0:58 The Sierpinski Arrowhead 1:23 The Dragon Curve 2:02 The Levy C Curve 2:41 The Hilbert Curve 3:03 The Peano Curve 3:17 The Gosper Curve 3:34 The Quadratic Koch Island 3:48 The Minkowski Sausage 4:02 The Terdragon 4:29 The Moore Curve 4:49 The Sierpinski Square Curve 5:06 The Crystal 5:22 The Quadratic Koch Curve 5:42 The Fractal Plant 6:04 The Fractal Tree 6:21 The Binary Tree 6:51 The Barnsley Fern HOW IT WORKS Each fractal (except the fern) is an L-system: a starting shape plus one replacement rule. "Iteration" in the top corner counts how many times the rule has been applied. The Barnsley fern is different: each dot jumps to a new spot chosen at random from four rules, and the fern appears on its own. Which fractal was your favourite? Tell me in the comments. #fractals #math #mathematics #recursion #geometry #satisfying #relaxing #stem #science