01 Mandelbrot Set
Color each point c by how long the dance z → z² + c stays small. The points that never run away form the famous bug-shaped frontier.
02 Julia Set
Same rule z → z² + c, but now c is fixed and we color the starting point. Slide the seed and watch the shape morph from blobs to dust.
03 Sierpinski Triangle
The chaos game: drop a dot, then keep jumping halfway toward a random corner. From pure randomness a perfect fractal triangle appears.
04 Lissajous Curve
Two waves at right angles: x = sin(a·t), y = sin(b·t + φ). The ratio of a to b draws looping knots and ribbons.
05 Ulam Prime Spiral
Wind the counting numbers 1, 2, 3… into a square spiral and light up the primes. Mysteriously, they line up along diagonal streaks.
06 Golden Spiral
Plant each seed a turn of 137.5° (the golden angle) from the last, stepping outward. That single rule packs a sunflower’s perfect spiral head.
07 Logistic Bifurcation
Repeat x → r·x·(1−x) and plot where it settles. As r grows the answer splits, splits again, then dissolves into chaos.
08 Rose Curve
Polar petals from r = cos(k·θ). Connect equally-spaced points with straight lines (a Maurer rose) and woven lace appears.