A simple rule, repeated - and the universe builds itself.
Look closely at a fern. Each leaf is a smaller copy of the whole frond. Zoom into that leaf, and each leaflet repeats the same shape again. This is self-similarity - the signature of a fractal.
Nature doesn't design from blueprints. It gives a simple instruction, repeats it at every scale, and lets complexity emerge.
Four affine transformations, chosen at random with weighted probabilities. Each point is born from the previous one - and yet a perfect fern appears. The algorithm of every frond that ever unfurled.
move the mouse to stir the windThe same principle that shapes a fern also sculpts one of the most extraordinary vegetables on Earth. The romanesco arranges its buds in Fibonacci spirals, and each bud is a perfect miniature of the whole.
Fractals you can eat.
Golden angle phyllotaxis - 137.508° - distributes each floret without overlap. Each one is a recursive copy of the whole, spirals within spirals, down to the smallest bud.
move the mouse to shift the lightFractals don't only grow slowly. Sometimes they explode into existence - in milliseconds. When lightning searches for the path of least resistance, it branches recursively through the atmosphere.
Each fork is a smaller version of the main bolt.
Recursive branching through the atmosphere. The main channel forks, and each fork forks again - probability decreasing, thickness thinning, until the charge dissipates into the finest filaments.
click to summon a boltSome fractals are born from pure geometry. Take a triangle. Replace each edge with a smaller triangle. Repeat forever. The Koch snowflake has infinite perimeter trapped inside a finite area.
A paradox that mirrors the crystalline symmetry of real snowflakes.
Start with a triangle. Subdivide each edge into four. Repeat six times. The perimeter grows toward infinity while the area barely changes - geometry at the edge of reason.
hover to illuminate the edgesAnd then there are fractals that grow with you. The nautilus adds a new chamber to its shell as it grows - each one slightly larger than the last, following a logarithmic spiral.
The golden ratio, made habitable.
A logarithmic spiral where each chamber is roughly 1.618 times larger than the last. The animal builds its home by following one rule - grow, seal, repeat - and a masterpiece of geometry emerges.
hover to reveal the chambers