archetype.boo

Germination

Every form in nature begins as a seed -- a compact instruction set encoding infinite possibility. An archetype is the mathematical seed underlying all visible pattern: the branching rule that generates both river deltas and lung bronchi, the spiral equation that shapes both galaxies and nautilus shells, the tessellation logic that tiles both crystal lattices and honeycomb walls.

Here, we cultivate these seeds. We plant simple rules in computational soil and watch as complexity emerges -- not designed, but grown. Each archetype is a generative grammar, a recipe for form that has been rediscovered independently by every civilization that has ever looked closely at the natural world.

Explore the seed

Taxonomy of Form

The Spiral

Where growth remembers its origin, turning always toward the light it cannot reach.

divergence: 137.508° | ratio: 1.618 | decay: 0.92

The Tree

A single axiom repeated, branching into a canopy of self-similar whispers.

angle: 25.7° | generations: 6 | ratio: 0.68

The Crystal

Order without repetition -- an infinite puzzle that never completes, never contradicts.

tiling: penrose | symmetry: 5-fold | inflation: 1.618

The Wave

Energy moving through matter, the shape of transmission without transportation.

frequency: 0.04 | amplitude: 80 | harmonics: 5

The Territory

Where influence meets influence, boundaries crystallize from invisible forces.

sites: 32 | metric: euclidean | lloyd: 3

The Reaction

Two substances, locked in chemical dialogue, painting patterns no hand could draw.

diffusion: 0.082 | feed: 0.062 | kill: 0.061

The Flow

Paths of least resistance, carved by persistence into the topology of the possible.

particles: 200 | noise: perlin | scale: 0.005

The Fractal

Self-similarity at every scale -- the coastline, the fern, the infinite in the finite.

iterations: 5 | scale: 0.5 | rotation: 60°

All patterns converge
in the substrate of being

From the simplest seed, the most intricate tapestry. From the same equations, the leaf and the galaxy. The archetypes are not inventions but discoveries -- the mathematical bones of reality, unearthed by computation, fired in the kiln of iteration.