9500 interactive explorations — Iris Compendium Vol. V
Quantum Harmonic Oscillator — Wigner Phase Space
The Wigner function is a quasi-probability distribution on phase space. Coherent states are Gaussian blobs; Fock states show circular fringes; superpositions reveal quantum interference — negative regions forbidden to classical physics.
Gray-Scott Reaction-Diffusion — Turing Morphogenesis
u_t = Du∇²u − uv² + F(1−u), v_t = Dv∇²v + uv² − (F+k)v. Different feed/kill rates produce spots, stripes, corals, and solitons — the chemical basis of biological pattern formation (Turing 1952).
Hyperbolic Tiling — Poincaré Disk {5,4}
In the Poincaré disk model of hyperbolic geometry, geodesics are circular arcs meeting the boundary at right angles. The {5,4} tiling fills the disk with pentagons (5 sides, 4 at each vertex) — impossible in Euclidean space where 5×72°=360° gives exactly flat.
Langton's Ant — Emergent Highway Behavior
Langton's ant follows two rules: turn right on white, left on black, flip color, move forward. After ~10,000 steps of apparent chaos, the ant spontaneously builds a periodic "highway" — order emerging from local disorder.
Double Pendulum — Chaos & Sensitivity
Two double pendula started with a tiny angle difference diverge exponentially — classical chaos, positive Lyapunov exponent. The phase portrait fills densely with chaotic trajectories interspersed with KAM tori at low energy.