PROOFS

The editions

Mathematics, demonstrated.

Collection · 6 editions · 2026

Design · Music · Interactive

Tools · Claude Opus 5.5 · Nano Banana Pro · JavaScript/WebGL2 · Python

A proof is a trial print. A proof is also a demonstration.

Each PROOFS edition begins as exact mathematics written in JavaScript, then crosses into other mediums. The same equations are heard as sound, pictured as an imagined object, set as an editorial print and cut into a film. The six pieces also run as live interactive code.

The code render supplies the reference for each generated object image. Sand on steel, marble and brass, cloisonné, engraved crystal, travertine and a brass harmonic machine give the equations different material settings. These objects have not been fabricated.

Edition 001

Resonance

Each resonance leaves its own figure in the sand.

Mathematics: Chladni figures: u = cos nπx cos mπy + cos mπx cos nπy
The proof inside it: 1,048,576 grains find the nodal lines; f = (196/34)(n² + m²) Hz
Imagined object: Sand on blackened steel

Thin white curves form four repeating lobed patterns on a black ground. — Code edition

Pale sand forms four lobed patterns around a central fixing on a dark steel plate. — Object edition

Compare Resonance: code and object editions

Edition 002

Aperiodic

Order that never repeats.

Mathematics: Penrose rhombus tiling by Robinson-triangle deflation
The proof inside it: thick : thin → φ live; ten-fold diffraction of its own vertices
Imagined object: Marble and brass floor

Small green, cream and gold geometric tiles form an irregular star pattern. — Code edition

Sunlight through tall columns crosses a green-and-cream geometric marble floor. — Object edition

Compare Aperiodic: code and object editions

Edition 003

Limit

Infinity, held in a circle.

Mathematics: The {7,3} tiling of the hyperbolic plane, Poincaré disk
The proof inside it: loops on an exact symmetry: a translation of 2(s + R + r) = 2.89815
Imagined object: Cloisonné charger

Blue and green circles of diminishing size fill a circular gold-edged pattern on black. — Code edition

A gold-rimmed blue and green cloisonné charger is filled with nested circular motifs. — Object edition

Compare Limit: code and object editions

Edition 004

Tempest

Two paths, a billionth apart.

Mathematics: The Lorenz attractor, σ = 10, ρ = 28, β = 8/3
The proof inside it: two float64 paths 10⁻⁹ apart separate at t = 22.46
Imagined object: Laser-engraved crystal

Fine white trajectories form two sweeping wings against a black ground. — Code edition

A wing-shaped cloud of white lines is engraved inside a clear crystal block on a dark base. — Object edition

Compare Tempest: code and object editions

Edition 005

Morphogen

How pattern begins.

Mathematics: Gray–Scott reaction–diffusion seeded only with the AD-5 mark
The proof inside it: the mark survives as a change of (F, k): spots inside, labyrinth outside
Imagined object: Carved travertine

Dense gray winding lines and small dots form a maze-like pattern on cream. — Code edition

Winding grooves and small pits form a maze-like pattern in a warm stone surface. — Object edition

Compare Morphogen: code and object editions

Edition 006

Epicycle

Any closed curve is a sum of circles.

Mathematics: The AD-5 glyphs as a Fourier series of 401 circles
The proof inside it: the score's left/right channels draw the mark on an XY oscilloscope
Imagined object: Brass harmonic machine