The Cantor Rainbow

Every surviving exponent carries its ternary history d₁d₂…dₖ, digits 0 or 1 only — the 2s are what burned. Read that history as a ternary fraction x = 0.d₁d₂…dₖ and each survivor owns one band of a single spectrum: sound, then the jump to c, then light as seen, then the wavelengths not seen. Each stroke splits every band in three; the top third goes dark — that is the burn, the colour break — and its exhaust rings down. The bands that remain are a Cantor set, dimension log 2 / log 3.

the ringdown · this stroke's burns, one damped wave each

the spectrum · one row per stroke · bright = survives · dark = burned

Jesse Daniel Brown (OP-JESSE) — the design: a gradiated wave, sound first, then the speed of light, the colours as seen, then the wavelengths not seen; the brakes are the colour breaks, and the predictors belong to the colour they were born in (Book of Laws, voice-07, turns 676–680).
Every survivor, burn and band edge is computed with exact integers (BigInt) over complete residue systems; numbers become colour and sound only at the last step. The burned child's new digit is always 2; which of its three lifts burns, j = 0, 1, 2, varies from parent to parent and is fixed by the parent's own next ternary digit d: j = (2 − d) mod 3. Colour and pitch come from each band's position on the spectrum; the ringdown is a sonification of the burns. Receipt: python rainbow_check.py. Prior work on the underlying tree: Narkiewicz (1980), Lagarias (2009), Saye (2022) — see the README.