Visualisations

Interactive instruments of the Gap Geometry framework. The papers prove; these make the structure directly observable. Every preview below is the live instrument itself — click any window to enter it.

Interactive Instruments

All tools run entirely in the browser — no server, no data collection, nothing tracked. Most are single self-contained HTML files; the Dashboard and the Chladni explorer additionally load their rendering library (React) from a public CDN, so they need an internet connection on first view. All source is readable in the files themselves. Click a preview to open the instrument in place (Esc returns here), or use the full-page link on each card.
The Binary Tower
Entrance

Start here. What the tower is, what KAUD is, what it computes and why the Gap matters — explained from the ground up, with a hands-on widget: type any number and watch the rungs of its binary recipe light. Exact arithmetic (no float rounding), true periods, true 96-bit expansions for the framework constants, and a compare mode where relations between numbers become shapes.

loading live preview…
Live
▶  Enter
What it shows: The binary-recipe ladder (rung n holds (1/2)n) — distinct from the framework’s G-staircase, and the page explains the difference. Lit rungs are arithmetic, never significance.
Anchored in: the framework overview (About) and the evidence-label discipline of the Methodology.
Open full page ↗
KAUD Dashboard
Dashboard

The main interactive dashboard. Core constants G and KAUD, the Binary Tower step structure, and key landmarks in one navigable interface — the entry point for hands-on exploration.

loading live preview…
Live
▶  Enter
What it shows: Five tabs — Dynamics (α-coupling presets), the 64-step Tower, Scaling (the 2k·G ladder against its golden targets, constant ε = −0.671% by construction), the 400/11 three-term residual, and the Architecture view of constants and identities. All values computed live in the page.
Anchored in: the framework overview (About) and the Living Document.
Open full page ↗
Telescope Tower
Visual

Feed it any dimensionless ratio — a mass ratio, a coupling, a number you are curious about — and it reports where that number lives on the G-staircase: nearest step, exact deviation, and any landmark in the neighbourhood. The instrument’s discipline is the framework’s: the deviation is always stated.

loading live preview…
Live
▶  Enter
What it shows: The G-staircase (steps = multiples of G = 1 − √2·ln 2): feed it any dimensionless ratio and it reports the nearest step n = round(value/G), the deviation, and landmark proximity — always with the deviation stated.
What it makes visible: the integer staircase of Papers 3 and 8 — the same tower that telescopes the dome: ∑k≥0 g(2kx) = 1 − tanh(x).
Open full page ↗
The Corridor Sonifier
Audio

The Coherence Corridor and the Binary Tower, translated into sound. Corridor position as tone; the 64-step tower with landmarks glowing at canonical positions; the Blues interval connection; the 2% Gap. Sometimes the ear catches what the eye misses. (Audio starts only inside the instrument, on your click — previews stay silent.)

loading live preview…
Live
▶  Enter
What it sounds like: The corridor as a continuous tone sweep from 1/φ to KAUD; the tower as 64 discrete steps with landmark glows; the half-diminished seventh 5:6:7:9 holding the corridor as the 9/7 interval.
What it makes audible: the corridor floor and ceiling of Papers 1–2, the tower landmarks at steps 18 · 32 · 35 · 36 · 37 · 50 · 64.
Open full page ↗
Chladni Staircase
Visual

The Binary Tower as a Chladni-style vibration pattern: step structure mapped to a 2D resonance field, nodal lines and symmetry emerging the way a physical resonance pattern does — not imposed, but revealed.

loading live preview…
Live
▶  Enter
What it shows: Free-free plate modes (real Euler-Bernoulli eigenvalues, Ritz basis), just-intonation frequency ratios including the Blues 9/7, and the tower landmarks as a declared display mapping on the resonance field.
What it makes visible: the tower’s landmark structure (Paper 3) as resonance geometry.
Open full page ↗

About These Instruments

These visualisations are companion instruments to the published documents. They do not replace the formal work — they make aspects of it directly explorable. Each tool is a single HTML file whose full source — physics, constants, and mappings — is readable in the file itself. Most run offline once downloaded; the Dashboard and the Chladni explorer load their rendering library (React) from a public CDN and therefore need a connection on first view.

The tools evolve alongside the framework. The Living Document tracks the current state of the framework; this page tracks the current state of its instruments.

Source

All tool source code is in the main repository:
github.com/Gap-geometry/sqrt2-ln2-geometric-constants-