Visualisations

Interactive tools for exploring the Gap Geometry framework. Each tool makes a different aspect of the Binary Tower and its structure directly observable.

Interactive Tools

All tools run entirely in the browser — no server, no dependencies, no data collection. They are self-contained HTML files hosted on GitHub Pages.
KAUD Dashboard
Dashboard

The main interactive dashboard for the Gap Geometry framework. Displays the core constants G and KAUD, the Binary Tower step structure, and key landmarks in a single navigable interface. This is the entry point for hands-on exploration of the framework.

What it shows: Core constants, step-by-step tower values, prime corridor positions, Landauer crossing region, and the π/3 hinge.
Open KAUD Dashboard →
Telescope Tower
Visual

A visual instrument for zooming into the Binary Tower at arbitrary depth. Step through the tower level by level, observe how the gap constant G manifests at each scale, and inspect the structural landmarks up close. Designed to make the tower’s recursive geometry directly visible.

What it shows: The (1/2)n staircase structure, G-scaled residuals at each step, and the visual rhythm of the tower as it descends through the prime corridor.
Open Telescope Tower →
The Corridor Sonifier
Audio

Translates the Coherence Corridor and the Binary Tower into sound. Four sections: (I) the Coherence Corridor from floor 1/φ ≈ 0.618 to ceiling KAUD ≈ 0.980, with position mapped to tone; (II) the 64-step Binary Tower with landmarks glowing at canonical structural positions — step 18 (√2/4, Shell 3), 32 (√φ/2, k=5 target), 35 (ln 2, Landauer crossing), 36 (1/√2, geometric-damping threshold), 37 (1/(2·ln 2), Shannon bound), 50 (KAUD ceiling), 64 (√φ pivot); (III) the Blues interval connection between log₂(9/7) and the corridor width; (IV) the 2% Gap between KAUD and unity. A different way of perceiving the framework — sometimes the ear catches what the eye misses.

What it sounds like: The Coherence Corridor as a continuous tone sweep; the Binary Tower as 64 discrete steps with landmark glows; the half-diminished seventh chord 5:6:7:9 containing the corridor as the 9/7 interval.
Open Corridor Sonifier →
Chladni Staircase
Visual

Renders the Binary Tower as a Chladni-style vibration pattern. The tower’s step structure is mapped to a 2D resonance field, revealing nodal lines and symmetry that correspond to the framework’s structural claims. The visual analogy to Chladni plates is deliberate: the tower’s structure emerges the way a physical resonance pattern does — not imposed, but revealed.

What it shows: Nodal patterns corresponding to tower landmarks, with the prime corridor visible as a structural backbone in the vibration field.
Open Chladni Staircase →

About These Tools

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 built as a single self-contained HTML file with no external dependencies, so it can be downloaded, inspected, and run offline.

The tools evolve alongside the framework. As new structures are identified and verified, new visualisations may be added. The Living Document tracks the current state of the framework; this page tracks the current state of its interactive instruments.

Source

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