Part 9: Visualizer Modes – Prime Fields, Harmonic Maps, and Toroidal Trails

Designing the UI for a generative canvas of structure, symmetry, and scale


🎛️ Visualizer Overview

The PTS Visualizer will be the interactive canvas module that renders both:

  • Structured 3×3 origin-based walks (low-rank, digits visible)
  • High-rank fractal matrices (rank ≥6 rendered as pixel fields)

The user can zoom, scroll, animate, and toggle display modes that reveal latent harmonic structures.


🔧 UI Controls

Core Controls

  • Matrix Rank (n): slider or input (1–8), defines 3ⁿ × 3ⁿ size
  • PTS Source: dropdown to select scale (3PTS, 4PTS, etc)
  • Base Grid: Lo Shu or Pythagorean
  • Rendering Mode:
    • Grid (1–3) → digit tables
    • Tile (4–5) → symbolic blocks
    • Canvas (6+) → pixel render

Visualization Mode

Choose one at a time:

  1. Digit Root Mapping (DRM)
    • 3 → red
    • 6 → green
    • 9 → blue
    • Others → gray/white
  2. Prime Highlight (PFP)
    • Single prime selected (slider or dropdown)
    • Cells with that prime = highlight color
  3. Prime Spectrum Composition (PSC)
    • Hue = prime identity
    • Brightness = exponent (log-scaled)
    • Combined factors = blended hue
  4. Composite Density (Advanced)
    • Brightness = number of prime factors (with multiplicity)
    • High composite = brighter
  5. Walk Phase Animation
    • Animate cells that form each toroidal walk (sequentially or by step phase)

Hover Tooltip

  • Value
  • Prime factorization
  • Digit root
  • Walk origin/direction (if applicable)

🧪 Behind the Scenes (Pluggable Modules)

Each cell:

  • Is precomputed once per matrix
  • Stores value, digit root, prime factor vector
  • Encodes data as an object for rendering logic

Example:

{
  value: 333,
  root: 9,
  factors: { 3: 2, 37: 1 },
  walk: { origin: [2,1], direction: [-1,0] }
}

🌀 Future Additions

  • Audio Mode: map walk values to tones
  • Export Mode: save canvas as PNG, download JSON of matrix
  • Custom Walk Editor: drag-path to define custom harmonics
  • Tiling Explorer: see how subgrids mirror across the full field

🧭 First Module Recommendation

Start with:

  • Rank = 3 (81×81 grid)
  • Visualization = Digit Root Mapping
  • Mode = Grid/Tile
  • Animate by direction

Use this as an onboarding interface for seeing harmony emerge visually before diving into prime soup or full-rank canvas maps.


Don’t just analyze the grid — inhabit it.

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