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

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

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🎛️ 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.

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🔧 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)

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🧪 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] }
}

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🌀 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

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🧭 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.

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Don’t just analyze the grid — inhabit it.