Ga Visualization

ga-visualization

Render geometric algebra elements as interactive SVG/WebGL graphics

Version: 1.0.0
Trit: +1 (PLUS - generative output)

Overview

ganja.js provides a powerful graph() function that automatically renders:

• 1D functions → Canvas line plots
• 2D functions → Canvas heatmaps
• PGA2D elements → SVG points/lines
• PGA3D elements → WebGL 3D scenes
• CGA elements → Circles, spheres (OPNS/IPNS)

The graph() Function

// From ganja.js lines 781-1000
static graph(f, options) {
  // Detect mode from input
  if (typeof f === 'function' && f.length === 1) return graphCanvas1D(f);
  if (typeof f === 'function' && f.length === 2) return graphCanvas2D(f);
  if (Array.isArray(f) || f instanceof Function) return graphSVG(f);
  // ...
}

Rendering Modes

1. 1D Functions

Algebra(0).graph(x => Math.sin(x * 5));
// Renders sine wave on canvas

2. 2D Functions (Heatmaps)

Algebra(0).graph((x, y) => x * x + y * y);
// Renders radial gradient

3. PGA2D Elements (SVG)

Algebra(2,0,1, () => {
  var point = (x,y) => 1e12 - x*1e01 + y*1e02;
  var A = point(-1, 0), B = point(1, 0.5);
  
  return this.graph([
    0xFF0000,           // Color (red)
    A, "Point A",       // Point with label
    B, "Point B",
    A & B, "Line AB",   // Vee product = join
    [A, B],             // Line segment
  ], {grid: true});
});

4. PGA3D Elements (WebGL)

Algebra(3,0,1, () => {
  var point = (x,y,z) => 1e123 - x*1e023 + y*1e013 - z*1e012;
  var origin = 1e123;
  
  return this.graph([
    0x00FF00, origin, "Origin",
    0xFF0000, point(1, 0, 0), "X",
    0x0000FF, point(0, 1, 0), "Y",
  ], {gl: true, camera: 1 + 0.5*1e01});
});

5. CGA (Conformal) Elements

Algebra(4,1, () => {
  // Conformal embedding
  var ni = 1e4 + 1e5, no = 0.5*(1e5 - 1e4);
  var point = (x,y,z) => no + x*1e1 + y*1e2 + z*1e3 + 0.5*(x*x+y*y+z*z)*ni;
  
  // Circle through 3 points
  var A = point(0,0,0), B = point(1,0,0), C = point(0,1,0);
  var circle = A ^ B ^ C;
  
  return this.graph([circle], {conformal: true, gl: true});
});

Interactive Features

Draggable Points

Points in 2D PGA can be made draggable:

this.graph([
  A, B, C,  // Users can drag these
  () => A & B,  // Dynamic line updates when points move
], {animate: true});

Animation

Lambda expressions are re-evaluated each frame:

this.graph([
  () => {
    var t = Date.now() * 0.001;
    return rotor(t, 1e12) >>> point(1, 0);
  }
], {animate: true});

Graph Options

Color Encoding for GF(3)

Map trits to colors for visual debugging:

const tritColors = {
  '-1': 0xFF5555,  // MINUS: Red
  '0':  0x55FF55,  // ERGODIC: Green  
  '+1': 0x5555FF   // PLUS: Blue
};

function colorByTrit(element) {
  var trit = computeTrit(element);
  return tritColors[trit];
}

this.graph([
  colorByTrit(A), A,
  colorByTrit(B), B,
  colorByTrit(A & B), A & B,
]);

SVG Element Types

From the wedge game CSS:

WebGL Rendering Pipeline

Elements → Project to 3D → Build mesh → Vertex shader → Fragment shader → Canvas

Sphere Tracing (OPNS)

For implicit surfaces defined by null vectors:

// From ganja.js graphGL2() 
// Sphere traces the distance function defined by the algebra

Integration with Gay.jl Coloring

using Gay

function visualize_with_colors(elements, seed=1069)
    Gay.seed!(seed)
    colors = [Gay.color_at(i) for i in 1:length(elements)]
    
    # Export to ganja.js format
    js_array = map(zip(colors, elements)) do (c, e)
        "0x$(c[2:end]), $(element_to_js(e))"
    end
    
    return "this.graph([$(join(js_array, ", "))])"
end

GF(3) Triads

ga-visualization (+1) ⊗ ganja-wedge-game (+1) ⊗ three-match (-1) → need -1
→ Add: sheaf-cohomology (-1) ⊗ ga-visualization (+1) ⊗ gay-mcp (+1) → need -1

Commands

# Start coffeeshop examples server
npx serve node_modules/ganja.js/examples

# Open specific example
open https://enkimute.github.io/ganja.js/examples/coffeeshop.html#pga3d_icosahedron

# Generate SVG from CLI
node -e "var A=require('ganja.js'); console.log(A(2,0,1,function(){
  return this.graph([1e12, 1e1, 1e2]).outerHTML;
})())"

Files

• Renderer: lib/ga_renderer.js
• Color mapping: lib/gf3_colors.js
• Examples: examples/visualization_gallery.html

References

• ganja.js coffeeshop
• ganja.js graph() source
• bivector.net tutorials

Autopoietic Marginalia

The interaction IS the skill improving itself.

Every use of this skill is an opportunity for worlding:

• MEMORY (-1): Record what was learned
• REMEMBERING (0): Connect patterns to other skills
• WORLDING (+1): Evolve the skill based on use

Add Interaction Exemplars here as the skill is used.

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