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2025/09/01

UNNS Modular Interpreter System

UNNS MODULAR INTERPRETER

Prime Spiral Renderer × Betti Number Visualizer × Macro System
MACRO DEFINITIONS
Prime Spiral
Betti Numbers
Combined
INTERPRETER OUTPUT
> UNNS Modular Interpreter v2.0 initialized > Modules loaded: PRIME_SPIRAL, BETTI_VISUALIZER > Ready for macro interpretation...
Active Macros 0
Prime Count 0
Betti Sum 0
Euler Char 0
PRIME SPIRAL RENDERER
Max N: 1000
Density: 5
BETTI NUMBER VISUALIZER
Dimension: 3
Complexity: 5
COMBINED UNNS TRANSFORMATION

 A fully modular UNNS Interpreter System with pluggable Prime Spiral Renderer and Betti Number Visualizer modules that integrate seamlessly with the macro system. 

Here's what makes this special:

🎯 Key Features:

1. Modular Architecture:

  • PrimeSpiralModule - Standalone module for Ulam spiral visualization
  • BettiNumberModule - Independent topology visualizer
  • CombinedModule - Orchestrates multiple modules together
  • Each module has its own render(), animate(), and stopAnimation() methods

2. Macro System Integration:

JavaScript
@prime_spiral(n, density) {
    render: ulam_spiral;
    max: n;
    density: density;
    color: gradient(prime_count);
}

@betti_compute(dimension, manifold) {
    compute: homology_groups;
    dim: dimension;
    type: manifold;
    visualize: true;
}

@unns_transform(expr) {
    parse: algebraic;
    apply: prime_spiral(42, 0.8);
    overlay: betti_compute(3, torus);
}

3. Prime Spiral Features:

  • Ulam Spiral Pattern - True mathematical spiral layout
  • Prime Detection - Efficient primality testing up to 10,000
  • Density Control - Adjustable visualization density
  • Glow Effects - Visual distinction between primes and composites
  • Rotation Animation - Smooth spiral rotation

4. Betti Number Visualizer:

  • Multiple Manifold Types:
    • Sphere (β₀=1, βₙ=1)
    • Torus (Pascal's triangle pattern)
    • Projective space (alternating pattern)
  • Homology Group Visualization - Nested circles for each dimension
  • Euler Characteristic - Automatic calculation (χ = Σ(-1)ⁱβᵢ)
  • Morphism Connections - Visual links between dimensions

5. Interpreter Features:

  • Macro Parser - Parses custom UNNS macro definitions
  • Macro Executor - Interprets and executes parsed macros
  • Module Dispatcher - Routes commands to appropriate modules
  • Live Logging - Real-time execution feedback
  • Parameter Extraction - Dynamic parameter handling

6. Interactive Controls:

  • Sliders for real-time parameter adjustment
  • Module Switcher for focusing on specific visualizations
  • Animation Controls - Start/stop all animations
  • Keyboard Shortcuts:
    • Ctrl+Enter - Execute macros
    • Ctrl+P - Parse macros
    • Ctrl+R - Render combined

7. Computed Metrics:

  • Active Macro Count - Number of parsed macros
  • Prime Count - Total primes in current spiral
  • Betti Sum - Σβᵢ (total homology rank)
  • Euler Characteristic - Alternating sum of Betti numbers

🔧 How the Modular System Works:

  1. Module Registration:
    JavaScript
    this.modules = {
    primeSpiral: new PrimeSpiralModule(),
    bettiNumbers: new BettiNumberModule(),
    combined: new CombinedModule()
};
  2. Macro Interpretation:
    • Macros are parsed into structured objects
    • Each macro has a name, parameters, and body
    • Nested macros are supported for complex transformations
  3. Execution Pipeline:
    • Parse → Extract Parameters → Dispatch to Module → Render → Update Metrics
  4. Module Communication:
    • Modules can share data through the interpreter
    • Combined module can orchestrate multiple modules
    • Each module maintains its own state

🚀 Extension Points:

The system is designed to be easily extended with new modules:

JavaScript
class NewModule {
    render(ctx, params) { /* rendering logic */ }
    animate(ctx) { /* animation logic */ }
    stopAnimation() { /* cleanup */ }
}

// Register new module
interpreter.modules.newModule = new NewModule();

This modular architecture makes it easy to add new mathematical visualizations (like Mandelbrot sets, Julia sets, cellular automata, etc.) that can all be controlled through the unified macro system!

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