๐Ÿ”ฎ UNNS Many-Faces Theorem Explorer

Interactive exploration of Unbounded Nested Number Sequences across multiple mathematical domains

Welcome to the UNNS Explorer

๐Ÿš€ Getting Started

The UNNS framework unifies various linear recurrence sequences through a common mathematical substrate. Each tab explores a different "face" of the theorem.

  • Start with the Attractor Visualizer to see geometric patterns
  • Explore prime distributions in sequences
  • Analyze entropy and randomness properties
  • Discover mappings between sequences

๐Ÿ“š Theoretical Background

The Many-Faces Theorem states that UNNS systems can:

  1. Embed any linear recurrence
  2. Generate dominant-root attractors
  3. Partition into modular domains
  4. Support cross-domain homomorphisms
  5. Achieve computational completeness

๐ŸŽฏ Key Sequences

This tool implements four classical sequences:

  • Fibonacci: F(n) = F(n-1) + F(n-2), ratio โ†’ ฯ† โ‰ˆ 1.618
  • Pell: P(n) = 2P(n-1) + P(n-2), ratio โ†’ 1+โˆš2 โ‰ˆ 2.414
  • Tribonacci: T(n) = T(n-1) + T(n-2) + T(n-3), ratio โ†’ โ‰ˆ 1.839
  • Padovan: P(n) = P(n-2) + P(n-3), ratio โ†’ โ‰ˆ 1.325

๐ŸŒ€ Attractor Visualizer

๐Ÿ”ข Prime Analysis Module

๐Ÿ“Š Entropy & Randomness Analyzer

๐Ÿ”„ Cross-Sequence Mappings

๐Ÿ” Sequence Detector Module

๐Ÿ“ Proof Explorer

Fibonacci Embedding

Click to explore the proof that Fibonacci sequences are embeddable in UNNS

Pell Convergence

Click to explore the Pell sequence convergence proof

Tribonacci Properties

Click to explore Tribonacci sequence properties

General Theorem

Click to explore the general Many-Faces Theorem

๐ŸŽญ Interactive Faces Map

Click on different regions to explore the many faces of UNNS