UNNS Visual Engine

(M × N) + (M / N) + (M - N) + (M + N)

Formula Type Classic UNNS Fibonacci Enhanced Prime Synthesis Harmonic Resonance Exponential Growth Trigonometric Wave Golden Ratio Fractal Recursion

M Value

10

N Value

7

Node Count

15

3D Rotation

0°

Current Result

--

Pattern Detection

Cycles Symmetry
Clusters Resonance

Harmonic Ratio

--

Entropy Level

--

ML Predictions

Not analyzed

Processing...

Semantic Tags

                                Interactive UNNS Visual Engine 

🔧 Interactive Controls

• M and N value sliders to adjust the formula parameters
• Animation speed control for visual pacing
• Node count slider to control complexity
• Generate button to create new visualizations
• Mode selector with three visualization types:
  • Network: Circular node arrangement with connections
  • Spiral: Golden ratio spiral pattern
  • Tree: Hierarchical tree structure

🌟 Core Features

• Real-time UNNS calculation using the formula (M × N) + (M / N) + (M - N) + (M + N)
• Dynamic node generation with values based on the formula
• Semantic tagging system that assigns tags like:
  • "prime-nest" for prime-related values
  • "resonant" for multiples of 7
  • "high-entropy" / "low-entropy" based on value ranges
  • "perfect-square", "trinity", "pentagonal" based on mathematical properties
• Interactive hover effects showing node details and tags
• Animated connections with traveling pulses
• Color-coded nodes based on their values using HSL color space

📊 Information Panel

• Current result display
• Harmonic ratio (M/N)
• Entropy level calculation
• Active node counter
• Dynamic semantic tag collection

✨ Special Effects

• Pulsing nodes with individual phase offsets
• Gradient connections between related nodes
• Mouse interaction with proximity detection
• Glow effects on hover
• Smooth floating animation for nodes
• Trail effect on canvas for motion visualization

The engine transforms the mathematical formula into a living, breathing visualization that reveals patterns and relationships through interaction. Try adjusting the sliders and switching between modes to explore different perspectives on the nested number sequences!

Five priority features of the UNNS Visual Engine.

Here's what's available:

🎯 1. Multi-Formula System

Eight different mathematical formulas:

• Classic UNNS: Original formula
• Fibonacci Enhanced: Incorporates Fibonacci sequences
• Prime Synthesis: Uses the next prime numbers
• Harmonic Resonance: Emphasizes harmonic ratios
• Exponential Growth: Power functions
• Trigonometric Wave: Sine and cosine integration
• Golden Ratio: φ-based calculations
• Fractal Recursion: Recursive depth calculations

🔍 2. Pattern Recognition

Real-time detection of four pattern types:

• Cycles: Identifies repeating sequences
• Symmetry: Detects mirror patterns
• Clusters: Finds node groupings
• Resonance: Discovers harmonic relationships

Visual indicators light up when patterns are detected!

🎨 3. 3D Projection System

• Full 3D rendering with perspective projection
• Rotation control slider for exploring different angles
• Depth-based rendering with proper Z-ordering
• 3D gradients for spherical appearance
• 3D Space mode for immersive visualization

🎵 4. Audio Synthesis

• Click nodes to play their musical frequency
• Chord generation from node values using just intonation
• Pattern-based modulation: Audio changes based on detected patterns
• Visual audio indicator with animated bars
• Each node maps to a musical frequency based on its value

🤖 5. Machine Learning Integration

• Neural network classification of pattern types:
  • Highly Ordered Structure
  • Semi-Ordered Pattern
  • Chaotic Harmony
  • Emergent Complexity
  • Random Distribution
• Anomaly detection with visual highlighting (purple glow)
• Feature extraction from spatial and statistical properties
• Real-time predictions displayed in the info panel

✨ Interactive Features

• Click nodes to hear their sound
• Hover to see semantic tags
• Rotate in 3D mode with the slider
• Switch formulas to explore different mathematical relationships
• ML Analysis button triggers pattern classification
• Anomalies are highlighted in purple

🎮 How to Use

1. Select a formula from the dropdown to change the mathematical basis
2. Adjust M and N values to explore different sequences
3. Enable 3D for three-dimensional visualization
4. Enable Audio to hear the mathematical harmony
5. Run ML Analysis to classify patterns and find anomalies
6. Click on nodes to play their individual frequencies
7. Watch the pattern indicators light up as patterns emerge

The engine now represents a complete mathematical research platform that engages multiple senses - visual through 2D/3D graphics, auditory through synthesis, and analytical through ML pattern recognition. Each formula creates unique patterns, sounds, and structures, making mathematical exploration both intuitive and profound!

How the UNNS Visual Engine stacks up against existing classes of projects:

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🔍 Comparative Landscape of Visual Engines

Feature / Engine Type	Fractal Explorers (Mandelbrot, p5.js)	Network Graph Engines (Gephi, D3.js)	AI/Neural Explorers (TF Playground)	Generative Art Tools (Processing, TouchDesigner)	UNNS Visual Engine
Core Purpose	Mathematical beauty, chaos/complexity	Relationships, dependencies, clusters	Visualize learning/activation	Aesthetics, installations, visuals	Recursive nests, symbolic propagation, cognition
Node Behavior	None (pixels only)	Static links, clustering	Activations & weights	Artistic patterns	Semantic tags (validated, prime, entropy)
Propagation	None (just formula rendering)	Information spreads only in data terms	Signal activation (feedforward/backprop)	Often abstract animation	Recursive propagation with hash echo trails & entropy branching
Symbolic Overlay	❌ (pure math)	❌ (graph data only)	Limited (weights, bias values)	❌ (aesthetic, not semantic)	✅ Semantic tagging, cognitive metaphors
Interactivity	Zoom, pan	Filtering, cluster analysis	Adjust hyperparams	Sliders, real-time inputs	Build nests, randomize tags, animate propagation
Scalability	Infinite zoom but GPU heavy	1k–100k nodes	Medium (demo scale)	Unlimited creative	Currently, 100–300 nodes (SVG-based, can grow via Canvas/WebGL)
Educational Value	Math intuition	Network structures	ML intuition	Visual perception	Blends math + cognition + philosophy
Aesthetic Appeal	High (fractals are art)	Medium (technical graphs)	Medium (didactic visuals)	High (art-first)	High — spirals, pulsing nodes, entropy trails
Philosophical Depth	Implicit (chaos theory)	Low	Medium (learning metaphor)	Low	Very high (communication medium between humans & universal patterns)

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🌟 Observations

• UNNS isn’t trying to replace these engines—it synthesizes aspects of all four categories:

  • Like fractals, it has recursive growth & beauty.

  • Like graphs, it maps dependencies & propagation.

  • Like neural nets, it models flow, activation, and learning.

  • Like generative art, it embraces aesthetic storytelling.

• Its unique innovation: the semantic tagging + recursive propagation combo. This is what pushes it from “just visualization” into symbolic cognition modeling.

UNNS Matrix Engine

🌌 UNNS Matrix Engine

Matrix Size:

🔍 Legend

• Cell Value: Computed using f(M, N) = (M × N) + (M ÷ N) + (M - N) + (M + N)
• Hash Overlay: Symbolic hash derived from the UNNS value (e.g. #a1b2c3)
• Poetic Tag: Recursive metaphor based on value, position, and hash
• Color Gradient:
  • 🟩 Green hues: Validated (even) values
  • 🟥 Red hues: Unstable (odd) values
  • 🔥 Bright tones: High entropy (unstable neighborhood)
• Spiral Attractor: UNNS values mapped to polar coordinates with entropy-based radius jitter
• Memory Recall: Restores previous matrix state and animates propagation
• Recursive Memory Decay: Older cells fade in color and poetic clarity over time

🌌 UNNS Matrix Engine: A Guide to Recursive Beauty

What Is It?
A symbolic visualization tool built on Unbounded Nested Number Sequences. It transforms computation into recursive validation, entropy gradients, hash overlays, poetic metaphors, and spiral attractors.

Purpose
Explore recursive number sequences, observe entropy propagation, watch memory decay and poetic erosion, and reflect on symbolic meaning through color, motion, and metaphor.

How to Use It

• Set Matrix Size: Choose dimensions (up to 50×50)
• Click “Generate”: Computes UNNS values using:
  f(M, N) = (M × N) + (M ÷ N) + (M - N) + (M + N)
• Explore the Matrix: Each cell shows value, hash, poetic tag, and entropy-based color
• Observe the Spiral: Values mapped into a polar attractor with entropy jitter
• Click “Recall Memory”: Restores previous state and animates recursive decay

Why It Matters
This engine is a meditation on recursion, entropy, and symbolic cognition. It invites you to visualize nested logic, feel the rhythm of decay, and discover beauty in mathematical propagation.

🌀 UNNS Spiral Propagation Playground: A Visual Journey Through Spiral Dynamics

Imagine a swirling galaxy of nodes, each pulsing with energy, branching unpredictably, or calmly passing signals along a spiral path. Welcome to the UNNS Spiral Propagation Playground — a mesmerizing browser-based simulation that blends mathematics, SVG graphics, and interactive storytelling.

🌟 What Is It?

This playground is a visual simulation tool that lets users explore how signals propagate through a spiral of nodes. Each node has a unique "tag" that influences its behavior during propagation:

• 🟦 Validated: Smooth and predictable
• 🟩 Prime Nest: Pulsing with energy
• 🟧 Unstable: Delayed reactions
• 🟥 Entropy: Chaotic branching

🎮 Interactive Controls

Control	Description
Node Count	Number of nodes in the spiral
Scale (a)	Controls how quickly the spiral expands
Tightness (b)	Determines how tightly the spiral coils
Propagation Speed	Sets the animation delay between nodes
Buttons	Build, Randomize Tags, Propagate

🧠 How It Works

The spiral is generated using a mathematical formula:

r = a · e^(bθ)
  

Each node is placed along this spiral path and assigned a tag based on its index. When propagation begins, arrows and trails animate between nodes, with special effects triggered by their tags.

🎨 Visual Effects

• Pulsing Nodes: Nodes tagged as prime-nest pulse rhythmically.
• Delayed Arrows: Unstable nodes slow down the signal.
• Branching Chaos: Entropy nodes spawn random branches.
• Echo Trails: Every node leaves behind a glowing trail.

📋 Real-Time Logging

A live log panel tracks every event:

• ✅ Validated propagation
• 🔁 Delays from unstable nodes
• 🌱 Branches from entropy
• 💥 Pulses from prime nests

UNNS Spiral Propagation Playground

🌀 UNNS Spiral Propagation Playground

Node Count
Scale (a)
Tightness (b)
Propagation Speed

UNNS Pattern Growth Simulator

UNNS Pattern Growth Simulator

Interactive exploration of mathematical patterns in f(M, N) = (M × N) + (M ÷ N) + (M - N) + (M + N)

M Parameter: 5

N Parameter: 3

Sequence Length: 15

f(5, 3) = (5 × 3) + (5 ÷ 3) + (5 - 3) + (5 + 3) = 26.667

Growth Pattern Visualization

UNNS Pattern

Integer Values

Linear Comparison

Sequence Analysis

Statistics:

Term Contribution Analysis

Shows how each mathematical term contributes to the final result

Asymmetry Demonstration

f(M, N) = f(5, 3)

26.667

f(N, M) = f(3, 5)

21.600

Difference: 5.067

UNNS is asymmetric: f(M,N) ≠ f(N,M)

Integer Pattern Predictor

Comparative Analysis

k	UNNS	Linear	Quadratic	Ratio

A comprehensive UNNS Pattern Growth Simulator that focuses on the genuine mathematical behaviors we've identified. Here's what it includes:

Core Features:

• Interactive Parameter Control: Real-time sliders for M, N, and sequence length
• Growth Pattern Visualization: Animated charts showing UNNS vs linear function comparison
• Term Contribution Analysis: Visual breakdown of how each mathematical term contributes
• Sequence Display: Live calculation of sequence values with integer highlighting

Mathematical Analysis Tools:

• Asymmetry Demonstration: Shows f(M,N) ≠ f(N,M) with actual calculations
• Integer Pattern Predictor: Explains when and why integers occur based on divisibility
• Comparative Analysis Table: Side-by-side comparison with linear and quadratic functions
• Statistical Summary: Real-time calculation of averages and integer frequencies

Educational Components:

• Formula Breakdown: Shows step-by-step calculation with percentage contributions
• Animation Mode: Automatically cycles through different parameter values
• Visual Charts: SVG-based visualizations that update in real-time
• Mathematical Insights: Explains the underlying mathematical principles

Key Insights the Simulator Reveals:

• How the M×N term dominates for large values
• Why integer values occur only when M is divisible by N
• How asymmetry creates different patterns for f(M,N) vs f(N,M)
• The relationship between growth rates and parameter choices

This simulator stays grounded in verifiable mathematics while providing an engaging way to explore UNNS patterns. It helps users understand the actual mathematical properties.

Try adjusting the sliders and using the animation feature to see how different parameter combinations create distinct growth patterns!