UNNS VISUAL ENGINE
Substrate Instrument Guide
What this instrument is: UNNS Visual Engine is a substrate instrument for exploring operator-driven recursion in UNNS (Unbounded Nested Number Sequences). It does not "predict physics"; it produces UNNS-internal structure diagnostics.
The Workflow
1. Pick Seed (M) and Parameter (N)
2. Choose an Operator Stack (Φ, Ψ, τ, XII)
3. Choose a Projection (2D / τ-Geometry 3D / Collapse View)
4. Optionally start τ-Flow to evolve the state over time
5. Read the Invariant Diagnostics and Structure Classification
6. Export JSON to preserve a run or τ-flow history
Controls
Seed (M)
Sets the initial value of the recursion. Changing M changes the entire sequence and its invariants.
Parameter (N)
Controls Φ expansion intensity (how strongly Φ generates new values each application).
Node Count
Controls how many nodes are rendered (visual sampling). It does not change the underlying recursion—only the visualization density.
Operator Stack
Each operator can be toggled on/off. Operator order matters strongly—this is why commutativity is tracked as an invariant.
Φ Generate: Expands the sequence through recursive growth. Creates new values from existing structure.
Ψ Normalize: Constrains values into a stable range. Enforces consistency and prevents unbounded growth.
τ Curvature: Applies damping and curvature to the sequence. Creates stability through compression.
XII Collapse: Filters survivors based on threshold. Reality-enforcement stage that removes weak values.
Tip: Operator order matters. That is why "commutativity" is tracked. Φ→Ψ→τ→XII produces different results than XII→τ→Ψ→Φ.
Projections
2D Abstract
A clean view of the graph structure. Shows nodes and connections in their base layout.
τ-Geometry 3D
A projection where depth (z-axis) encodes τ-pressure. This is not physical 3D space; it is a substrate projection showing curvature geometry. During τ-Flow, this projection becomes dynamic—nodes flow along τ-gradients and depth changes with evolving curvature.
Collapse View
Shows only post-XII survivors, with post-collapse reorganization. If the view looks "empty", that means collapse was strong—most values failed to survive the threshold.
τ-Flow (Evolution)
τ-Flow evolves the state over time by iteratively applying the operator stack. This is temporal recursion, not visualization animation.
Use τ-Flow to observe:
- Phase transitions: emergence → stable → overcurved → collapse
- Topology changes: node births/deaths, edge rewiring
- Invariant drift: how metrics stabilize or diverge over time
- Structural irreversibility: two runs with same seed diverge under τ-noise
τ-Flow Phases
| Phase |
Condition |
Behavior |
| Emergence |
τ-stability < 0.7 |
Φ operator active, nodes spawn, rapid growth |
| Stable |
0.7 ≤ τ-stability ≤ 1.2 |
Ψ and τ active, balanced damping |
| Overcurved |
τ-stability > 1.2 |
Excessive curvature, edge rewiring intensifies |
| Collapse |
survival ratio < 0.3 |
XII operator triggers, topology destruction |
Buttons
- ▶ Start τ-Flow / ⏸ Pause: Begins or pauses evolution at 5 Hz (5 steps per second)
- ⟳ Reset τ-Flow: Clears evolution history and regenerates base state
- Evolution View: Shows multi-invariant timeline with phase bands and event markers
Invariant Diagnostics
These are UNNS-internal invariants. They measure structural properties of the recursive state, not physical quantities.
τ-Stability: Ratio of variance after τ / variance before τ. Near 1.0 means stable damping. Values below 0.7 indicate emergence; above 1.2 indicate overcurvature.
Survival Ratio: Fraction of values surviving XII collapse. Lower values mean stronger reality-enforcement. Below 0.3 triggers collapse phase.
Coherence: Smoothness of recursive differences (measures step-to-step variation). Higher coherence means smooth recursive progression.
Commutativity: How sensitive the system is to operator order. Lower values mean operator sequence strongly matters. Values near 1.0 indicate order-independence.
Resonance: Harmonic correlation in the value sequence. Higher resonance means strong periodic/harmonic structure.
Traffic-Light Coloring
- Green: Invariant in healthy range
- Amber: Invariant in transition zone
- Red: Invariant outside stable range
Structure Classification
A lightweight classifier describing the overall regime:
- Stable Curved: Balanced τ-stability, low curvature, smooth evolution
- Emergent Transitional: Low survival ratio or commutativity, rapid change
- Ordered Recursive: High resonance and τ-stability, harmonic lock
- Chaotic: Low coherence, high structural noise
- Collapsed: XII operator triggered, minimal survivors
"Why This Pattern?" Button
Generates a natural-language explanation of the current structure using:
- Active operators in the stack
- Dominant invariant driving behavior
- Interpretation of collapse/resonance/stability
- Structure classification reasoning
Export JSON
The Export button creates a JSON file containing:
For Single-Run Mode:
- Seed and parameters
- Operator stack trace
- Current invariants
- Structure classification
- State metrics (entropy, curvature, depth)
- First 20 values
For τ-Flow Mode:
All of the above, plus:
- Steps: Number of evolution steps
- Phase: Current τ-flow phase
- Topology: Node and edge counts
- Events: Timestamped structural events (node deaths, collapses)
- History: Step-by-step invariants, classifications, and phases
Use exports for:
- Sharing runs with collaborators
- Comparing different operator configurations
- Publishing chamber logs
- Replaying τ-flow evolution
Audio Modes
Three sonification modes are available:
- Follow Value: Frequency maps directly to value magnitude
- Follow Structure: Frequency driven by resonance invariant, damped by τ-curvature
- Follow Operator: Each operator (Φ, Ψ, τ, XII) maps to a musical ratio (golden, √2, √3, octave)
Technical Notes
What τ-Flow Does
τ-Flow is not cosmetic animation. It performs:
- Iterative operator application: Stack is reapplied every 200ms
- Dynamic τ-field evolution: Curvature evolves via damping + noise
- Structural mutations: Nodes spawn/die, edges rewire, topology changes
- Operator gating: Different operators activate in different phases
What τ-Geometry Shows
The z-axis in τ-Geometry mode represents curvature pressure, not distance. During τ-Flow:
- Nodes drift along τ-gradients (toward/away from center)
- Depth modulates size and opacity
- Collapse compresses z → 0
Entropy Definition
Entropy is Shannon distribution entropy (10-bin histogram), not variance. It measures value distribution structure.
Non-Goals
This engine does not:
- Simulate physics
- Predict probabilities
- Train neural networks
- Claim external validity
All outputs are UNNS-internal diagnostics.