⚡ CHAMBER XX: RECURSIVE TENSOR FIELD EXPLORER v2.3

Phase F • Multi-τ Dynamics with Maxwell-Analog Visualization
Configuration
Maxwell-Analog Visualization
Φ: Divergence (Electric)
Ψ: Curl (Magnetic)
Diagnostics
Step
0
||Φ||
—
||Ψ||
—
E·B
—
Antisym
—
FPS
—
📚 Laboratory Guide

Chamber XX: Recursive Tensor Field Explorer

Theoretical Foundation: Implements cross-field recursive tensors:

Rij = Oi(τj) - Oj(τi)

where Oi are differential operators (∇², ∇, I) applied to τ-fields.

Maxwell-Analog Structure

  • Divergence (Φ): Electric-like charge density from ∇·R
  • Curl (Ψ): Magnetic-like vorticity from ∇×R
  • E·B Coupling: Bridge energy between electric and magnetic modes

Visualization Features (v2.3)

  • Differential Colormaps: Blue→White→Yellow (Φ), Purple→Black→Cyan (Ψ)
  • Vector Overlays: E-field arrows (radial), B-field arrows (circular)
  • Bridge Mode: Green→Red coupling intensity visualization

Validation Criteria

  • C_F1: Tensor antisymmetry Rij = -Rji
  • C_F2: Divergence-free regions (∇·Ψ ≈ 0)
  • C_F3: Curl-free regions (∇×Φ ≈ 0)
  • C_F4: E·B coupling emergence
  • C_F5: Performance ≥180 fps @ 128²

Version: 2.3 | Phase: F | Status: Production

Field Overview

Each run generates two τ-fields updated through recursive coupling. Φ (divergence) represents charge-like intensity, Ψ (curl) represents rotational vorticity. The Bridge Mode overlays their product E·B, visualizing τ-field resonance.

Functional Controls

  • Run Evolution: Starts the τ-field recursion engine using current grid and λ values.
  • Stop: Halts recursion mid-cycle, keeping current field states.
  • Bridge Mode: Toggles Φ–Ψ coupling visualization.
  • Vector Overlay: Enables E (∇Φ) and B (∇×Ψ) arrow visualization.
  • Export Data: Saves JSON file with derived metrics and configuration.

Operator Reference

  • XIII: Base τ-field initialization (sets random recursive seeds).
  • XIV: Φ-Scale (electric divergence synthesis via ∇·R).
  • XV: Prism (magnetic curl extraction via ∇×R).
  • XVI: Recursive Transfer (cross-field coupling of Rij).
  • XVII: Maxwell Bridge (E·B coherence mapping).

Validation and Observables

  • ||Φ||, ||Ψ||: Norms of derived fields (stability check).
  • E·B: Mean coupling magnitude between divergence and curl.
  • Antisymmetry: Rxy + Ryx ≈ 0 ensures correct tensor parity.
  • FPS: Frame rate, must exceed 180 @ 128².

Remarks

This chamber provides a functional approximation of Maxwell-analog recursion fields within the UNNS substrate. Divergence–curl coherence demonstrates the emergence of coupled tensor dynamics without enforcing physical electromagnetic constraints.

Field Overview

Φ uses a violet→white→amber palette for electric field visualization. Ψ uses cyan→blue→black for magnetic field visualization.

The Maxwell-Analog Bridge visualizes coupling intensity (E·B = |ΦΨ|) using a green→red gradient.

Maxwell-Analog Bridge

The bridge overlay visualizes the divergence–curl duality, mapping the interaction between Φ and Ψ as a recursive field transfer.