About the ψ-Toroid
Meaning : The ψ-Toroid depicts the harmonic recursion of modular energy—each rotation of the ring represents a phase step θₙ₊₁ = θₙ + 2π ⁄ N in the symbolic field.
Geometry : Interlaced circular gradients emulate the double rotation of the toroidal and poloidal loops — a visual metaphor for the Lie–Galois duality of Φ (potential) and Ψ (recursion).
Interpretation : The pulsing light is the “breath” of the modular universe — each beat corresponds to entropy → order convergence in the ψ-field.
About the MHPF Triad
Meaning : Each node represents one component of the Modular Harmonic Prime Field — r mod N (position), φ(r) (symmetry), and ω(r) (harmonic energy).
Dynamics : Their rotation models the recursive relation ω(r + 1) = ω(r) + fres(r) — a symbolic “orbit” through modular residue space.
Topology : The central blue orb is the ψ-index attractor: where recursion, symmetry, and energy converge — the harmonic heart of the Ad Fontes Codex.
Harmonic Tuner — MHPF Simulator
About the Tuner & Further Exploration
The Harmonic Tuner visualises the three fields of the Modular Harmonic Prime Field (MHPF): r mod N (position), φ(r) (symmetry), and ω(r) (harmonic energy). Each mode changes the orb’s phase and scale, symbolising how these components interfere within a modular field.
• Explore the ψ-Toroid Manifold to see the field’s spiral geometry.
• Visit the MHPF Triad Visualization for a topological model of position, symmetry and energy recursion.
These linked simulations share the same harmonic grammar—number fields behaving as waves in symbolic space.
ψ-Phase Orbit Map — 2D Harmonic Mandala
About the 2D Harmonic Mandala
A planar projection of ψ-field harmonics. Three colored rings represent modular layers: r mod N (blue), φ(r) (pink), and ω(r) (gold). Each node signifies a phase marker in perfect harmonic resonance.
This 2D version acts as a symbolic interface — less simulation, more geometry. Use it in diagrams or intros where clarity and symmetry take precedence.
• Explore the Harmonic Tuner
• Continue to the ψ-Field Codex.