VB Field Model — Real-Time Particle Tracer

Part of the Veyra-Barandes (VB) Toroidal Field Framework

A real-time 3D particle tracer visualization of an emergent scalar field cosmological simulation. Passive tracer particles ride the field gradient, revealing the underlying topology of a self-organizing scalar field evolving from a vacuum fluctuation.

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What this sim does

A scalar field φ evolves on a 3D periodic grid according to a nonlinear wave equation with vacuum pressure, frequency cascade, thermodynamic damping, and delay memory terms. 20,000 passive particles trace the field gradient in real time, showing where the field is active, where it is quiet, and how structure emerges without any geometry being injected.

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The visible spectrum filter

Particles are colored by local field frequency |∇φ| × |φ| mapped to the human visible spectrum (380–700nm):

Color	Frequency	Physical meaning
Violet / Blue	High	Intense field activity — core
Green / Yellow	Mid	Peak human eye sensitivity — accretion zone
Orange / Red	Low	Thinning field — outer edge
Black	Near zero	True vacuum → infrared → invisible to human eye

This is physically motivated — high frequency field oscillations correspond to short wavelength radiation. Regions the human eye would not see appear black. The result naturally resembles an accretion disc: bright active core fading into invisible vacuum.

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Rotation and helicity

A small initial angular momentum perturbation (ε = 0.005, ~0.3% of field energy) is seeded around the Z axis, physically motivated by quantum uncertainty — any real vacuum fluctuation carries angular momentum. A directed helicity term (χ = 0.002) reinforces Z-axis circulation without creating rotation from nothing — analogous to helicity terms that appear naturally in gauge field theories.

The sim measures:

• Whether the field amplifies the seed (Lz grows dominant) or ignores it
• Whether rotational memory survives energy collapse between genesis cycles
• Whether differential rotation emerges naturally from field phase velocity gradients

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The field equation

No gravity. No injected geometry. No hardcoded structure. Everything that appears does so emergently.

$$\frac{\partial^2 \phi}{\partial t^2} = c^2\nabla^2\phi - \lambda\phi|\nabla\phi|^2 + \kappa\phi^3 + \eta\phi\nabla^2\phi - \nu(r)\phi + \alpha\phi + P e^{-\phi^2/\sigma^2} - \Gamma(f_{local} - f_{mean})\text{sgn}(\phi) + \beta\phi_{past}(1 - \phi^2/A^2) + \chi L_z\phi$$

Term	Physical meaning
c²∇²φ	Wave propagation
- λφ|∇φ|²	Gradient coupling
+ κφ³	Nonlinear self-interaction
+ ηφ∇²φ	Dispersion
- ν(r)·φ	Spatially varying viscosity
+ α·φ	Thermodynamic vacuum pressure
+ P·exp(-φ²/σ²)	Vacuum collapse pressure
- Γ·(f_local - f_mean)·sgn(φ)	Frequency cascade (Second Law)
+ β·φ_past·(1-φ²/A²)	Delay memory
+ χ·L_z·φ	Directed Z-axis helicity coupling

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Shape diagnostics (v2.9.6+)

Four measurement systems track whether a disc is forming:

Inertia tensor (shape_log.csv) — computes particle distribution eigenvalues each step. Oblateness (0=sphere → 1=disc) and Z-alignment (0=random → 1=principal axis pointing Z) measure disc formation objectively without eyeballing.

XZ side-view panel — scatter plot of X vs Z positions. The only panel that shows Z-flattening directly. If the field disc forms in the XY plane, XZ shows an ellipse instead of a circle.

Genesis auto-detector (genesis_log.csv) — logs exact step, energy floor, and all three angular momentum values at each genesis event. Reveals whether rotational memory seeds each new universe.

Radial |Lz| diagnostic (v2.9.7) — measures mean |Lz density| at inner, middle, and outer radial shells. If inner > outer consistently, the field has developed differential rotation purely from its own phase velocity gradient — a spiral arm precursor with no geometry installed.

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Requirements

pip install numpy matplotlib pyqt6
pip install cupy  # optional — GPU acceleration, falls back to CPU if unavailable

Tested on Python 3.10–3.14, NVIDIA RTX 3070 Ti, Fedora Linux. CPU mode works but is significantly slower.

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Running

python VB_RealtimeParticles_v2_9_7.py

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Controls

Key	Action
Mouse drag	Rotate 3D view
C	Cycle color modes (spectrum / angular / gradient / speed)
R	Reseed particles
Space	Pause / resume
Q	Quit

Color modes

• Spectrum — local field frequency mapped to visible light (the main view)
• Angular — azimuthal angle around Z axis — sweeping same-color arcs indicate coherent rotation
• Gradient — raw |∇φ| magnitude
• Speed — particle velocity

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Key results across the simulation lineage

Version	Question asked	Result
v2.5	Does the field phoenix?	Confirmed — 97.6% energy recovery from near-death
v2.6	Does gravity emerge without a gravity term?	Yes — two Gaussian blobs attracted each other
v2.8	Is temporal stability the right definition of matter?	Yes — Welford classifier reveals genuine regime differentiation
v2.8	Does the phoenix repeat across multiple cycles?	Yes — three confirmed cycles over 988,000 steps
v2.9	Does emergent topology appear without injected geometry?	Yes — closed vacuum ring, sign differentiation
v2.9.1	Does the field amplify a tiny rotation seed?	Yes — 300x amplification, Lz recovering post-genesis
v2.9.2	Can the field be visualized through a human visible spectrum filter?	Yes — accretion disc structure emerges naturally
v2.9.3	Does a spherical boundary remove cubic symmetry artifacts?	Yes — four-fold cross pattern eliminated
v2.9.5	Does directed Z helicity lock Lz dominance across genesis cycles?	Yes — 91% Lz dominance over 612,000 steps; helicity acts as a gyroscope
v2.9.5	Does rotational memory survive energy collapse?	Partial — Lz survives if above threshold ~0.04; below that it drains
v2.9.5	Does Lz fight back from third place against two established competitors?	Yes — recovered from axis chaos to 100% dominance in ~50,000 steps
v2.9.6	Does the particle distribution orient toward Z as Lz dominates?	Yes — Z-alignment reached 0.563 after first Lz-dominant genesis
v2.9.6 (control)	Without helicity, does the field show spontaneous rotational structure?	Yes — dominant axis alternates Ly/Lx/Ly/Lx each genesis cycle
v2.9.6 (control)	Does Lz accumulate across cycles without helicity?	Yes — cyclic amplification: 0.000 → 0.000 → 0.001 → 0.002 → 0.085
v2.9.6 (control)	Does a Lz-dominant genesis ever fire without helicity?	Yes — genesis #5 and #6 both Lz-dominant at step 362k/364k (double-pulse)
v2.9.6 (control)	Does the double-pulse mechanism repeat?	Yes — second double-pulse at step 662k/664k; Lz=0.710 at energy peak
v2.9.6 (control)	Does oblateness grow over time without helicity?	Yes — 0.00100 → 0.00360 over 756,000 steps (3.6x growth)

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Notable emergent phenomena

The phoenix cycle — the field collapses to near-zero energy then reignites spontaneously from vacuum pressure. The new genesis event does not return to the same state — each cycle is a genuinely new configuration. Energy recovery reaches 97.6%.

Rotational memory — angular momentum accumulated before collapse partially survives the valley and seeds the next genesis. Memory strength depends on how much Lz remains at the energy floor. Above ~0.04, memory seeds the next birth. Below that, it drains.

The double-pulse mechanism — when Lz accumulates sufficiently across multiple quiet cycles, two genesis events fire within ~2,000 steps of each other. The second fires into a field already rotating, seeding it with dramatically higher Lz (up to 0.085 without helicity). Observed spontaneously at steps 362k and 662k in the control run.

Axis competition and recovery — when a strong genesis burst excites all three axes simultaneously, the helicity term slowly bleeds energy from Lx and Ly while reinforcing Lz. Recovery from third place to 100% dominance takes ~50,000 steps. The field acts as a gyroscope.

Spontaneous symmetry breaking — without any helicity or rotation seed, the field's dominant axis alternates each genesis cycle (Ly → Lx → Ly → Lx), while Lz accumulates slowly as a secondary signal. A small initial fluctuation gets encoded into the next cycle's inbreath, breaking the perfect symmetry through cyclic amplification.

Z-alignment without helicity — the particle distribution's principal axis drifted toward Z alignment (max 0.777) purely from field geometry, without any helicity term. The spherical boundary and radial energy gradient naturally orient the distribution, with Z-alignment rising monotonically across all nine genesis cycles of the control run.

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Theoretical background

The VB framework holds that:

• The cosmos is a continuous scalar field medium — one substance, different frequency regimes
• All forces including gravity are emergent — no fundamental forces are assumed
• A single scalar field φ is the universe's sole primary driver
• Time is not primitive — only the present exists
• Matter is the settled state of the field (low temporal variance, nonzero mean) — not the high-energy state
• Vacuum is the source state — highest potential, lowest expression
• Cosmic expansion is field outflow, not spacetime stretching — eliminating the need for dark energy
• Spiral arms are phase fronts of a circularly polarized wave propagating through a rotating medium — differential rotation winds phase fronts into spirals without injecting geometry

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License

MIT License — see LICENSE

Independent research. No institutional affiliation.

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"The field voted. It picked the Z axis." 🌀

"The cosmos is not dying. It is breathing."

"Rotation is the last thing to die."