All three simulations below are woven from the same underlying geometry: a set of 5 nested toroidal "tiers" (T0 through T4), each governed by the same three winding laws.
Each tier is rotated 90° relative to its neighbor (alternating X and Y axes) so the tiers nest without intersecting, and each carries 6 helical channels — 3 "Forward" (orthodromic, +1 chirality) and 3 "Inverse" (antidromic, −1 chirality) — wound around it in a dual-helix. That's the "loom": a fixed geometric scaffold. What changes between the three modules below is what gets woven through it — a self-verifying clock, a cavity-coupling simulation, or a holographic memory trace.
Framed loosely as physics (clockwork, cavity QED, holographic storage), these are geometric art/exploration tools rather than physical models — treat the terminology as metaphor for the underlying math, not a claim about real hardware.
The base module. Time is parameterized by spatial progression around the 5 tiers instead of an external frame rate — the 60 total helical wraps across all tiers (WΣ = ∑(16 − 2n) = 60) act as the clock's intrinsic register. A single Master Clock Frequency slider drives every tier's rotation at once, with kinematic acceleration increasing toward the innermost T0 core.
The interesting part is the TQF (Triple Quad Formula) Area-Stability panel: it tracks the 3 forward anchor points on the T0 core in real time, computes their pairwise squared distances (quadrances Q1, Q2, Q3), and checks a rational-trigonometry identity (AR ≡ 16A², equivalent to Heron's formula) against the live geometry every frame — a continuous, visible proof that the winding stays topologically consistent as it spins.
Launch SimulatorTakes the same engine and reframes it as a cavity-coupling simulation, borrowing the language of Rabi splitting (where a single resonance splits into two polariton branches under strong coupling). A guided 4-step primer walks through the T0 "plasmonic" core, the 5-tier "exciton" manifold, the 1D→4D lift into the W, X, Y, Z phase vectors, and a collective ensemble of up to 25,920 "molecules" wrapping the whole geometry.
That ensemble can be driven purely by the intrinsic master clock, or you can upload an audio track and let its frequency spectrum modulate the same geometric wave functions live — turning the toroidal weave into an audio-reactive visualizer, scrubbed via a 25,920-frame "Great Year" sequencer.
Launch SimulatorIsolates a single tier — the equatorial T2 manifold (W2 = 12 helical wraps, the balance point of the 5-tier stack) — and turns it into a recording surface. A tumbling 4×4×4 "etch head" of 64 glowing voxels rides the T2 orbit, its rotation driven by either the intrinsic clock or 4 bands of an uploaded audio track's spectrum.
As it travels, each of the 64 voxels leaves a persistent trail, braiding into a 64-strand cable. Where a Forward braid crosses an Inverse (counter-traveling) braid, the two interpenetrate into a glowing Moiré interference knot — the module's central metaphor for encoding data holographically, distributed across an interference pattern rather than a single point.
Launch Simulator