Modulo 9 · period 24
A mathematical instrument
Phi Code Observatory
Cycle 1
01 / 24
Fibonacci · unrestricted
The Lift
Current identity
963
Root 9 · 369 family
A · phase 0
9
F₀ = 0
B · phase +16
6
F₁₆ = 987
C · phase +8
3
F₄ = 3
Invariant
Tn = (Sn, Sn+16, Sn+8)
9 + 6 + 3 = 18 → 9
One cycle · constructed in time
Emergence
Each triad leaves its geometry behind. Isolate a root family to see its contribution to the complete form.
One sequence · three phases
Three Streams
The same Fibonacci digital-root cycle is read at phases 0, +16, and +8. Every vertical alignment becomes one triad.
9 · 6 · 3
963
Position0
Phase indices0 · 16 · 8
Digital-root sum18 → 9
Family369
The cycle as a field
Circulant Matrix
Every row is the same 24-value cycle rotated one position. The three illuminated diagonals carry the phase values that form the selected triad.
Phase 0
Phase +16
Phase +8
The repeating shadow · unrestricted source
Recursive Lift
Successive 24-term Fibonacci cycles retain the same digital-root pattern while their unreduced values continue growing.
Radial encodingLog φ
Camera
Radius is proportional to step index, which is asymptotically proportional to logφ(Fₙ). Auto-zoom keeps the unfolding in view.
Explicit geometry · inspectable mapping
3D Projection Lab
The sequence is embedded in a declared 3D coordinate system. These are chosen geometric projections of the Code—not claims that Fibonacci uniquely implies a particular shape.
Drag the orientation sliders to inspect depth. Colour records the 3–6–9 triad family; perspective affects only appearance.
Infinite circulant field · surface mapping
Wrap Studio
Repeat the 24×24 Code field as a seamless mathematical texture, then inspect how that same field folds or wraps onto selected surfaces.
Drag to rotate · Shift-drag to move · Scroll to zoom · Double-click to reset
Source field24 × 24
Cells576
MappingPlanar repeat
SeamPeriodic in both directions
Section 09 · 576 identical tiles
Radial Sphere Wrap Explorer
576 equal hexagonal tiles arranged around a sphere. Close spacing slightly overlaps some edges; every tile remains the same size. Each matrix cell maps to one tile.
2D wrap sourceManual mode: click a cell to toggle its radial line. With pairs enabled, its opposite switches too: same column, 12 rows away.
Sphere frequency generator
With headphones, listen from the exact centre of the surrounding sphere. Sound sources stay fixed around you when you rotate, move or zoom the visual sphere.
Exact Code frequencies: each sector plays its full three-digit triad in Hz, using its position in the sequence.
Selected frequencies · Hz × number of spatial sourcesNo sectors selected.
Audio stopped. Select cells in Manual cells mode, then play.
Each selected sector has its own spatial voice, even when pitches repeat. Dense combinations blend together; front/back and height perception vary with headphones and listener.576 identical spherical tiles
Drag to rotate · Shift-drag to move · Scroll to zoom · Double-click to reset
Interior wave experiment
Orange: compression · blue: rarefaction. Visual time runs 1,000× slower; audio stays at the actual frequencies.
Enable the simulation to calculate a field.
Steady-state response of the selected sectors, available with or without audio. Brightness is relative to this selection, not a calibrated sound level. The outer 10% of the radius is omitted.Model and accuracy
Linear pressure acoustics in an empty spherical enclosure. Equal normal-velocity drives share one phase clock; each sector is approximated by a small circular speaker patch. Fresh water fills the entire sphere, with no free surface. The wall is locally reacting with a purely resistive impedance; absorption is its normal-incidence energy absorption, not a measured material preset.
The pressure field is calculated with a spherical Bessel/Legendre expansion. The display requires at least six sample intervals per shortest wavelength and compares 64 with 80 expansion orders. Unresolved settings show no field. These checks do not replace validation against a physical device.
No speaker frequency response, vibrating wall, viscosity, heating, streaming or particle motion is modelled. Headphone playback remains a spatial audition of the sources, without the enclosure response.
ModeMaster unfolding
Revealed radial lines64
ProgressionStep 1 · triad 963
Geometrysurface point → sphere centre
Chladni figures · triadic excitation · nodal geometry
Code Cymatic Plate
Drive a virtual plate with any of the 24 Code triads. Fine particles migrate away from vibration and collect along the resulting nodal lines, revealing the plate’s cymatic geometry.
Plate A
Plate B
Settled particles
Stream A · 0
Stream B · +16
Stream C · +8
Drag to rotate the 3D view · scroll to zoom · choose any Code position and excitation
Measure · compare · test
Analysis Lab
Frame measurements describe the currently selected 3D embedding. The Offset Explorer separately tests every phase pair against the numerical rules of the Code.
Canonical reference
Tn = (Sn, Sn+16, Sn+8)
Camera-invariant · embedding-dependent
Frame Invariants
Edges AB · BC · CA0 · 0 · 0
Triangle area0
Centroid radius0
Normal0 · 0 · 0
Frame twist0°
Current family369 · root 9
AreaTwistNormalized within this embedding
Numerical test · all phase pairs
Offset Explorer
One complete cycle
Click any position to inspect it