Spatial coordinates
Position locates a sample in three dimensions. Wavelength is an axial length. Diameter defines the transverse envelope. A three-component position vector does not alone encode all those field properties.
A field in motion.
A state you can interrogate.
The surface, volumetric samples and time graph share the same field. Follow the crests across the observer planes, then investigate why the state remains present at a zero node.
The same wave, graphed over time
Selected sample · amplitude . The graph uses the same phase, envelope and time as the 3D view. Its white endpoint is the current sample value.
How is this achieved? Open the mathematics and configure the field
This renderer samples a scalar field inside a declared cylindrical envelope in 3D. Its fixed sample addresses preserve spatial context across zero-amplitude planes. A spatial origin, a field-amplitude zero and an absent record are different conditions.
A(x,y,z,t) = exp[−2(y²+z²)/R²] cos[2π(x/λ−ft)]
R = D/2 · propagation speed v = fλ
x, y and z in this equation are local reference coordinates. World position is O+B·q with O=(1,1,1) and a declared rotation basis B. Length uses reference units; time uses reference seconds. The display maps scalar amplitude to transverse height y_display=y+0.45DA to make the wave geometry visible. This is a declared graphical encoding; exported physical sample positions remain unchanged. The surface shows the y=0 slice across x and z; the surrounding sample glyphs retain the full 3D inventory. The envelope is the selected support, rather than a measured physical boundary. This mathematical reference is not native QZL hardware execution or empirical wave data.
XY, XZ and YZ planes share one origin identity U=1. The symbolic layer label (−1+) and numerical coordinate projection are retained as separate fields.
Positive amplitude is cyan; negative amplitude is violet. Numerically zero samples are white and remain present. The meshed surface displays crests and troughs travelling along x. Volumetric sample glyphs follow the same amplitude display; their original coordinates remain in the export. Drag to orbit the view, or use the keyboard-accessible view buttons below.
Reference time0 s
Stable sample inventoryCalculated when enabled
Zero-amplitude samplesCalculated when enabled
Propagation speed2 reference units/s
Paired action moments · −2 / −2
The two repeated labels identify distinct forward and inverse events. The inverse restores the sampled field parameters; its later execution record remains. Field phase time and event chronology are separate, as required by the source correction on timestamped inversions.
No sampled actions yet.
Local rendering cost: .
Time progression starts paused.
The export contains the declared frame, parameters, time and every sample’s identity, 3D position, envelope, phase and amplitude. Rendering tolerance is 10⁻¹²; the calculated amplitude remains in the record. Camera orbit changes the view; frame controls change B. The two are recorded and interpreted separately.
Keep the graph and its claims aligned.
Orientation
The reference uses a rotation matrix for its declared yaw/pitch family. Sign parity tracks reflections; it cannot represent arbitrary 3D rotation or shear. The native orientation contract remains separately defined.
Temporal continuation
Time updates the declared field on the same sample inventory. The current exported volume is a snapshot, not an immutable event ledger. Existing native continuation and history obligations are described in the research paper.