SYSTEM NOTE
Transforms make one field repeat.
This is a conceptual visual model for modular transformations, not a rigorous modular-form calculator.
OBSERVATION CHAMBER / MVP
Modular Forms Field
A visual modular-transformation field for observing the upper half-plane, fundamental domain, T-periodicity, S-inversion, and weight response.
modular
Prototype
MODULAR FORMS FIELD
Observe how the upper half-plane folds into a fundamental domain through T-shift, inversion, and visual weight response.
First observation
Use T-SHIFT to emphasize periodic copies, INVERT for the unit-arc fold, and DOMAIN to read the fundamental region.
UPPER HALF-PLANE
copies 7 / weight 2
OBS-000 / DOMAIN / 00:00
OBSERVATION POINTS
Period, inversion, and fundamental domain.
- DOMAIN frames the standard representative region of the upper half-plane.
- T-SHIFT emphasizes the horizontal repetition suggested by z -> z + 1.
- INVERT highlights the unit-arc fold suggested by z -> -1 / z.
- Weight is a visual response: it changes glow, wave thickness, and copy brightness rather than evaluating an exact function.
SYSTEM NOTE
T:z -> z + 1 and S:z -> -1 / z generate the visual modular action. A general transform is z -> (az + b) / (cz + d), ad - bc = 1; the standard domain is |z| >= 1 and |Re(z)| <= 1/2.
OBSERVATION GUIDE
Touchpoints for Observation
Observe the upper half-plane as a field that repeats under T-periodicity, folds under S-inversion, and is represented by a fundamental domain.
- Use T-SHIFT, INVERT, FOLD, DOMAIN, LATTICE, WAVE, FUNDAMENTAL, PERIOD, and INVERSION to compare copies, arcs, and visual weight response.
- T-SHIFT makes horizontal copies read as the same field.
- INVERT highlights the unit arc that folds distant points back inward.
- Weight changes brightness and wave thickness as a conceptual response, not as exact function evaluation.
This is a visual modular-transformation model, not a rigorous modular-form calculator or proof tool.
Runs inside the browser with no upload and no registration.
OBSERVATION POLICY
This lab runs in your browser. No image, pointer trace, or input is uploaded by this prototype.
OBSERVATION LOG
Observation logging will be connected with moderation in a later build.