Bounded safe-function catalog · local only

Domain-coloring Canvas lab

This sampled phase plot and winding estimate are numerical illustrations, not proof of analyticity, multiplicity, zero or pole count, or branch structure. Principal log uses a declared negative-real-axis cut.

Equivalent content: the selected safe complex function maps pixel-center inputs to phase hue and one named log-magnitude lightness transfer. Numeric probes, zero/pole/cut warnings, winding estimate, and hashes appear in the adjacent semantic table and receipt.

Semantic edition state

Ready.

Fixed numeric probes
InputOutputPhaseMagnitudeState

Mapping contract

Sampling
Pixel centers; y-axis increases upward; 1× or 2× fixed grid. Render samples, four probes, and every winding evaluation share one 1,048,576 total-evaluation cap that is checked before drawing.
Phase
atan2(Im f, Re f), wrapped cyclically with the seam on the negative real output direction.
Magnitude
log2 |f(z)| drives bounded lightness bands. The fixed transfer IDs are log-v1 (base .38, pulse .28), soft-log-v1 (base .46, pulse .16), and contrast-log-v1 (base .30, pulse .38); zero, pole, principal-log cut, and non-finite states remain explicit.
Contour safety
A reciprocal or rational pole declared exactly on the circular contour is labeled by catalog geometry before sampling, including when it falls between sample angles.
Catalog
z; z^n−a for n 1…6; 1/(z−a); (z−a)/(z−b); principal log(z). No executable expressions.

Canonical edition receipt

Render an edition.