Complex Mapping Studio V2.1

General complex-to-complex domain coloring, full range-plane coloring, warped grids, path tracing, and known analytic continuation.

Expression in z

Analytic continuation

ON uses implemented continuation-aware formulas. Unknown functions are not faked.

View mode

Color style

Center Re

Center Im

Half width

Grid spacing

Domain output contours

White curves on the left show where Re(f(z)) and Im(f(z)) hit output-grid lines.

Full range color

Makes the right panel a fully colored w-plane with warped z-grid lines over it.

Input-plane axes

Draw axes and ticks in the visible z-plane.

Render quality

0.70

Grid morph animation

1.00

Auto animate morph

In split mode, animates the grid from z to f(z).

Path tracer

Path Re

Path Im

Radius / length

Path angle

Samples

Presets

What the panels mean
Left: domain coloring of f(z) over the input z-plane.
Right: full colored range plane, with the input z-grid warped through f.

Supported special functions
zeta, eta, xi, gamma, beta, factorial, geom, erf, sinc, lambertw, sec, csc, cot, cis

Continuation-aware examples
geom(z) is direct series when continuation is OFF and 1/(1-z) when ON.
zeta(z) is direct Dirichlet-series mode when OFF and continuation-aware mode when ON.
eta(z) uses alternating-series mode when OFF and Euler-transformed mode when ON.

Expression

(z^2 + 2i)/(z - 1 - i)

Ready

Drag: pan z-plane

Scroll: zoom

Hover: inspect z and f(z)

Right panel: colored range + warped grid