Function f(z)
z²
order-2 zero at origin
z³ − 1
3 zeros at cube roots of 1
(z²−1) / (z²+1)
zeros ±1, poles ±i
sin(z)
zeros at nπ — strips in Im
tan(z)
interleaved zeros and poles
e𝤜
entire function — no zeros
log(z)
branch cut on negative real axis
sin(1/z)
essential singularity at 0
Color Mode
● Rings
○ Flat
░ Dark/Bright
▓ Checker
♯ Grid
⊕ Axes
Hue encodes arg f(z).
Brightness encodes |f(z)|.
Zeros: all hues converge.
Poles: all hues diverge.
Essential sing.: wild chaos.
z =
—
f(z) =
—
|f| =
—
arg =
—
zoom =
1×
hue = arg f(z) • brightness = |f(z)|
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