Hue = arg Γ(z), brightness = |Γ(z)|.
Poles at z = 0,−1,−2,… (rainbow vortices).
No zeros anywhere in ℂ.
Violet lines: Re(z) = 0, 1 (fundamental strip).

z = —

Γ(z) = —

|Γ| = —

arg = —

zoom = 1×

Γ(z+1) = zΓ(z) • Γ(½) = √π • Lanczos approximation (g = 7)