Visualizing complex functions by hue = argument, brightness = modulus
f(z) = z²
Domain coloring maps a complex function f: ℂ→ℂ to color. Hue encodes arg(f(z)) (phase), brightness encodes |f(z)| (modulus). Zeros appear as black points where all colors meet; poles appear as white explosions. Winding numbers count zeros minus poles inside any contour — this is the argument principle.