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Here are some particularly nice examples from math function that show real and imaginary parts of special functions on complex axes and on the complex plane.

bessel( n, x ) — the first five Bessel function of the first kind of real or complex order n of a real or complex number.

Bessel functions of the first kind for both positive (blue) and negative (red) real order

Bessel function of the first kind

Bessel function of the second kind

Hankel function of the first kind

Hankel function of the second kind

Jacobi elliptic sine

Jacobi elliptic cosine

Jacobi delta amplitude function

Gamma function

Riemann zeta function

Proper spherical harmonics in 3D

coloring butterfly

bianchi-pinkall-animation

bianchi-pinkall-animation zoomed

harmonic

radar

heart

helicoid

sinc(x,y) in 3D graph

sin(x*y) in 3D graph

tori

x3D