Julia Sets:

zn+1 = c sin(zn) zn+1 = c exp(zn)

zn+1 = c i cos(zn) zn+1 = c zn (1 - zn)

A property of the the Julia Set is that if the domain of c is real numbers the the Julia Set it mirrored about the Real axis. If c is a complex number with an imaginary component then then the symmetry is rotational at 180 degrees.