The Realm of Complex Numbers

I had great fun playing with a great visualizer for the complex-valued functions, built by David Bau of MIT.

I have tried hundreds of arbitrary functions, and some interesting ones are given below in text. My interest in this was to explore Reimann's zeta function by using some kind of approximation.

Functions

The following are the functions I have used to generate the above visualizations. The function for each visulization is also displayed in the picture itself.

sum(z^(n+1))
sum(z^n)
sum(z^-(n+1))
iter(z+z'^2,0,10)
iter((z'+0.6)^5,z,6)
iter((z'+0.5)^3,z,6)
z(1+z)/(1-z)
z/(z-1)
(2i)^z
2^z+1.001^z
i-z+1/z
1-z^2
z^3+1/z^3
z^6+z
z^2+z
z^2+z+1.25
z^2+1
z^3+z^7
z^6+z^11
z^10+z^16
z^15+z^22
z^21+z^29
z^2+z^3
2^(1/z)
2^(z^3)
2^(z^-2)
1/z^4+1/z^10
(e^(i*pi))^z
log(z^5+1)
log(z^-4+1)
(z)^4/(z^5+0.05)
z(z^6-1)
(1-zi-0.05)(1+iz)
z + z^20
1/z + z^20
zlog(z)