Complex Domain Coloring » Modular functions

Complex Domain Coloring
Portraits of complex functions of complex variable, created using so called complex domain coloring.

Modular functions

Modular functions and functions related to them

The Klein's absolute invariant J(q).	The argument of J(q).	The argument of J(q²).

The Weierstrass eliptic function ℘(z,q) is an elliptic function of the variable z and a modular function of q. This picture shows the argument of ℘(0,q).	℘(1,q²).	Jacobi ϑ(i,q²).

The q-theta function ϑ(0.01,q).	Q-theta function ϑ(z,.95).	Q-theta function ϑ(z,.7 + .7i), argument only.

Q-theta function ϑ(z,.7 + .7i).