## Conformal Maps

This page demos a conformal map in the complex plane. For a complex number, a+bi, the vertical axis represents b, and the horizontal a.

Below you will see controls for the parameters of the conformal map:

z \mapsto \left(1-a\right)\left(\alpha_0+\alpha_1z+\alpha_2z^2\right) + a\cos\left(\beta_0+\beta_1z+\beta_2z^2\right)

a:

a0:

a1:

a2:

b0:

b1:

b2: