Conformal Plot in Maple

Question

I'm trying to plot some conformal maps in polar coordinates on maple using the conformal function.

I want to specify the domain to be the unit disk in $\mathbb{C}$. How do I do this?

Answer 1

Is this the sort of thing you're after?

plots:-conformal(z, z=-1..1+I*Pi,
                 coords=polar);

plots:-conformal(arctanh(z), z=-1..1+I*Pi,
                 -2-2*I..2+2*I, coords=polar,
                 grid=[31,11], numxy=[101,201]);

plots:-conformal(z/sqrt(z^4+1), z=-1..1+I*Pi,
                 -2-2*I..2+2*I, coords=polar,
                 grid=[41,13], numxy=[101,401]);

Sometimes the grid and numxy options have to be tweaked, for a nicer visual. And that tweaking might be quite different if you used an alternate "range" for the unit disk as domain, eg.

plots:-conformal(arctanh(z), z=0..1+I*2*Pi,
                 -2-2*I..2+2*I, coords=polar,
                 grid=[11,21], numxy=[101,201]);

plots:-conformal(z/sqrt(z^4+1),z=0..1+I*2*Pi,
                 -2-2*I..2+2*I, coords=polar,
                 grid=[21,21], numxy=[101,701]);