# Question:w-plane Maple mapping does not agree with comformal mapping webpage

## Question:w-plane Maple mapping does not agree with comformal mapping webpage

Maple 18

I created some simple maple 9 code to do some z->w mappings long time ago, on my web page:

https://ingalidakis.com/math/ComplexMaps.html

Upon revising my webpage, I've stumbled upon a page for comformal mappings, by David Bau:

http://davidbau.com/conformal/#exp(z)

Here's the current version of my code in Maple 18:

rrestart;
NULL;
with(plots);
xMax := 1;
yMax := 1;
N := 10;
step := abs(xMax)/N;
GL := proc (x, y) options operator, arrow; x+I*y end proc;
f := sin;
G := {};
for k from -N+1 to N+1 do

G := `union`(G, {complexplot(f(GL(x, (k-1)*step)), x = -xMax .. xMax, color = brown)});

G := `union`(G, {complexplot(f(GL((k-1)*step, y)), y = -yMax .. yMax, color = brown)})

end do;
display(G, scaling = constrained);

The code is pretty simple: I am simply scanning the 1x1 unit square complex grid and create a complex plot of it on the w-plane, by passing it through whatever function is at: f:=x.

Does anyone have any idea why the grid lines on the w-plane do not agree with Bau's grid lines mapping of the w-plane? To try it for exp for example, input "exp(z)" in Bau's home page.

The difference is quite noticeable, especially on exp and log, where the orientation of the w-grid on the left and right half-planes, seem to be opposite of what my code displays.

The reason may be Mathematical, but from what I see from the description on Bau's page, there's no difference on the identity function, so I am clueless.