complex numbers – w-plane Maple mapping does not agree with comformal mapping webpage?


(I’ve posted this question on mapleprimes, but as a precaution I am posting it here, because I suspect the question may be related to a theoretically different implementation on both sides of the difference).

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:

restart;
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 := exp;
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 ridiculously simple: I am simply scanning the 1×1 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 of the same function? 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. In particular, exp looks expansive on the right half plane with my implementation, while it looks contractive on the right halfplane with Bau’s implementation.

Can anyone see why the difference (implementation or otherwise)? I tried it with all the functions (except Lambert’s W) and there are always differences.

Many thanks in advance