How to plot the Wolfram Alpha grid?

Good afternoon,

I would like to plot for any function this grid :

This is the special case for f(z) -> 1/z

This is a typical graph you can find on wolfram alpha. Nevertheless I don't know how to proceed. The idea would be to see where the lines of the complex grid of the 1-square is sent after applying f.

One thing that could be great would be to add colors on the grid in order to see where the left part is sent. (like here : https://www.youtube.com/watch?v=JX3VmDgiFnY)

If you have any idea... thank you.

[Jitender Gangwar]

Hi Ni,

I found a similar question on stackoverflow and you may want to consider having a look at it.

https://stackoverflow.com/questions/53472184/how-to-plot-the-wolfram-alpha-grid-matlab

clear
clc

N = 101;
x = linspace(-1, 1, N);
y = x;
[X,Y] = meshgrid(x,y);

Z = X + Y*1i;

f = 1./Z;

U = real(f);
V = imag(f);

%Plot transformed mesh
hold off
plot(U,V,'b-');
hold on
plot(U',V','r-');

xlim([-5,5]);
ylim([-5,5]);
axis equal

[Ni Cark]

thank you,

Do you know how to improve this in order to set a wallpaper (like a range of colors) behind the grid in order to know where the left part and the right part is sent? thank you !