How to plot the Wolfram Alpha grid? [MATLAB]

Question

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.

Answer 1

Try the code below. I have updated the answer to show the lines in different colors.

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