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. Nevert

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