How do I plot this in MATLAB ?

Above is the image of circular grid under f(z)=z/(1-z) in "complex tool" given by jim rolf.

I want to plot images of such circular grids (|z|<1) under any complex map f(z)=x(z)+i*y(z) in MATLAB. so if anyone could help me with the code so that i can plot these in MATLAB .

Thanks, i would really appreciate the help!

Answer 1

[Angelo Yeo]

n_rays = 16 + 1;
n_circles = 9 + 1;

n_samples = 200;
rays = linspace(0, 1, n_samples)' * exp(1j*linspace(0, 2*pi, n_rays));
interior_circles = linspace(0, 1, n_circles)' * (cos(linspace(0, 2*pi, n_samples)) + 1j * sin(linspace(0, 2*pi, n_samples)));
interior_circles = transpose(interior_circles);

%% plotting
figure;
subplot(1,2,1);
for i_rays = 1:n_rays
    plot(real(rays(:,i_rays)), imag(rays(:,i_rays)),'Color',[88, 140, 102]/ 255)
    hold on;
end

for i_circle = 1:n_circles
    plot(real(interior_circles(:,i_circle)), imag(interior_circles(:,i_circle)),'Color','r')
end
axis square
xlim([-2, 2])
ylim([-2, 2])
grid on;

subplot(1,2,2);
f = @(z) z./(1-z); % complex function to apply
for i_rays = 1:n_rays
    plot(real(f(rays(:,i_rays))), imag(f(rays(:,i_rays))),'Color',[88, 140, 102]/ 255)
    hold on;
end

for i_circle = 1:n_circles
    plot(real(f(interior_circles(:,i_circle))), imag(f(interior_circles(:,i_circle))),'Color','r')
end
axis square
xlim([-2, 2])
ylim([-2, 2])
grid on;

[simran]

Thankyou very much for the help! It is exactly what i wanted. Also, if you could recommend me some ways to make it look more attractive and colorful with some styles? like in the picture attached or maybe you could recommend some other sources where i can learn different styles of such coloring ?

[Angelo Yeo]

Please refer to the doc for "plot".

https://www.mathworks.com/help/matlab/ref/plot.html?s_tid=srchtitle_site_search_1_plot#btzitot_sep_mw_3a76f056-2882-44d7-8e73-c695c0c54ca8