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;
