Try this:
theta = linspace(0, 2*pi, 100);
[X, Y] = meshgrid(1:1:4, theta);
a = 0;
b = 0;
figure(2)
plot(a+cos(Y).*X, b+sin(Y).*X);
axis([-1 1 -1 1]*6)
hold on
patch([xlim fliplr(xlim)], [min(ylim)*[1 1] max(ylim)*[1 1]], 'k')
for k1 = 4 : -1 : 1
color = [1 1 1]*(mod(k1,2)==0);
patch(a+cos(Y(:,k1)).*X(:,k1), b+sin(Y(:,k1)).*X(:,k1), color);
end
hold off
axis equal
axis tight
It creates patch objects going from the largest radius to the smallest, changing the colours with each iteration of the for loop. It colours the background black first. If you want a larger background, area, increase the multiplier (here 6) in the axis call.
Experiment to get the result you want.
