theta = -(50*pi/180:pi/180:3*pi);
polar(theta, theta .^ 1.2)
a = get(gca, 'children');
xx = get(a, 'xdata');
yy = get(a, 'ydata');
rot2 = 2*pi/4;
pp2 = [cos(rot2) -sin(rot2);sin(rot2) cos(rot2)] * [xx; yy];
rot3 = 4*pi/4;
pp3 = [cos(rot3) -sin(rot3);sin(rot3) cos(rot3)] * [xx; yy];
rot4 = 6*pi/4;
pp4 = [cos(rot4) -sin(rot4);sin(rot4) cos(rot4)] * [xx; yy];
plot(xx, yy, 'k-', pp2(1, :), pp2(2, :), 'k-', pp3(1, :), pp3(2, :), 'k-', pp4(1, :), pp4(2, :), 'k-')
axis equal
set(get(gca, 'children'), 'linewidth', 2)
set(gca,'xcolor', [1 1 1], 'ycolor', [1 1 1])
set(gcf, 'color', [1 1 1])
axis([-19 19 -12 12])

