%% mu graph data
mu = [1.1 1.2 1.5 2 5 8 10 20 30 40 50 60 70 80 90 100 150 200 300 400 500 1000 10000 1e6];
newton_iteration_num_case1 = [486 286 138 90 54 45 45 43 42 40 46 42 40 40 39 41 41 44 59 60 58 56 141 702];
newton_iteration_num_case2 = [635 388 206 146 87 79 78 78 72 73 77 73 71 78 82 91 76 87 91 118 142 101 585 565];

%% mu graph plot
semilogx(mu, newton_iteration_num_case1, 'r-*');
hold on;
semilogx(mu, newton_iteration_num_case2, 'b-o');
hold off;
xlabel('mu');
ylabel('Newton Iterations');
legend('pi rotation case', '2pi degrees rotation case');
title('Number of Newton Iterations vs. mu');