% 4-8-2008
% Golden Ratio
clear all;
close all;

% Start out the Fibonacci sequence and record what the true golden ratio is
x = [1 1];
phi = (1+sqrt(5))/2;

% Iterative loop
for i=3:1000
    x(i) = x(i-1) + x(i-2); % Calculate the next member in the sequence
    r(i-2) = x(i) / x(i-1); % Calculate the ratio value
    
    if ( abs(r(i-2) - phi) < 10^(-10) ) % Check to see if we have reached our tolerance
        break;
    end
end

% Plot the convergence
plot(r);
axis([1 i 1.4 2])
title('Golden Ratio Convergence');
xlabel('Iteration');
ylabel('\phi');