%computes lyapunov exponent 
clear;

r = 3.6;
x0 = 0.3;   %initial data

%%%%% first converge to attractor
x = x0;
for i=1:200;
   x = r*x*(1-x);     %apply logistic map
end;

%%%%% find (1/n) Sum ln(f'(x_i))  -  limit should be lyapunov exponent
sum = 0;
for i=1:200;
    x = r*x*(1-x);     %logistic map
    sum = sum + log(abs(r - 2*r*x));   % note  that  f' = r - 2*r*x
                                              %print out average
    average(i) = sum/i;             %collect into vector for later plotting
end;

plot(average);      %plots sucessive averages so a trend can be observed
xlabel('N');
ylabel('(1/N)\Sigma_{i=1}^N ln| df/dx(x_i) |');