clear;%computes lyapunov exponent r = 4.0;%%%%% first converge to attractorx = rand;   %choose random initial datafor i=1:200;   x = r*x*(1-x);     %apply logistic mapend;%%%%% find (1/n) Sum ln(f'(x_i))  -  limit should be lyapunov exponentsum = 0;for i=1:500;    x = r*x*(1-x);     %logistic map    sum = sum + log(abs(r - 2*r*x));    sum/i                                    %print out average    average(i) = sum/i;             %collect into vector for later plottingend;plot(average);      %plots sucessive averages so a trend can be observed