%Fibonacci sequence

clear all

%number of months to simulate
N=20;

%make ``blank" list of pairs in seqential months
f=zeros(1,N) ; 

%initial conditions
f(1) = 1;
f(2) = 2;

%iterate
for n=3:N
     f(n) = f(n-1) + f(n-2);
end
  
figure
subplot(311)
plot(1:N,f,'-','Linewidth',2) ; hold on 
ylabel('f','FontSize',18)
xlabel('n','FontSize',18) 

subplot(312)
plot(1:N,log(f),'-','Linewidth',2) ; hold on 
ylabel('log f','FontSize',18)
xlabel('n','FontSize',18) 


%analyze !

%ratio of successive fibonnaci numbers
ratios=zeros(1,(N-1)) ; 

for n=1:N-1
    ratios(n) = f(n+1)/f(n) ;
end

subplot(313)
plot(1:N-1,ratios,'-','Linewidth',2) ; hold on 
ylabel('ratios','FontSize',18) 
xlabel('f','FontSize',18)


%find first month where number of rabbits exceeds 1500
for n=1:N
    if f(n) > 1500
        break
    end
end

disp('first month where number of rabbits exceeds 1500 is')
n

save critical_fibonacci_month.dat n -ascii