Why isn't this plot looking correct?

Calculate P250 for 1000 different r values, ranging between 3 ≤ r ≤ 4 (linspace would be a good tool to use here), and save them as you go in a big vector. Plot your r values against your P250 values. What do you see? How are the points changing as r increases?

% Plotting a dynamical system
r = linspace(3,4,1000); %creates vector of length 1000 with evenly spaced values between 3 and 4
seed = linspace(0.1,0.9,100);
P_250 = zeros(1,1000); %creates zero vector of length 1000
hold on
for s = 1:100  
  P = zeros(1,250); %creates zero vector of length 25  
  seed_index = seed(s);  
  P(1) = seed_index; %seed value
  for r_index = 1:1000    
    r_current = r(r_index);    
    for n = 1:250      
      P(n + 1) = r_current*P(n)*(1 - P(n)); %dynamical system      
    end
    P_250(r_index) = P(250); %stores value of P(250) for each value of
  end  
end

plot(r,P_250,'.');

The plot just doesn't look right when this runs. I can't find the problem.

[Image Analyst]

What is it supposed to look like?

Answer 1

[Mischa Kim]

Tyler, I am not sure what you are looking for. However, it seems like you did get what the exercise is asking for. Note, that the exercise is not asking you to create the entire bifurcation diagram. If you increase the number of data points (e.g. 100000) and add another bifurcation branch the plot starts looking more like the diagram you would expect for the logistic map.

 r = linspace(3,4,100000); %creates vector of length 1000 with evenly spaced values between 3 and 4
 seed = linspace(0.1,0.9,100);
 P_250 = zeros(1,100000); %creates zero vector of length 1000
 P_249 = zeros(1,100000); %creates zero vector of length 1000
 hold on
 for s = 1:100  
   P = zeros(1,250); %creates zero vector of length 25  
   seed_index = seed(s);  
   P(1) = seed_index; %seed value
   for r_index = 1:100000    
     r_current = r(r_index);    
  for n = 1:250      
    P(n + 1) = r_current*P(n)*(1 - P(n)); %dynamical system      
  end
     P_249(r_index) = P(249); %stores value of P(250) for each value of
     P_250(r_index) = P(250); %stores value of P(250) for each value of
   end  
 end
 plot(r,[P_250;P_249],'b.');