%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math 3520: Differential Equations and Dynamical Systems
%  Compute and plot the Henon map strange attractor. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Henon mapping
a = 1.4; b=0.3;   % Henon's choices
henon = @(X) [X(2)+1-a*X(1)*X(1), b*X(1)] ;  % [y+1-ax^2, bx]

N = 10000; 

% Generate N pairs (xn,yn) for plotting as points
X=[0,0];   % Initial values [x0,y0] used by Henon
for(i=2:N)
 X(i,:) = henon(X(i-1,:)); 
end
figure; hold on;   % New graph, accumulate points
xmax=max(X(:,1)); ymax=max(X(:,2)); 
xmin=min(X(:,1)); ymin=min(X(:,2));
plot(xmin, ymin,"."); plot(xmax, ymax,".");  % big enough
plot(X(:,1), X(:,2), ".");    % plot trajectory
title("Henon Map Iteration");
xlabel("Xn"); ylabel("Yn");