In my studying of dynamical systems I stumbled upon the Hénon Map today, a two-dimensional dynamical system with a strange attractor which demonstrates chaotic behaviour. The system is described by a coupled pair of equations. Here’s what the classical version looks like:

There are only two parameters, but playing around with them yields some interesting results:

Again, the code to implement this is pretty simple, so I’ll post it here as opposed to GitHub (though I’ll probably post a version on GitHub which draws the system state after each iteration):

a = 1.4;

b = 0.3;

iterations = 10000;

x = zeros(1, iterations);

y = zeros(1, iterations);

% simulation

for i=1:iterations

x(1,i+1) = 1-(a*x(1,i)^2) + y(1,i);

y(1,i+1) = b*x(1,i);

end

% plotting

plot(x(5:iterations),y(5:iterations), '.k','MarkerSize',3)

line1 = sprintf('Henon Map with %.0f iterations', iterations);

line2 = sprintf('a = %.2f, b = %.5f', a, b);

title({line1, line2});

xlabel('x')

ylabel('y')