% We solve the Lorentzian ODE IVP with ode45 numerically, then plot the
% results parametrically on plane, and in space. For fun play around with
% parameter values sigma, beta and rho -- and remember, under no
% circumstances are you to disturb the butterfly. 

sig = 10;
beta = 8/3;
rho = 28;
f = @(t,x)([-sig*x(1)+sig*x(2); rho*x(1)-x(2)-x(1).*x(3); -beta*x(3)+x(1)*x(2)]);
y0 = [-6.2 12.5 3.7]';
[t,y] = ode45(f,[0,20],y0);
plot(y(:,1),y(:,3));
figure;
plot3(y(:,1),y(:,2),y(:,3))
grid