% Integrate the Lorenz equations. % Lorenz, E. N., 1963, Deterministic nonperiodic flow, Journal of the % Atmospheric Sciences, 20, 130-141. % Equations: % \dot{x}(1) = -\sigma*x(1) + \sigma*x(2) % \dot{x}(2) = -x(1)*x(3) + r*x(1) - x(2) % \dot{x}(3) = x(1)*x(2) - b*x(3) % Written by Jim Hansen, Feb 2003 for 12.990 students % Specify the dimension of the system dim = 3; % Specify the initial conditions x = [10 20 30]; % Specify the parameter values (sigma, r, and b) par = [10 28 8/3]; % Specify the integration step size h = 0.01; % Specify the length of integration steps = 2^12; % Integrate the equations over length steps to remove any transient behavior for i=1:steps xout=step_it('derivsL63',x,par,h,dim); x=xout; end % Integrate the equations over length steps and record state for plotting for i=1:steps xout=step_it('derivsL63',x,par,h,dim); state(i,:)=xout; x=xout; end % Make a pretty picture figure;plot3(state(:,3),state(:,2),state(:,1)'.'); title('The Lorenz attractor'); xlabel('z');ylabel('y');zlabel('x'); print -djpeg90 L63.jpg