This figure shows you a stable manifold for a periodic halo orbit with a z-amplitude of .00634 AU. The black stripes represent time contours of the surface. If a space craft were to get on this surface with the correct velocity, it would be taken to the periodic orbit. The periodic orbit is represented by the purple circle surrounding the libration point L1. The Earth is at the origin, where the axes intersect. The red line is the x-axis, the green line is the y-axis, and the blue line is the -z-axis.
This figure shows the same manifold as above from a slightly different viewpoint. The black stripes represent trajectories on the manifold. The periodic orbit is the oval opening pointed towards the viewer.