The invariant manifold is a line of infinite length, therefore only part of it is shown. Distance along the invariant manifold is measured in terms of the number of iteration steps that are needed to get to a certain segment of the manifold close to the fixed point. This number is called the type. The different types are given different colors, where blue is type 1 and red is type 4. Every intersection of the stable and unstable manifolds is a homoclinic point.
Homoclinic points are forward and backward asymptotic to the fixed point.
The main picture shows the manifolds up to type 5, but for a smaller parameter, i.e. there are fewer loops. Increasing the type increase the amount of details shown, in principle the amount of detail is unbounded, but it can obviously not be resolved on a T-shirt. The picture up to type 7 is already at the limit of a typical screen resolution. On the right you can see the loops up to type 6. On the T-shirt we also showed the actual formula for the iteration of the map in a somewhat cryptic form.