  Embedding techniques allow the approximations of finite dimensional
attractors and manifolds of infinite dimensional dynamical systems via
subdivision and continuation methods. These approximations give a topological
one-to-one image of the original set. In order to additionally reveal their
geometry we use diffusion mapst o find intrinsic coordinates. We illustrate our
results on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky
equation, as well as for the attractor of the Mackey-Glass delay differential
equation.
