The recursive process of substitution tiling is a method of generating aperiodic tilings. Substitution tiling systems provide a rich source of aperiodic tilings. Several methods for constructing aperiodic tilings are known. The Penrose tilings are the best-known examples of aperiodic tilings. There are a few constructions of aperiodic tilings known. With respect to tilings the term aperiodic was sometimes used synonymously with the term non-periodic. Today there is a large amount of literature on aperiodic tilings. The second type, icosahedral quasicrystals, are aperiodic in all directions. A Penrose tiling is an example of an aperiodic tiling. An irreducible Markov chain only needs one aperiodic state to imply all states are aperiodic. Sometimes an energetical minimum or a maximum of entropy occur for such aperiodic structures. A task can be classified as either a periodic or aperiodic process. A Markov chain is aperiodic if every state is aperiodic. Acknowledging inspiration from Kepler, Penrose found matching rules for these shapes, obtaining an aperiodic set. Faraday waves have been observed to form large patches of aperiodic patterns.