11. It forms an aperiodic pattern known as a quasicrystal. 12. A sequence is Sturmian if and only if it is balanced and aperiodic . 13. A tiling is called aperiodic if its hull contains only non-periodic tilings. 14. The Fourier Bessel series expansion employs aperiodic and decaying Bessel functions as the basis. 15. It operates on an aperiodic or irregular schedule. 16. Many of these patterns are aperiodic penrose tilings. 17. An irreducible Markov chain only needs one aperiodic state to imply all states are aperiodic. 18. An irreducible Markov chain only needs one aperiodic state to imply all states are aperiodic . 19. Marcel-Paul Sch�tzenberger characterized star-free languages as those with aperiodic syntactic monoids. 20. In particular, the celebrated Penrose tiling is an example of an aperiodic substitution tiling.
