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