| 41. | He discovered several new aperiodic tilings, each among the simplest known examples of aperiodic sets of tiles.
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| 42. | He discovered several new aperiodic tilings, each among the simplest known examples of aperiodic sets of tiles.
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| 43. | In 1973 and 1974, Roger Penrose discovered a family of aperiodic tilings, now called Penrose tilings.
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| 44. | In turn, the interest in quasicrystals led to the discovery of several well-ordered aperiodic tilings.
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| 45. | As a corollary, infinitely many distinct tilings may be obtained from a single aperiodic set of tiles.
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| 46. | There are few constructions of aperiodic tilings known, even forty years after Berger's groundbreaking construction.
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| 47. | Owing to their combination of periodic and aperiodic structure, FK phases belong to the class of quasicrystals.
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| 48. | It can be shown that a finite state irreducible Markov chain is ergodic if it has an aperiodic state.
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| 49. | The theorem of Sch�tzenberger provides an algebraic characterization of star-free languages by means of aperiodic syntactic monoids.
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| 50. | However, the tiles shown below force the chair substitution structure to emerge, and so are themselves aperiodic.
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