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aperiodic group

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  • Aperiodic tiling — are an aperiodic set of tiles, since they admit only non periodic tilings of the plane:] Any of the infinitely many tilings by the Penrose tiles is non periodic. More informally, many refer to the Penrose tilings as being aperiodic tilings , but… …   Wikipedia

  • Aperiodic monoid — In mathematics, an aperiodic semigroup is a semigroup S such that for every x ∈ S , there exists a nonnegative integer n such that xn = xn + 1 .An aperiodic monoid is an aperiodic semigroup which is a monoid. This notion is in some sense… …   Wikipedia

  • Wallpaper group — A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and… …   Wikipedia

  • Quasicrystal — Atomic model of an aluminum palladium manganese (Al Pd Mn) quasicrystal surface. Similar to Fig. 6 in Ref.[1] A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can… …   Wikipedia

  • List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A …   Wikipedia

  • Krohn–Rhodes theory — In mathematics and computer science, Krohn Rhodes theory is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These turn out to correspond to finite aperiodic semigroups and …   Wikipedia

  • Necklace (combinatorics) — In combinatorics, a k ary necklace of length n is an equivalence class of n character strings over an alphabet of size k, taking all rotations as equivalent. It represents a structure with n circularly connected beads of up to k different colors …   Wikipedia

  • Special classes of semigroups — In mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying additional properties or conditions. Thus the class of commutative semigroups consists… …   Wikipedia

  • Substitution tiling — A tile substitution is a useful method for constructing highly ordered tilings. Most importantly, some tile substitutions generate aperiodic tilings, which are tilings whose prototiles do not admit any tiling with translational symmetry. The most …   Wikipedia

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

  • Markov chain — A simple two state Markov chain. A Markov chain, named for Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized …   Wikipedia

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