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construction, and that in fact, there exist aperiodic sets of tiles for which there can be no proof of their aperiodicity. However, there are three principles...

In mathematics, an aperiodic semigroup is a semigroup S such that every element is aperiodic, that is, for each x in S there exists a positive integer...

Markov chain is aperiodic if and only if this graph is aperiodic. Thus, aperiodicity of graphs is a useful concept in analyzing the aperiodicity of Markov chains...

function. Aperiodic may also refer to: Aperiodic finite state automaton Aperiodic frequency Aperiodic graph Aperiodic semigroup Aperiodic set of prototiles...

Aperiodic crystals lack three-dimensional translational symmetry but still exhibit three-dimensional long-range order. In other words, they are periodic...

such that all possible tessellation patterns are non-periodic. The aperiodicity referred to is a property of the particular set of prototiles; the various...

strongly aperiodic if it admits no infinite cyclic group of Euclidean motions as symmetries, and that only tile sets which enforce strong aperiodicity be called...

then this set of tiles is called aperiodic. The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking...

property loosely described as long-range order. Experimentally, the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that...

called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern (an aperiodic set of prototiles). A tessellation...

that exhibit periodicity. Any function that is not periodic is called aperiodic. A function f is said to be periodic if, for some nonzero constant P,...

recording can show in which of these general regions the recording was made. Aperiodic frequency is the rate of incidence or occurrence of non-cyclic phenomena...

search to prove that 10 tiles or 3 colors are insufficient to force aperiodicity. This set, shown above in the title image, can be examined more closely...

similar technique has been used in aftermarket car audio; it is called "aperiodic membrane" (AP). A resistive mat is placed in front of or directly behind...

: 108  Stroboscopy may be relatively normal or may reveal asymmetry, aperiodicity, and reduced mucosal wave patterns. Other features of the laryngeal tissues...

Bridlington, England, who is best known for his discoveries related to aperiodic monotiles that helped to solve the einstein problem. Smith discovered...

prototile. A set of prototiles is said to be aperiodic if every tiling with those prototiles is an aperiodic tiling. In March 2023, four researchers, Chaim...

of tiles consisting of a dart and a kite shape can be used to create aperiodic Penrose tilings, though there is no evidence that such a set was used...

allow a periodic tiling, but this constraint is not sufficient to force aperiodicity, as figure 1 above shows. There are two kinds of tile, both of which...

M.V. Jaric, ed, Introduction to the Mathematics of Quasicrystals (Aperiodicity and Order, Vol 2) ISBN 0-12-040602-0, Academic Press, 1989. Devadoss...