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aperiodic

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aperiodic
aperiodic, a. (ˌeɪpɪərɪˈɒdɪk) [f. Gr. ἀ- priv. (a- prefix 14) + periodic a.1] Not periodic; without regular recurrence. In various techn. senses (see quots.); spec. of a galvanometer, without periodic vibrations, ‘dead-beat’.1879 Encycl. Brit. X. 50/2 An intermediate stage called the aperiodic state... Oxford English Dictionary
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Aperiodic (disambiguation)
Aperiodic means non-periodic. Typically it refers to aperiodic function. Aperiodic may also refer to: Aperiodic finite state automaton Aperiodic frequency Aperiodic graph Aperiodic semigroup Aperiodic set of prototiles wikipedia.org
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Aperiodic crystal
To understand aperiodic crystal structures, one must use the superspace approach. Superspace Dimensionalities of aperiodic crystals: , , . wikipedia.org
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Turn aperiodic function to periodic I got a quick question regarding aperiodic functions. Let's suppose I have an aperiodic function $$ f(x) = \left\\{ \begin{array}{l l} \exp(-t) & \quad -2\leq t \leq2,\\\ 0 & \quad ...
You could represent the function as a Fourier series: $$g(x) = \sum_{n=-\infty}^{\infty} c_n \, e^{i n \pi x/2}$$ where $$\begin{align}c_n &= \frac1{4} \int_{-2}^2 dt\, e^{-t} \, e^{-i n \pi t/2}\\\ &= \frac1{4} \int_{-2}^2 dt \, e^{-(1 + i n \pi/2) t}\\\ &= \frac{(-1)^n}{4(1 + i n \pi/2)}\left ( e^...
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Aperiodic graph
if and only if the graph is aperiodic. graph is aperiodic. wikipedia.org
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Show that $x \cos(cx)$ is aperiodic I'm using the function $f(x)=x~cos(cx)$ in a paper and the periodicity of the function is relevant. Is there a simple way to show that a function of this form is aperiodic, or is it...
For $c=0$ it's obvious. If $c>0$ $$\lim_{n\to\infty }\frac{2\pi n}{c}\cos\left(c\frac{2\pi n}{c}\right)=+\infty $$ and $$\lim_{n\to\infty }\frac{\pi+2n\pi}{c}\cos\left(c\frac{\pi+2\pi n}{c}\right)=-\infty $$ therefore it's not periodic. For $c<0$ you the proof goes the same.
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Aperiodic set of prototiles
However, an aperiodic set of tiles can only produce non-periodic tilings. The known aperiodic sets of prototiles are seen on the list of aperiodic sets of tiles. wikipedia.org
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Aperiodic hexagonal tiling? Is there any known aperiodic tiling of the plane using hexagons? Wang tiles are a known aperiodic tiling using squares. I'm looking for something similar using hexagons.
A quick Google search turned up <
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List of aperiodic sets of tiles
If a given set of tiles allows only nonperiodic tilings, 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 it is the tiles themselves that are aperiodic wikipedia.org
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non-trivial non-repetitive aperiodic tiling of the plane Which is the less trivial example of non-repetitive aperiodic tiling of the plane you know? I cannot come up with a famous non-repetitive tiling. Are there an...
I guess take any Penrose tiling (or some other repetitive aperiodic tiling) and replace a single tile with the same tile but of a new colour, or if you
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why is this Markov Chain aperiodic I have this Matrix: $$P=\begin{pmatrix} 0 & 1 \\\ 0.3 & 0.7 \end{pmatrix}$$ this markov chain is said to be aperiodic, I dont understand how it comes to it. Period $\delta$ is the...
Since my comment provided sufficient clarification: When there's a stationary state, your system will evolve towards that state. In your case, the two left eigenvectors are $(−1,1)$ and $(3,10)$ with corresponding eigenvalues $−0.3$ and $1$. Every other state of the system can be decomposed into tho...
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Sufficient condition for a Markov chain to be Aperiodic If I want to prove that a Markov chain is aperiodic, then if I can show that $P(X_{n+1}=i\mid X_n=i)\gt 0$ $ \forall i$. Then can I say that the chain is aperiodic?
It is true that $p_{ii}(1) > 0$ implies that the state $i$ is aperiodic. So your idea can work if you're lucky. However, it is possible for a state $i$ to be aperiodic when $p_{ii} (1) = 0$.
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Is there an aperiodic tiling consisting of deformed hexagons? The typical Penrose tiling consists of two deformed quadrangles. But it's there any aperiodic tiling consisting entirely of two or more deformed hexagons? ...
Yes. Use the Penrose Rhombus Tiling as a start. The edges with a round bump, use a straight line. Those with the triangle, use two lines. !enter image description here
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Why is the movement of a Chess King aperiodic? Imagine we have a king by itself on a chess board, making random moves around the board. Although it is apparently aperiodic, wouldn't the corresponding Markov chain to t...
Your mathematics is correct but your understanding of the rules of chess is not. A king on any square that is not on the edge of the board can move to any of eight squares: the four that share a common edge with the one he's on and the four that share only a common vertex.
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Aperiodicity of Markov chain If a markov chain which has many states but only one state has a self-loop edge, then does it mean that the markov chain is aperiodic? Or every state in the markov chain has to have self-l...
Yes, the Markov chain you gave is aperiodic. the underlying graph is strongly connected (or, in other words, the MC is irreducible) and contains at least one self-loop, then the Markov chain is aperiodic
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