aperiodicity造句

• Aperiodicity is also an important necessary condition for solving the road coloring problem.
• Aperiodicity of prototiles requires two or more dimensions.
• The aperiodicity of prototiles implies that a shifted copy of a tiling will never match the original.
• Joshua Socolar also gave another way to enforce aperiodicity, in terms of " alternating condition ".
• The orientation of the vertex arrows which force aperiodicity, then, can only be deduced from the entire infinite tiling.
• The " aperiodicity " referred to is a property of the particular set of prototiles; the various resulting tilings themselves are just non-periodic.
• A graphical illustration of the changing attractor over a range of c values illustrates the general behavior seen for all of these parameter analyses  the frequent transitions between periodicity and aperiodicity.
• Since some of these tilings are periodic, it follows that no decoration of the tiles which does force aperiodicity can be determined by looking at any finite patch of the tiling.
• The first movement is characterized by a sharp contrast between the aperiodicity of the first subject group, characterized by Arnold Schoenberg as " prose-like, " and the " wholly periodic " second subject group.
• Five sets of tiles discovered by Ammann were described in " Tilings and Patterns " and later, in collaboration with the authors of the book, he published a paper proving the aperiodicity for four of them.
• Despite this, the undecidability of the Domino Problem ensures that there must be infinitely many distinct principles of construction, and that in fact, there exist aperiodic sets of tiles for which there can be no proof of their aperiodicity.
• Chaim Goodman-Strauss suggested that a tiling be considered " 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 strongly aperiodic, while other sets are to be called " weakly aperiodic ".
• We let p n be the probability that, after n iterations, the cards are found in increasing order : first, I need to show that p n converges to some p as n-> infinity, regardless of the initial ordering, and find this p, apparently using the property of aperiodicity.
• The system was organized around seven major meters, state Annette Wilke and Oliver Moebus, called the " seven birds " or " seven mouths of Brihaspati ", and each had its own rhythm, movements and aesthetics wherein a non-linear structure ( aperiodicity ) was mapped into a four verse polymorphic linear sequence.
• However, long before the publication of " What is Life ? ", geneticist and 1946 Nobel-prize winner H . J . Muller had in his 1922 article " Variation due to Change in the Individual Gene " already laid out all the basic properties of the " heredity molecule " ( then not yet known to be DNA ) that Schr鰀inger was to re-derive in 1944 " from first principles " in " What is Life ? " ( including the " aperiodicity " of the molecule ), properties which Muller specified and refined additionally in his 1929 article " The Gene As The Basis of Life " and during the 1930s.