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Wang Tile
Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, ''without'' rotating or reflecting them. The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern. Domino problem In 1961, Wang conjectured that if a finite set of Wang tiles can tile the plane, then there also exists a ''periodic'' tiling, which, mathematically, is a tiling that is invariant under translations by vectors in a 2-dimensional lattice. This can be likened to the periodic tiling in a wallpaper pattern, where the overall pattern is a repetition of some smaller pattern. He also observed that this con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wang 11 Tiles
Wang may refer to: Names * Wang (surname) (王), a common Chinese surname * Wāng (汪), a less common Chinese surname * Titles in Chinese nobility * A title in Korean nobility * A title in Mongolian nobility Places * Wang River in Thailand * Wang Township, Minnesota, a township in the United States * Wang, Bavaria, a town in the district of Freising, Bavaria, Germany * Wang, Austria, a town in the district of Scheibbs in Lower Austria * An abbreviation for the town of Wangaratta, Australia * Wang Theatre, in Boston, Massacheussetts * Charles B. Wang Center, an Asian American center at Stony Brook University Other * Wang (Tibetan Buddhism), a form of empowerment or initiation * Wang tile, in mathematics, are a class of formal systems * Wang (musical), ''Wang'' (musical), an 1891 New York musical * Wang Film Productions, Taiwanese-American animation studios * Wang Laboratories, an American computer company founded by Dr. An Wang * WWNG, a radio station (1330 AM) licensed to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The very first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 0.87. Notable publications * The 1972 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge-matching Puzzle
An edge-matching puzzle is a type of tiling puzzle involving tiling an area with (typically regular) polygons whose edges are distinguished with colours or patterns, in such a way that the edges of adjacent tiles match. Edge-matching puzzles are known to be NP-complete, and capable of conversion to and from equivalent jigsaw puzzles and polyomino packing puzzle. The first edge-matching puzzles were patented in the U.S. by E. L. Thurston in 1892. Current examples of commercial edge-matching puzzles include the Eternity II puzzle, Tantrix, Kadon Enterprises' range of edge-matching puzzles, and the Edge Match Puzzles iPhone app. Notable variations MacMahon Squares MacMahon Squares is the name given to a recreational math puzzle suggested by British mathematician Percy MacMahon, who published a treatise on edge-colouring of a variety of shapes in 1921. This particular puzzle uses 24 tiles consisting of all permutations of 3 colors for the edges of a square. The tiles must be arra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greg Egan
Greg Egan (born 20 August 1961) is an Australian science fiction writer and amateur mathematician, best known for his works of hard science fiction. Egan has won multiple awards including the John W. Campbell Memorial Award, the Hugo Award, and the Locus Award. Life and work Egan holds a Bachelor of Science degree in Mathematics from the University of Western Australia. He published his first work in 1983. He specialises in hard science fiction stories with mathematical and quantum ontology themes, including the nature of consciousness. Other themes include genetics, simulated reality, posthumanism, mind uploading, sexuality, artificial intelligence, and the superiority of rational naturalism to religion. He often deals with complex technical material, like new physics and epistemology. He is a Hugo Award winner (with eight other works shortlisted for the Hugos) and has also won the John W. Campbell Memorial Award for Best Science Fiction Novel. His early stories feature s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diaspora (novel)
''Diaspora'' is a hard science fiction novel by the Australian writer Greg Egan which first appeared in print in 1997. It originated as the short story "Wang's Carpets" which originally appeared in the Greg Bear-edited anthology ''New Legends'' (Legend, London, 1995). The story appears as a chapter of the novel. Setting and premise An appended glossary explains many of the specialist terms in the novel. Egan invents several new theories of physics, beginning with Kozuch Theory, the dominant physics paradigm for nearly nine hundred years before the beginning of the novel. Kozuch Theory treats elementary particles as semi-point-like wormholes, whose properties can be explained entirely in terms of their geometries in six dimensions. Certain assumptions common to Egan's works inform the plot. This novel's setting is a posthuman future, in which transhumanism long ago (during the mid 21st century) became the default philosophy embraced by the vast majority of human cultures. Most of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Phenomena
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Problem
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers ''x'' and ''y'', does ''x'' evenly divide ''y''?". The answer is either 'yes' or 'no' depending upon the values of ''x'' and ''y''. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem. A decision procedure for the decision problem "given two numbers ''x'' and ''y'', does ''x'' evenly divide ''y''?" would give the steps for determining whether ''x'' evenly divides ''y''. One such algorithm is long division. If the remainder is zero the answer is 'yes', otherwise it is 'no'. A decision problem which can be solved by an algorithm is called ''decidable''. Decision problems typically appear in mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of '' states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that determines the new state of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heightfield
In computer graphics, a heightmap or heightfield is a raster image used mainly as Discrete Global Grid in secondary elevation modeling. Each pixel stores values, such as surface elevation data, for display in 3D computer graphics. A heightmap can be used in bump mapping to calculate where this 3D data would create shadow in a material, in displacement mapping to displace the actual geometric position of points over the textured surface, or for terrain where the heightmap is converted into a 3D mesh. A heightmap contains one channel interpreted as a distance of displacement or "height" from the "floor" of a surface and sometimes visualized as luma of a grayscale image, with black representing minimum height and white representing maximum height. When the map is rendered, the designer can specify the amount of displacement for each unit of the height channel, which corresponds to the “contrast” of the image. Heightmaps can be stored by themselves in existing grayscale ima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Procedural Texture
In computer graphics, a procedural texture is a texture created using a mathematical description (i.e. an algorithm) rather than directly stored data. The advantage of this approach is low storage cost, unlimited texture resolution and easy texture mapping. These kinds of textures are often used to model surface or volumetric representations of natural elements such as wood, marble, granite, metal, stone, and others. Usually, the natural look of the rendered result is achieved by the usage of fractal noise and turbulence functions. These functions are used as a numerical representation of the "randomness" found in nature. Solid texturing Solid texturing is a process where the texture generating function is evaluated over \mathbb^ at each visible surface point of the model so the resulting material properties (like color, shininess or normal) depends only on their 3D position, not their parametrized 2D surface position like in traditional 2D texture mapping. Consequently, soli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Procedural Synthesis
In computing, procedural generation is a method of creating data algorithmically as opposed to manually, typically through a combination of human-generated assets and algorithms coupled with computer-generated randomness and processing power. In computer graphics, it is commonly used to create textures and 3D models. In video games, it is used to automatically create large amounts of content in a game. Depending on the implementation, advantages of procedural generation can include smaller file sizes, larger amounts of content, and randomness for less predictable gameplay. Procedural generation is a branch of media synthesis. Overview The term ''procedural'' refers to the process that computes a particular function. Fractals are geometric patterns which can often be generated procedurally. Commonplace procedural content includes textures and meshes. Sound is often also procedurally generated, and has applications in both speech synthesis as well as music. It has been used to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peptide Nucleic Acid
Peptide nucleic acid (PNA) is an artificially synthesized polymer similar to DNA or RNA. Synthetic peptide nucleic acid oligomers have been used in recent years in molecular biology procedures, diagnostic assays, and antisense therapies. Due to their higher binding strength, it is not necessary to design long PNA oligomers for use in these roles, which usually require oligonucleotide probes of 20–25 bases. The main concern of the length of the PNA-oligomers is to guarantee the specificity. PNA oligomers also show greater specificity in binding to complementary DNAs, with a PNA/DNA base mismatch being more destabilizing than a similar mismatch in a DNA/DNA duplex. This binding strength and specificity also applies to PNA/RNA duplexes. PNAs are not easily recognized by either nucleases or proteases, making them resistant to degradation by enzymes. PNAs are also stable over a wide pH range. Though an unmodified PNA cannot readily cross the cell membrane to enter the cytosol, cov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
