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Pattern Matching Programming Languages
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. Any of the senses may directly observe patterns. Conversely, abstract patterns in science, mathematics, or language may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual patterns in nature are often chaotic, rarely exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection. Patterns have an underlying mathematical structure; indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict reg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Abstraction
Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or " concrete") signifiers, first principles, or other methods. "An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a ''group'', ''field'', or ''category''.Suzanne K. Langer (1953), ''Feeling and Form: a theory of art developed from Philosophy in a New Key'' p. 90: " Sculptural form is a powerful abstraction from actual objects and the three-dimensional space which we construe ... through touch and sight." Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Sea Anemone
Sea anemones are a group of predatory marine invertebrates of the order Actiniaria. Because of their colourful appearance, they are named after the '' Anemone'', a terrestrial flowering plant. Sea anemones are classified in the phylum Cnidaria, class Anthozoa, subclass Hexacorallia. As cnidarians, sea anemones are related to corals, jellyfish, tube-dwelling anemones, and ''hydra (genus), Hydra''. Unlike jellyfish, sea anemones do not have a Jellyfish#Life history and behavior, medusa stage in their life cycle. A typical sea anemone is a single polyp (zoology), polyp attached to a hard surface by its base, but some species live in soft sediment, and a few float near the surface of the water. The polyp has a columnar trunk topped by an oral disc with a ring of tentacles and a central mouth. The tentacles can be retracted inside the body cavity or expanded to catch passing prey. They are armed with cnidocytes (stinging cells). In many species, additional nourishment comes from a sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Rotational Symmetry
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids. Formal treatment Formally the rotational symmetry is symmetry with respect to some or all rotations in ''m''-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore, a symmetry group of rotational symmetry is a subgroup of ''E''+(''m'') (see Euclidean group). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Reflection Symmetry
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry splits the shape in half and those halves should be identical. Symmetric function In formal terms, a mathematical object is symmetric with respect to a given operation such as reflection, rotation or translation, if, when applied to the object, this operation preserves some property of the object. The set of operations that preserve a given property of the object form a group. Two objects are symmetric to each other with respect to a given group of operations if one is obtained from the other by some of the operations (and vice versa). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, if the radius of a filled s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Decorative Arts
] The decorative arts are arts or crafts whose object is the design and manufacture of objects that are both beautiful and functional. It includes most of the arts making objects for the interiors of buildings, and interior design, but not usually architecture. Ceramic art, metalwork, furniture, jewellery, fashion, various forms of the textile arts and glassware are major groupings. Applied arts largely overlaps with decorative arts, and the modern making of applied art is usually called design. The decorative arts are often categorized in distinction to the "fine arts", namely painting, drawing, photography, and large-scale sculpture, which generally produce objects solely for their aesthetic quality and capacity to stimulate the intellect. Distinction from the fine arts The distinction between the decorative and fine arts essentially arose from the post-Renaissance art of the West, where the distinction is for the most part meaningful. This distinction is much less me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Die (manufacturing)
A die is a specialized machine tool used in manufacturing industries to cut and/or form material to a desired shape or profile. Stamping dies are used with a press, as opposed to drawing dies (used in the manufacture of wire) and casting dies (used in molding) which are not. Like molds, dies are generally customized to the item they are used to create. Products made with dies range from simple paper clips to complex pieces used in advanced technology. Continuous-feed laser cutting may displace the analogous die-based process in the automotive industry, among others. Die stamping Blanking and piercing are two die cutting operations, and bending is an example of a die forming operation. Die forming Forming operations work by deforming materials like sheet metal or plastic using force ( compression, tension, or both) and rely on the material's mechanical properties. Forming dies are typically made by tool and die makers and put into production after mounting into a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Software Design Pattern
In software engineering, a software design pattern is a general, reusable solution to a commonly occurring problem within a given context in software design. It is not a finished design that can be transformed directly into source or machine code. Rather, it is a description or template for how to solve a problem that can be used in many different situations. Design patterns are formalized best practices that the programmer can use to solve common problems when designing an application or system. Object-oriented design patterns typically show relationships and interactions between classes or objects, without specifying the final application classes or objects that are involved. Patterns that imply mutable state may be unsuited for functional programming languages. Some patterns can be rendered unnecessary in languages that have built-in support for solving the problem they are trying to solve, and object-oriented patterns are not necessarily suitable for non-object-oriented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Motif (visual Arts)
In art and iconography, a motif () is an element of an image. The term can be used both of figurative and narrative art, and ornament and geometrical art. A motif may be repeated in a pattern or design, often many times, or may just occur once in a work. A motif may be an element in the iconography of a particular subject or type of subject that is seen in other works, or may form the main subject, as the Master of Animals motif in ancient art typically does. The related motif of confronted animals is often seen alone, but may also be repeated, for example in Byzantine silk and other ancient textiles. Where the main subject of an artistic work such as a painting is a specific person, group, or moment in a narrative, that should be referred to as the "subject" of the work, not a motif, though the same thing may be a "motif" when part of another subject, or part of a work of decorative art such as a painting on a vase. Ornamental or decorative art can usually be analysed in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |