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Peano-Gosper Curve
The Gosper curve, named after Bill Gosper, also known as the Peano-Gosper Curve and the flowsnake (a spoonerism of snowflake), is a space-filling curve whose limit set is rep-7. It is a fractal curve similar in its construction to the dragon curve and the Hilbert curve. The Gosper curve can also be used for efficient hierarchical hexagonal clustering and indexing. Lindenmayer system The Gosper curve can be represented using an L-system with rules as follows: * Angle: 60° * Axiom: A * Replacement rules: ** A \mapsto A-B--B+A++AA+B- ** B \mapsto +A-BB--B-A++A+B In this case both A and B mean to move forward, + means to turn left 60 degrees and - means to turn right 60 degrees - using a "turtle"-style program such as Logo. Properties The space filled by the curve is called the Gosper island. The first few iterations of it are shown below: The Gosper Island can tile the plane. In fact, seven copies of the Gosper island can be joined to form a shape that is similar, but sca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gosper Curve 4
Gosper may refer to: *Gosper County, Nebraska *Gosper curve *Bill Gosper (born 1943), American mathematician *Kevan Gosper (1933–2024), Australian athlete and 1956 Olympic medalist *John J. Gosper (1843–1913), Nebraska Secretary of State (1873–1875) and Secretary of Arizona Territory (1875–1882). {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Similarity (geometry)
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (geometry), scaling (enlarging or reducing), possibly with additional translation (geometry), translation, rotation (mathematics), rotation and reflection (mathematics), reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruence (geometry), congruent to the result of a particular uniform scaling of the other. For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other. This is because two ellipse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane (mathematics)
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so ''the'' Euclidean plane refers to the whole space. Several notions of a plane may be defined. The Euclidean plane follows Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set ..., and in particular the parallel postulate. A projective plane may be constructed by adding "points at infinity" where two otherwise parallel lines would intersect, so that every pair of lines intersects in exactly one point. The elliptic plane may be further defined by adding a metr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include '' regular tilings'' with regular polygonal tiles all of the same shape, and '' semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is 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 of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gosper Island 4
Gosper may refer to: *Gosper County, Nebraska *Gosper curve *Bill Gosper (born 1943), American mathematician *Kevan Gosper Richard Kevan Gosper, AO (19 December 1933 – 19 July 2024) was an Australian athlete who mainly competed in the 400 metres. He was a Vice President of the International Olympic Committee, and combined chairman and CEO of Shell Australia. ... (1933–2024), Australian athlete and 1956 Olympic medalist * John J. Gosper (1843–1913), Nebraska Secretary of State (1873–1875) and Secretary of Arizona Territory (1875–1882). {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gosper Island 3
Gosper may refer to: *Gosper County, Nebraska *Gosper curve *Bill Gosper (born 1943), American mathematician *Kevan Gosper (1933–2024), Australian athlete and 1956 Olympic medalist *John J. Gosper (1843–1913), Nebraska Secretary of State (1873–1875) and Secretary of Arizona Territory (1875–1882). {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gosper Island 2
Gosper may refer to: * Gosper County, Nebraska *Gosper curve The Gosper curve, named after Bill Gosper, also known as the Peano-Gosper Curve and the flowsnake (a spoonerism of Koch snowflake, snowflake), is a space-filling curve whose limit set is rep-tile, rep-7. It is a fractal curve similar in its cons ... * Bill Gosper (born 1943), American mathematician * Kevan Gosper (1933–2024), Australian athlete and 1956 Olympic medalist * John J. Gosper (1843–1913), Nebraska Secretary of State (1873–1875) and Secretary of Arizona Territory (1875–1882). {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gosper Island 1
Gosper may refer to: *Gosper County, Nebraska *Gosper curve *Bill Gosper (born 1943), American mathematician *Kevan Gosper Richard Kevan Gosper, AO (19 December 1933 – 19 July 2024) was an Australian athlete who mainly competed in the 400 metres. He was a Vice President of the International Olympic Committee, and combined chairman and CEO of Shell Australia. ... (1933–2024), Australian athlete and 1956 Olympic medalist * John J. Gosper (1843–1913), Nebraska Secretary of State (1873–1875) and Secretary of Arizona Territory (1875–1882). {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logo Programming Language
Logo is an educational programming language, designed in 1967 by Wally Feurzeig, Seymour Papert, and Cynthia Solomon. The name was coined by Feurzeig while he was at Bolt, Beranek and Newman, and derives from the Greek ''logos'', meaning 'word' or 'thought'. A general-purpose language, Logo is widely known for its use of turtle graphics, in which commands for movement and drawing produced line or vector graphics, either on screen or with a small robot termed a turtle. The language was conceived to teach concepts of programming related to Lisp and only later to enable what Papert called " body-syntonic reasoning", where students could understand, predict, and reason about the turtle's motion by imagining what they would do if they were the turtle. There are substantial differences among the many dialects of Logo, and the situation is confused by the regular appearance of turtle graphics programs that are named Logo. Logo is a multi-paradigm adaptation and dialect of Lisp, a func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
