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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. Algorithm 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. Logo A Logo program to draw the Gosper curve using turtle graphics: to rg :st :ln make "st :st - 1 make "ln :ln / sqrt 7 if :st > 0 g :st :ln rt 60 gl :st :ln rt 120 gl :st :ln lt 60 rg :st :ln lt 120 rg :st :ln rg :st :ln lt 60 gl :st :l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gosper Curve 3
Gosper may refer to: *Gosper County, Nebraska *Gosper curve *Bill Gosper, American mathematician *Kevan Gosper Richard Kevan Gosper, AO (born 19 December 1933) is an Australian former athlete who mainly competed in the 400 metres. He was formerly a Vice President of the International Olympic Committee, and combined Chairman and CEO of Shell Australia ..., 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] |
Turtle Graphics
In computer graphics, turtle graphics are vector graphics using a relative cursor (the "turtle") upon a Cartesian plane (x and y axis). Turtle graphics is a key feature of the Logo programming language. Overview The turtle has three attributes: a location, an orientation (or direction), and a pen. The pen, too, has attributes: color, width, and on/off state (also called ''down'' and ''up''). The turtle moves with commands that are relative to its own position, such as "move forward 10 spaces" and "turn left 90 degrees". The pen carried by the turtle can also be controlled, by enabling it, setting its color, or setting its width. A student could understand (and predict and reason about) the turtle's motion by imagining what they would do if they were the turtle. Seymour Papert called this "body syntonic" reasoning. A full turtle graphics system requires control flow, procedures, and recursion: many turtle drawing programs fall short. From these building blocks one can build ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gosper Island Tesselation
Gosper may refer to: *Gosper County, Nebraska *Gosper curve *Bill Gosper, American mathematician *Kevan Gosper Richard Kevan Gosper, AO (born 19 December 1933) is an Australian former athlete who mainly competed in the 400 metres. He was formerly a Vice President of the International Olympic Committee, and combined Chairman and CEO of Shell Australia ..., 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 Tesselation 2
Gosper may refer to: *Gosper County, Nebraska *Gosper curve *Bill Gosper, American mathematician *Kevan Gosper Richard Kevan Gosper, AO (born 19 December 1933) is an Australian former athlete who mainly competed in the 400 metres. He was formerly a Vice President of the International Olympic Committee, and combined Chairman and CEO of Shell Australia ..., 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 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. If two angles of a triangle h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane (mathematics)
In mathematics, a plane is a Euclidean space, Euclidean (flatness (mathematics), flat), two-dimensional surface (mathematics), surface that extends indefinitely. A plane is the two-dimensional analogue of a point (geometry), point (zero dimensions), a line (geometry), line (one dimension) and three-dimensional space. Planes can arise as Euclidean subspace, subspaces of some higher-dimensional space, as with one of a room's walls, infinitely extended, or they may enjoy an independent existence in their own right, as in the setting of two-dimensional Euclidean geometry. Sometimes the word ''plane'' is used more generally to describe a two-dimensional surface (mathematics), surface, for example the hyperbolic plane and elliptic plane. When working exclusively in two-dimensional Euclidean space, the definite article is used, so ''the'' plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graph of a function, graphing are p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, 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. 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gosper Island 4
Gosper may refer to: *Gosper County, Nebraska *Gosper curve *Bill Gosper, American mathematician *Kevan Gosper Richard Kevan Gosper, AO (born 19 December 1933) is an Australian former athlete who mainly competed in the 400 metres. He was formerly a Vice President of the International Olympic Committee, and combined Chairman and CEO of Shell Australia ..., 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, American mathematician *Kevan Gosper Richard Kevan Gosper, AO (born 19 December 1933) is an Australian former athlete who mainly competed in the 400 metres. He was formerly a Vice President of the International Olympic Committee, and combined Chairman and CEO of Shell Australia ..., 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 *Bill Gosper, American mathematician *Kevan Gosper Richard Kevan Gosper, AO (born 19 December 1933) is an Australian former athlete who mainly competed in the 400 metres. He was formerly a Vice President of the International Olympic Committee, and combined Chairman and CEO of Shell Australia ..., 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, American mathematician *Kevan Gosper Richard Kevan Gosper, AO (born 19 December 1933) is an Australian former athlete who mainly competed in the 400 metres. He was formerly a Vice President of the International Olympic Committee, and combined Chairman and CEO of Shell Australia ..., 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 0
Gosper may refer to: *Gosper County, Nebraska *Gosper curve *Bill Gosper, American mathematician *Kevan Gosper Richard Kevan Gosper, AO (born 19 December 1933) is an Australian former athlete who mainly competed in the 400 metres. He was formerly a Vice President of the International Olympic Committee, and combined Chairman and CEO of Shell Australia ..., 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] |
