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fractals - 3 dictionary results
frac⋅tal
[frak-tl] 
tl
–noun Mathematics, Physics.
| a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions) are greater than the spatial dimensions. |
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Based on the Random House Dictionary, © Random House, Inc. 2009.
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Based on the Random House Dictionary, © Random House, Inc. 2009.
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Link To fractals
| frac·tal (frāk'təl) n. A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature. [French, from Latin frāctus, past participle of frangere, to break; see fraction.] |
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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fractal (frāk'təl) Pronunciation Key
(click for larger image in new window) A complex geometric pattern exhibiting self-similarity in that small details of its structure viewed at any scale repeat elements of the overall pattern. See more at chaos. Our Living Language : Fractals are often associated with recursive operations on shapes or sets of numbers, in which the result of the operation is used as the input to the same operation, repeating the process indefinitely. The operations themselves are usually very simple, but the resulting shapes or sets are often dramatic and complex, with interesting properties. For example, a fractal set called a Cantor dust can be constructed beginning with a line segment by removing its middle third and repeating the process on the remaining line segments. If this process is repeated indefinitely, only a "dust" of points remains. This set of points has zero length, even though there is an infinite number of points in the set. The Sierpinski triangle (or Sierpinski gasket) is another example of such a recursive construction procedure involving triangles (see the illustration). Both of these sets have subparts that are exactly the same shape as the entire set, a property known as self-similarity. Under certain definitions of dimension, fractals are considered to have non-integer dimension: for example, the dimension of the Sierpinski triangle is generally taken to be around 1.585, higher than a one-dimensional line, but lower than a two-dimensional surface. Perhaps the most famous fractal is the Mandelbrot set, which is the set of complex numbers C for which a certain very simple function, Z2 + C, iterated on its own output (starting with zero), eventually converges on one or more constant values. Fractals arise in connection with nonlinear and chaotic systems, and are widely used in computer modeling of regular and irregular patterns and structures in nature, such as the growth of plants and the statistical patterns of seasonal weather. |
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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