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# fractal

[ **frak**-tl ]

## noun

*Mathematics, Physics.*an irregular geometric structure that cannot be described by classical geometry because magnification of the structure reveals repeated patterns of similarly irregular, but progressively smaller, dimensions: fractals are especially apparent in natural forms and phenomena because the geometric properties of the physical world are largely abstract, as with clouds, crystals, tree bark, or the path of lightning.*Architecture, Decorative Art.*a design or construction that uses the concept and mechanics of fractal geometry:*Fractals distinguish the facade of the library, revealing recursive patterns, the smaller parts mirroring the larger parts.*

## adjective

*Mathematics, Physics.*of or relating to a fractal:*fractal geometry; fractal dimensions; fractal curves.**Architecture, Decorative Art.*of or relating to a design or construction that uses the concept and mechanics of fractal geometry:*The progression of forms from distant view to excruciating detail is born of the fractal composition that brands her work.*

fractal

/ ˈfræktəl /

## noun

- a figure or surface generated by successive subdivisions of a simpler polygon or polyhedron, according to some iterative process

## adjective

- of, relating to, or involving such a process
*fractal geometry**fractal curve*

fractal

/ frăk**′**təl /

- 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

fractal

- Contraction of “fractional dimension.” This is a term used by mathematicians to describe certain geometrical structures whose shape appears to be the same regardless of the level of magnification used to view them. A standard example is a seacoast, which looks roughly the same whether viewed from a satellite or an airplane, on foot, or under a magnifying glass. Many natural shapes approximate fractals, and they are widely used to produce images in television and movies.

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## Word History and Origins

Origin of fractal^{1}

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## Word History and Origins

Origin of fractal^{1}

C20: from Latin

*frāctus*past participle of*frangere*to breakDiscover More

## A Closer Look

*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, Z

^{2}+ 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.

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