“fractal”的概念、定义、翻译、参考文献-科学参考

fractal

Physics

A curve or surface generated by a process involving successive subdivision. For example, a snowflake curve can be produced by starting with an equilateral triangle and dividing each side into three segments. The middle segments are then replaced by two equal segments, which form the sides of a smaller equilateral triangle. This gives a twelve-sided star-shaped figure. The next stage is to subdivide each of the sides of this figure in the same way, and so on. The result is a developing figure that resembles a snowflake. In the limit, this figure has ‘fractional dimension’—i.e. a dimension between that of a line (1) and a surface (2); the dimension of the snowflake curve is 1.26. The study of this type of self-similarity in figures is used in certain branches of physics, such as crystal growth. Fractals are also important in chaos theory and in computer graphics. See also Mandelbrot set.

Mathematics

A set whose fractal dimension exceeds its topological dimension. Fractals are sets with infinitely complex structure and usually possess some measure of self‐similarity, whereby any part of the set contains within it a scaled‐down version of the whole set. Examples are the Cantor set, the Koch curve, and the Sierpinski triangle.
http://sprott.physics.wisc.edu/fractals.htm Examples of colourful fractal images.

Statistics

An infinite set of points, usually in a plane, whose fractal dimension is not an integer. Fractals are usually self-similar, i.e. any part of the fractal contains scaled-down versions of the whole fractal. The word ‘fractal’ was coined by Mandelbrot in 1975. For a well-known example of a fractal, see snowflake curve.

Chemistry

A curve or surface generated by a process involving successive subdivision. For example, a snowflake curve can be produced by starting with an equilateral triangle and dividing each side into three segments. The middle segments are then replaced by two equal segments, which would form the sides of a smaller equilateral triangle. This gives a 12-sided star-shaped figure. The next stage is to subdivide each of the sides of this figure in the same way, and so on. The result is a developing figure that resembles a snowflake. In the limit, this figure has ‘fractional dimension’ – i.e. a dimension between that of a line (1) and a surface (2); the dimension of the snowflake curve is 1.26. The study of this type of ’self-similar’ figure is used in certain branches of chemistry – for example, crystal growth. Fractals are also important in chaos theory and in computer graphics.

Computer

A set whose Hausdorff-Besicovitch dimension strictly exceeds its topological dimension. Intuitively, a fractal is a set which at all magnifications reveals a set that is exactly the same (self-similar). Such sets can be generated by the repeated application of some collection of maps. The term is generally associated with Benoit Mandelbrot and appeared in the literature in the late 1970s. Many naturally occurring objects, such as trees, coastlines, and clouds, are considered to have fractal properties, hence their interest to computer graphics.

Geology and Earth Sciences

A geometric entity which has a basic pattern that is repeated at ever decreasing sizes. Fractal patterns are not able to fill spaces and are hence described as having fractal dimension. Fractals occur frequently in nature, such as in forked lightning or in chaotic systems (see chaos).

单词	fractal
释义	fractal Physics A curve or surface generated by a process involving successive subdivision. For example, a snowflake curve can be produced by starting with an equilateral triangle and dividing each side into three segments. The middle segments are then replaced by two equal segments, which form the sides of a smaller equilateral triangle. This gives a twelve-sided star-shaped figure. The next stage is to subdivide each of the sides of this figure in the same way, and so on. The result is a developing figure that resembles a snowflake. In the limit, this figure has ‘fractional dimension’—i.e. a dimension between that of a line (1) and a surface (2); the dimension of the snowflake curve is 1.26. The study of this type of self-similarity in figures is used in certain branches of physics, such as crystal growth. Fractals are also important in chaos theory and in computer graphics. See also Mandelbrot set. Mathematics A set whose fractal dimension exceeds its topological dimension. Fractals are sets with infinitely complex structure and usually possess some measure of self‐similarity, whereby any part of the set contains within it a scaled‐down version of the whole set. Examples are the Cantor set, the Koch curve, and the Sierpinski triangle. http://sprott.physics.wisc.edu/fractals.htm Examples of colourful fractal images. Statistics An infinite set of points, usually in a plane, whose fractal dimension is not an integer. Fractals are usually self-similar, i.e. any part of the fractal contains scaled-down versions of the whole fractal. The word ‘fractal’ was coined by Mandelbrot in 1975. For a well-known example of a fractal, see snowflake curve. Chemistry A curve or surface generated by a process involving successive subdivision. For example, a snowflake curve can be produced by starting with an equilateral triangle and dividing each side into three segments. The middle segments are then replaced by two equal segments, which would form the sides of a smaller equilateral triangle. This gives a 12-sided star-shaped figure. The next stage is to subdivide each of the sides of this figure in the same way, and so on. The result is a developing figure that resembles a snowflake. In the limit, this figure has ‘fractional dimension’ – i.e. a dimension between that of a line (1) and a surface (2); the dimension of the snowflake curve is 1.26. The study of this type of ’self-similar’ figure is used in certain branches of chemistry – for example, crystal growth. Fractals are also important in chaos theory and in computer graphics. Computer A set whose Hausdorff-Besicovitch dimension strictly exceeds its topological dimension. Intuitively, a fractal is a set which at all magnifications reveals a set that is exactly the same (self-similar). Such sets can be generated by the repeated application of some collection of maps. The term is generally associated with Benoit Mandelbrot and appeared in the literature in the late 1970s. Many naturally occurring objects, such as trees, coastlines, and clouds, are considered to have fractal properties, hence their interest to computer graphics. Geology and Earth Sciences A geometric entity which has a basic pattern that is repeated at ever decreasing sizes. Fractal patterns are not able to fill spaces and are hence described as having fractal dimension. Fractals occur frequently in nature, such as in forked lightning or in chaotic systems (see chaos).
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