fractal

Definition

Seemingly-irregular shape (such as a coastline or cloud) or structure (such as a tree or mountain) formed by repeated subdivisions of a basic form, and having a pattern of regularity underlying its apparent randomness. Every part of a fractal (irrespective of its scale) is essentially a reduced size copy of the whole (a property called 'self-similarity'), and forms an organized hierarchy with its upper level and lower level counterparts. A fractal is mathematically described as a set whose every point is contained in a scaled down copy of the set. Fractals are complex but structured, contain an infinite amount of detail, and can be generated by computer programs that repeat (iterate) certain mathematical equations. The concept of fractal has found applications in fields as diverse as astrophysics, chaos theory, and stockmarket analysis. The term was coined by the Polish-born French-US mathematician Benoît Mandelbrot (1924-) from the Latin 'fractus,' broken. See also Mandelbrot set.

单词	fractal
释义	fractal Definition Seemingly-irregular shape (such as a coastline or cloud) or structure (such as a tree or mountain) formed by repeated subdivisions of a basic form, and having a pattern of regularity underlying its apparent randomness. Every part of a fractal (irrespective of its scale) is essentially a reduced size copy of the whole (a property called 'self-similarity'), and forms an organized hierarchy with its upper level and lower level counterparts. A fractal is mathematically described as a set whose every point is contained in a scaled down copy of the set. Fractals are complex but structured, contain an infinite amount of detail, and can be generated by computer programs that repeat (iterate) certain mathematical equations. The concept of fractal has found applications in fields as diverse as astrophysics, chaos theory, and stockmarket analysis. The term was coined by the Polish-born French-US mathematician Benoît Mandelbrot (1924-) from the Latin 'fractus,' broken. See also Mandelbrot set.
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