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WIKIMEDIA LIST ARTICLE
List of fractals; List of fractals by hausdorff dimension
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  • The quadric cross is made by scaling the 3-segment generator unit by 5<sup>1/2</sup> then adding 3 full scaled units, one to each original segment, plus a third of a scaled unit (blue) to increase the length of the pedestal of the starting 3-segment unit (purple).
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Analysis on fractals         
Calculus on fractals
Analysis on fractals or calculus on fractals is a generalization of calculus on smooth manifolds to calculus on fractals.
Fractal         
MATHEMATICAL SET OF NON-INTEGRAL DIMENSION
Fractals; Fractal geometry; Fractal set; Fractal domain; Fractogeometry; Fractal mathematics; Factral; Fractal theory; Fractal math; Fractal tree; Fractles; Fractels; Fractal sets; Fractal Trees; Applications of fractals; Fractal island; History of fractals; Simulated fractals
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set.
fractal         
MATHEMATICAL SET OF NON-INTEGRAL DIMENSION
Fractals; Fractal geometry; Fractal set; Fractal domain; Fractogeometry; Fractal mathematics; Factral; Fractal theory; Fractal math; Fractal tree; Fractles; Fractels; Fractal sets; Fractal Trees; Applications of fractals; Fractal island; History of fractals; Simulated fractals
<mathematics, graphics> A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a smaller copy of the whole. Fractals are generally self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in). Many mathematical structures are fractals; e.g. {Sierpinski triangle}, Koch snowflake, Peano curve, Mandelbrot set and Lorenz attractor. Fractals also describe many real-world objects that do not have simple geometric shapes, such as clouds, mountains, turbulence, and coastlines. Benoit Mandelbrot, the discoverer of the Mandelbrot set, coined the term "fractal" in 1975 from the Latin fractus or "to break". He defines a fractal as a set for which the Hausdorff Besicovich dimension strictly exceeds the topological dimension. However, he is not satisfied with this definition as it excludes sets one would consider fractals. {sci.fractals FAQ (ftp://src.doc.ic.ac.uk/usenet/usenet-by-group/sci.fractals/)}. See also fractal compression, fractal dimension, {Iterated Function System}. Usenet newsgroups: news:sci.fractals, news:alt.binaries.pictures.fractals, news:comp.graphics. ["The Fractal Geometry of Nature", Benoit Mandelbrot]. [Are there non-self-similar fractals?] (1997-07-02)

ويكيبيديا

List of fractals by Hausdorff dimension

According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illustrate what it means for a fractal to have a low or a high dimension.