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  2. Rhind Mathematical Papyrus - Wikipedia

    en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus

    Happily the context of 51 and 52, together with the base, mid-line, and smaller triangle area (which are given as 4 + 1/2, 2 + 1/4 and 7 + 1/2 + 1/4 + 1/8, respectively) make it possible to interpret the problem and its solution as has been done here. The given paraphrase therefore represents a consistent best guess as to the problem's intent ...

  3. List of fractals by Hausdorff dimension - Wikipedia

    en.wikipedia.org/wiki/List_of_fractals_by...

    L-Systems branching pattern having 4 new pieces scaled by 1/3. Generating the pattern using statistical instead of exact self-similarity yields the same fractal dimension. Calculated: 1.2683: Julia set z 2 − 1: Julia set of f(z) = z 2 − 1. [9] 1.3057: Apollonian gasket

  4. Fractal art - Wikipedia

    en.wikipedia.org/wiki/Fractal_art

    Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still digital images, animations, and media. Fractal art developed from the mid-1980s onwards. [2] It is a genre of computer art and digital art which are part of new media art. The mathematical beauty of fractals lies at ...

  5. Sierpiński triangle - Wikipedia

    en.wikipedia.org/wiki/Sierpiński_triangle

    Shrink the triangle to ⁠ 1 / 2 ⁠ height and ⁠ 1 / 2 ⁠ width, make three copies, and position the three shrunken triangles so that each triangle touches the two other triangles at a corner (image 2). Note the emergence of the central hole—because the three shrunken triangles can between them cover only ⁠ 3 / 4 ⁠ of the area of the ...

  6. Wallpaper group - Wikipedia

    en.wikipedia.org/wiki/Wallpaper_group

    A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles, tiles, and wallpaper. The simplest wallpaper group, Group p 1 ...

  7. Mandelbrot set - Wikipedia

    en.wikipedia.org/wiki/Mandelbrot_set

    The quaternion (4-dimensional) Mandelbrot set is simply a solid of revolution of the 2-dimensional Mandelbrot set (in the j-k plane), and is therefore uninteresting to look at. [42] Taking a 3-dimensional cross section at d = 0 ( q = a + b i + c j + d k ) {\displaystyle d=0\ (q=a+bi+cj+dk)} results in a solid of revolution of the 2-dimensional ...

  8. Fractal - Wikipedia

    en.wikipedia.org/wiki/Fractal

    A fractal is formed when pulling apart two glue-covered acrylic sheets. High-voltage breakdown within a 4 in (100 mm) block of acrylic glass creates a fractal Lichtenberg figure. Romanesco broccoli, showing self-similar form approximating a natural fractal. Fractal defrosting patterns, polar Mars.

  9. Fractal dimension - Wikipedia

    en.wikipedia.org/wiki/Fractal_dimension

    A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale. [5]: 1 Several types of fractal dimension can be measured theoretically and empirically (see Fig. 2). [3][9] Fractal dimensions are used to characterize a broad spectrum of ...

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