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According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." [1] 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.
Download as PDF; Printable version; In other projects Wikimedia Commons; ... Pages in category "Fractals" The following 125 pages are in this category, out of 125 total.
Download QR code; Print/export Download as PDF; Printable version; In other projects ... This is a list of fractal topics, by Wikipedia page, See also list ...
Escape-time fractals – use a formula or recurrence relation at each point in a space (such as the complex plane); usually quasi-self-similar; also known as "orbit" fractals; e.g., the Mandelbrot set, Julia set, Burning Ship fractal, Nova fractal and Lyapunov fractal. The 2d vector fields that are generated by one or two iterations of escape ...
The Mandelbrot set within a continuously colored environment. The Mandelbrot set (/ ˈ m æ n d əl b r oʊ t,-b r ɒ t /) [1] [2] is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified.
A 4K UHD 3D Mandelbulb video A ray-marched image of the 3D Mandelbulb for the iteration v ↦ v 8 + c. The Mandelbulb is a three-dimensional fractal, constructed for the first time in 1997 by Jules Ruis and further developed in 2009 by Daniel White and Paul Nylander using spherical coordinates.
A Mosely snowflake is a cube-based fractal with corners recursively removed. [18] A tetrix is a tetrahedron-based fractal made from four smaller copies, arranged in a tetrahedron. [19] A Sierpinski–Menger snowflake is a cube-based fractal in which eight corner cubes and one central cube are kept each time at the lower and lower recursion steps.
In this approach, pixels that are sufficiently close to M are drawn using a different color. This creates drawings where the thin "filaments" of the Mandelbrot set can be easily seen. This technique is used to good effect in the B&W images of Mandelbrot sets in the books "The Beauty of Fractals [9]" and "The Science of Fractal Images". [10]