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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.
Fractals are self-similar geometric objects with both aesthetical and scientific uses. Subcategories. This category has the following 6 subcategories, out of 6 total. ...
List of fractals by Hausdorff dimension Examples of deterministic fractals, random and natural fractals. Assouad dimension, another variation of fractal dimension that, like Hausdorff dimension, is defined using coverings by balls; Intrinsic dimension; Packing dimension; Fractal dimension
Sierpiński Carpet - Infinite perimeter and zero area Mandelbrot set at islands The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)
This page was last edited on 21 August 2005, at 20:54 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
Chaotic maps and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal. See also Universality (dynamical systems).
The terms fractal dimension and fractal were coined by Mandelbrot in 1975, [16] about a decade after he published his paper on self-similarity in the coastline of Britain. . Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them in a new way to study complex geometries that defied description in ...
This is a list of fractal topics, by Wikipedia page, See also list of dynamical systems and differential equations topics. 1/f noise; Apollonian gasket; Attractor;