fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern...
44 KB (4,750 words) - 05:42, 4 June 2024
mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding...
74 KB (8,020 words) - 02:24, 21 August 2024
Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." Presented here...
52 KB (1,139 words) - 21:11, 7 August 2024
In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix...
24 KB (3,147 words) - 22:17, 26 April 2024
fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal...
10 KB (1,564 words) - 01:43, 25 August 2024
Coastline paradox (redirect from How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension)
This results from the fractal curve–like properties of coastlines; i.e., the fact that a coastline typically has a fractal dimension. Although the "paradox...
24 KB (2,756 words) - 15:02, 1 July 2024
as a general rule, fractal curves have different dimensions, also see fractal dimension and list of fractals by Hausdorff dimension. Starting in the 1950s...
5 KB (381 words) - 22:38, 22 June 2024
calculate the 'overall' fractal dimension of a real landscape can result in measures of negative fractal dimension, or of fractal dimension above 3. In particular...
9 KB (932 words) - 16:53, 27 October 2023
Koch snowflake (redirect from Sphereflake fractal)
as the Koch curve, Koch star, or Koch island) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve...
22 KB (2,535 words) - 16:11, 18 April 2024
universe shows a definite fractal aspect over a fairly wide range of scale, with a fractal dimension of about 2. The fractal dimension of a homogeneous 3D object...
9 KB (1,182 words) - 04:39, 10 June 2024
Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available, both...
24 KB (2,413 words) - 19:02, 27 April 2024
\sim l_{B}^{d_{B}}} , A network can be classified as fractal or not and the fractal dimension can be found. For example, the WWW, the human brain, metabolic...
9 KB (1,317 words) - 14:19, 28 January 2024
Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics...
34 KB (3,532 words) - 22:00, 21 August 2024
Hurst exponent (category Fractals)
(1859–1937) by Benoît Mandelbrot (1924–2010). H is directly related to fractal dimension, D, and is a measure of a data series' "mild" or "wild" randomness...
22 KB (2,999 words) - 19:21, 27 October 2023
impedance. In general, the fractal dimension of a fractal antenna is a poor predictor of its performance and application. Not all fractal antennas work well for...
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kind of three dimensional fractal. Fractal Expressionism is a term used to differentiate traditional visual art that incorporates fractal elements such...
20 KB (2,122 words) - 12:25, 30 June 2024
Granlund & Knutsson (1995). Dimension Fractal dimension Hausdorff dimension Topological dimension Intrinsic low-dimensional manifold Amsaleg, Laurent;...
20 KB (2,688 words) - 13:08, 22 August 2024
Chaos game (category Fractals)
referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it. The fractal is created by iteratively creating...
14 KB (1,725 words) - 15:08, 26 July 2024
Patterns in nature (redirect from Fractals in nature)
Statistical Self-Similarity and Fractional Dimension, crystallising mathematical thought into the concept of the fractal. Fibonacci number patterns occur widely...
61 KB (6,782 words) - 01:52, 25 April 2024
Multifractal system (redirect from Multi-fractal analysis)
multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead...
31 KB (3,325 words) - 23:45, 12 June 2024
Menger sponge (category Iterated function system fractals)
Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It...
15 KB (1,827 words) - 22:36, 1 July 2024
Box counting (category Fractals)
intensities. When box counting is done to determine a fractal dimension known as the box counting dimension, the information recorded is usually either yes...
16 KB (1,827 words) - 05:37, 29 August 2023
group. Fractal dimension – Ratio providing a statistical index of complexity variation with scale Krull dimension – In mathematics, dimension of a ring...
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published". Fractals: Form, Chance and Dimension, 1977, 2020 The Fractal Geometry of Nature, 1982 Mandelbrot, Benoît B. (1983). The Fractal Geometry of...
49 KB (4,917 words) - 17:02, 17 August 2024
The Fractal Dimension of Architecture is a book that applies the mathematical concept of fractal dimension to the analysis of the architecture of buildings...
4 KB (476 words) - 22:49, 28 September 2022
Olbers's paradox (section Fractal star distribution)
is proportional to r2. This would correspond to a fractal dimension of 2. Thus the fractal dimension of the universe would need to be less than 2 for this...
22 KB (2,750 words) - 03:01, 25 August 2024
and fractal dimension. They varied the fractal dimension of the boundary contour from 1.2 to 1.8, and found that the lower the fractal dimension, the...
39 KB (4,110 words) - 11:10, 24 August 2024
Mathematics and art (section Fractal dimensions)
designs have a fractal dimension between 1 and 2, varying in different regional styles. For example, the batik of Cirebon has a fractal dimension of 1.1; the...
117 KB (12,016 words) - 13:51, 27 August 2024
Cantor set (redirect from Cantor's fractal set)
ln ( 2 ) / ln ( 3 ) {\displaystyle d_{f}=\ln(2)/\ln(3)} is the fractal dimension) of all the surviving intervals at any stage of the construction process...
45 KB (6,916 words) - 19:55, 12 May 2024
In mathematics, the T-square is a two-dimensional fractal. It has a boundary of infinite length bounding a finite area. Its name comes from the drawing...
5 KB (504 words) - 05:45, 13 October 2022