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...

mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding...

Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." Presented here...

In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix...

fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal...

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...

as a general rule, fractal curves have different dimensions, also see fractal dimension and list of fractals by Hausdorff dimension. Starting in the 1950s...

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...

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...

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...

Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available, both...

\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...

Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics...

(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...

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...

kind of three dimensional fractal. Fractal Expressionism is a term used to differentiate traditional visual art that incorporates fractal elements such...

Granlund & Knutsson (1995). Dimension Fractal dimension Hausdorff dimension Topological dimension Intrinsic low-dimensional manifold Amsaleg, Laurent;...

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...

Statistical Self-Similarity and Fractional Dimension, crystallising mathematical thought into the concept of the fractal. Fibonacci number patterns occur widely...

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...

Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It...

intensities. When box counting is done to determine a fractal dimension known as the box counting dimension, the information recorded is usually either yes...

group. Fractal dimension – Ratio providing a statistical index of complexity variation with scale Krull dimension – In mathematics, dimension of a ring...

published". Fractals: Form, Chance and Dimension, 1977, 2020 The Fractal Geometry of Nature, 1982 Mandelbrot, Benoît B. (1983). The Fractal Geometry of...

The Fractal Dimension of Architecture is a book that applies the mathematical concept of fractal dimension to the analysis of the architecture of buildings...

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...

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...

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...

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...

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...