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...

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

\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...

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

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...

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

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

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...

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...

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...

a fractal such as the Cantor set. The heuristic idea of a fractal string is to study a (one-dimensional) fractal using the "space around the fractal."...

(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...

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

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...

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...

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...

Cayley-Dickson algebras Fractal terrains generated by random fractal processes Mandelbulbs are a form of three dimensional fractal. Fractal Expressionism is...

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

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

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

Look up fractal in Wiktionary, the free dictionary. A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension...

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

In mathematics — specifically, in fractal geometry — the Assouad dimension is a definition of fractal dimension for subsets of a metric space. It was...

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...

are the fractal dimensions of the stable and unstable manifolds, respectively and N=2 is the dimensionality of the system. The fractal dimension of the...

Exterior dimension Hurst exponent Isoperimetric dimension Metric dimension Order dimension q-dimension Fractal (q = 1) Correlation (q = 2) 0 dimension Point...

dimension (denoted by ν) is a measure of the dimensionality of the space occupied by a set of random points, often referred to as a type of fractal dimension...

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...