What is fractal?

  • (noun): (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry.

Fractal

A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far". Fractals may be exactly the same at every scale, or, as illustrated in Figure 1, they may be nearly the same at different scales. The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself.

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Some articles on fractal:

Fractal Cosmology - Fractals in Observational Cosmology
... The first attempt to model the distribution of galaxies with a fractal pattern was made by Luciano Pietronero and his team in 1987, and a more detailed view of the universe’s large-scale structure ... Pietronero argues that the 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 would be 3, and 2 for a homogeneous surface, whilst the fractal dimension for a fractal surface is between 2 and 3 ...
A Theory Of Architecture - Primary Topics - The Fractal Mind
... how our mind perceives and conceives architectural form, and postulates that fractal and other organizational mechanisms play a key role in perception ... It then argues that human beings naturally prefer fractal, organized structures, based on how the mind works ...
Fractal - Applications in Technology
... fractal antennas Fractal transistor fractal heat exchangers digital imaging urban growth Classification of histopathology slides Fractal landscape or Coastline complexity Enzyme/enzymology (Michaelis-Menten kinetics ...
Sterling (program)
... Sterling is a fractal-generating computer program written in the C programming language in 1999 for Microsoft Windows by Stephen C ... that are different are the 50 formulae for fractal generation ... Sterling is based on the notion that one way to generate interesting fractal images is by using elaborate color filters and shading ...
Fractal Analysis
... Fractal analysis is assessing fractal characteristics of data ... It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset or a pattern or signal extracted from phenomena including natural ... Fractal analysis is now widely used in all areas of science ...