## Fractal Dimension

A **fractal dimension** is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured. It has also been characterized as a measure of the space-filling capacity of a pattern that tells how a fractal scales differently than the space it is embedded in; a fractal dimension does not have to be an integer.

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### Some articles on fractal dimension:

Fractal Landscape - Behaviour of Natural Landscapes

... Whether or not natural landscapes behave in a generally

... Whether or not natural landscapes behave in a generally

**fractal**manner has been the subject of some research ... speaking, any surface in three-dimensional space has a topological**dimension**of 2, and therefore any**fractal**surface in three-dimensional space has a Hausdorff**dimension**between 2 ... This means that an attempt to calculate the 'overall'**fractal dimension**of a real landscape can result in measures of negative**fractal dimension**, or of**fractal dimension**above 3 ...Coastline Statistics - Measuring A Coastline

... Benoît Mandelbrot developed a new branch of mathematics,

... Benoît Mandelbrot developed a new branch of mathematics,

**fractal**geometry, to describe just such non-rectifiable complexes in nature as the infinite coastline ... the new figure serving as the basis for his study is I coined**fractal**from the Latin adjective fractus ... mean "irregular." A key property of the**fractal**is self-similarity that is, at any scale the same general configuration appears ...List Of Fractals By Hausdorff Dimension - Random and Natural Fractals

... Hausdorf

... Hausdorf

**dimension**(exact value) Hausdorf**dimension**(approx.) Name Illustration Remarks 1/2 0.5 Zeros of a Wiener process The zeros of a Wiener process (Brownian motion) are a nowhere dense ... Its Hausdorff**Dimension**satisfies ... Measured 1.25 Coastline of Great Britain**Fractal dimension**of the west coast of Great Britain, as measured by Lewis Fry Richardson and cited by Benoît ...Cauliflower -

... Cauliflower has been noticed by mathematicians for its distinct

**Fractal Dimension**... Cauliflower has been noticed by mathematicians for its distinct

**fractal dimension**, predicted to be about 2.8 ...**Fractal Dimension**- Estimating From Real-world Data

... The

**fractal dimension**measures described in this article are for formally-defined

**fractals**... phenomena also exhibit limited or statistical

**fractal**properties and

**fractal dimensions**have been estimated for sampled data from many such phenomena using computer based ... Practical

**dimension**estimates are affected by various methodological issues, and are sensitive to numerical or experimental noise and limitations in the ...

### Famous quotes containing the word dimension:

“God cannot be seen: he is too bright for sight; nor grasped: he is too pure for touch; nor measured: for he is beyond all sense, infinite, measureless, his *dimension* known to himself alone.”

—Marcus Minucius Felix (2nd or 3rd cen. A.D.)

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