What is fractal dimension?

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:

Coastline Statistics - Measuring A Coastline
... Richardson completed his work, Benoît Mandelbrot developed a new branch of mathematics, fractal geometry, to describe just such non-rectifiable complexes in nature as ... His own definition of the new figure serving as the basis for his study is I coined fractal from the Latin adjective fractus ... fractus should also mean "irregular." A key property of the fractal is self-similarity that is, at any scale the same general configuration appears ...
Cauliflower - 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 ... However, many real-world phenomena also exhibit limited or statistical fractal properties and fractal dimensions have been estimated for sampled data from many such phenomena using computer based fractal ... Practical dimension estimates are affected by various methodological issues, and are sensitive to numerical or experimental noise and limitations in the amount of data ...
List Of Fractals By Hausdorff Dimension - Random and Natural Fractals
... 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 ... 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 ...
Fractal Landscape - Behaviour of Natural Landscapes
... 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 and 3 ... 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 ...

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.)