fractal dimension
English
[edit]Noun
[edit]fractal dimension (plural fractal dimensions)
- (mathematical analysis) A dimension in which it is the most suitable to make measurements on a fractal set.
- 2005, John G. Holden, Gauging the Fractal Dimension of Response Times from Cognitive Tasks[1]:
- Conventional statistical analyses presuppose that intrinsic variability is white noise. White noise yields a jagged and irregular line with a fractal dimension of 1.5, because successive observations are statistically independent of each other. Its fractal dimension indicates the extent to which white noise occupies 2-D space. White noise is uncorrelated noise. By contrast, the successive observations of pink noise tend to be positively correlated. This results in a less jagged trial series, and lower fractal dimensions that fall in the interval between 1 and 1.5.
- The perimeter of Britain measured in the first dimension yields infinity, and measured in the second dimension yields zero, so it has to be measured in a fractal dimension of approximately 1.25.[2]
Hyponyms
[edit]- capacity dimension
- correlation dimension
- Hausdorff dimension
- information dimension
- Lyapunov dimension
- Minkowski-Bouligand dimension
Related terms
[edit]Translations
[edit]a dimension for making measurements on a fractal set
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