fractal dimension

English

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
  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.

a dimension for making measurements on a fractal set

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