English

Noun

fractal dimension ‎(plural fractal dimensions)

1. (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.

Hyponyms

• capacity dimension
• correlation dimension
• Hausdorff dimension
• information dimension
• Lyapunov dimension
• Minkowski-Bouligand dimension

Related terms

• dimension
• fractal

Translations