Dictionary

fractal dimension en · NOUN

Meanings

1. A dimension in which it is the most suitable to make measurements on a fractal set.
   • 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. 2005, John G. Holden, Gauging the Fractal Dimension of Response Times from Cognitive Tasks:
   • 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.

Forms

Hyponyms

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

Relateds

dimension · fractal

Translations (9)

ja フラクタル次元 (a dimension for making measurements on a fractal set) · es dimensión fractal (a dimension for making measurements on a fractal set) · el μορφοκλασματική διάσταση (a dimension for making measurements on a fractal set) · cmn 分形維數 /分形维数 (a dimension for making measurements on a fractal set) · ko 프랙털 차원 (a dimension for making measurements on a fractal set) · hu fraktáldimenzió (a dimension for making measurements on a fractal set) · cs fraktální dimenze (a dimension for making measurements on a fractal set) · fi fraktaalidimensio (a dimension for making measurements on a fractal set) · ru фракта́льная разме́рность (a dimension for making measurements on a fractal set)