Meaning of fractal dimension | Babel Free

Definitions

A dimension in which it is the most suitable to make measurements on a fractal set.

Equivalents

Examples

“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.”

CEFR level