Fractal Distribution Fractional Brownian Motion

From fractal geometry, used to describe the irregular nature of lines, curves, planes or volumes.

A measure of a geometric object that can take on fractional values. At first used as a synonym to Hausdorff dimension, fractal dimension is currently used as a more general term for a measure of how fast length, area, or volume increases with decrease in scale. (Peitgen, Jurgens, & Saupe, 1992a).

Submitted By The Authors The world as we know it is made up of objects which exist in integer dimensions. However, many things in nature are better described with a dimension which is part of the way between two whole numbers. Dimensions which are not integers, but a number between two whole numbers are refered to as fractal dimensions. More information is avaliable in the fractal dimension division of the fractal geometry main page.

a measure of the degree of self-similarity in geometric shapes

Dimension that, unlike a surface or a volume, is characterized by a non-integer exponent.

An extension of the notion of dimension found in Euclidean geometry.

In fractal geometry, the fractal dimension is a statistical quantity that gives an indication of how completely a fractal appears to fill space, as one zooms down to finer and finer scales. There are many specific definitions of fractal dimensions, none of them should be treated as universal one. From the theoretical point of view the most important are the Hausdorff dimension, the packing dimension and, more generally, the RÃ©nyi dimensions.