## Correlation Dimension

Define the correlation integral as

 (1)

where is the Heaviside Step Function. When the below limit exists, the correlation dimension is then defined as
 (2)

If is the Correlation Exponent, then
 (3)

It satisfies
 (4)

To estimate the correlation dimension of an -dimensional system with accuracy requires data points, where

 (5)

where is the length of the plateau region.'' If an Attractor exists, then an estimate of saturates above some given by
 (6)

which is sometimes known as the fractal Whitney embedding prevalence theorem.