# Correlation Dimension

**Definition:** [crh] An estimate of the Fractal Dimension which measures the probability that two points chosen at random will be within a certain distance of each other, and ex**Definition:** amines how this probability changes as the distance is increased. White noise will fill its space since its components are uncorrelated,**Definition:** and its correlation dimension is equal to whatever dimension it is placed in. A dependent system will be held together by its correlations and retain its dim**Definition:** ension whatever embedding dimension it is placed in, as long as it is greater than its fractal dimension.

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