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Fractal Dimension |
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Fractal DimensionA number that quantitatively describes how an object fills its space. In Euclidean, or Plane geometry, objects are solid and continuous. That is, they have no holes or gaps. As such, they have integer dimensions. Fractals are rough and often discontinuous, like a wiffle ball, and so have fractional, or fractal dimensions.Fractal Dimension Similar MatchesHigh dimensionHigh dimensionIn trade theory, this refers to having more than two goods, factors, and/or countries, or to having arbitrary numbers of these. Contrasts with the two-ness of the 2x2x2 Model. Correlation DimensionCorrelation DimensionAn 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 examines how this probability changes as the distance is increased. White noise will fill its space since its components are uncorrelated, 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 dimension whatever embedding dimension it is placed in, as long as it is greater than its fractal dimension. |
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