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• W347924419 abstract "The degree of ultrametricity of a given metric space, for example a phase space, provides a simple quantitative measure of the deviation from exact ultrametricity. For integer dimensions sets the degree of ultrametricity was shown to converge to 0 or 1. It is found that for fractal and multifractal sets the degree of ultrametricity reaches a noninteger limit between 0 and 1. In order to find a relation between the fractal dimension of the set and the noninteger value of the degree, we have studied the scaling behavior of the sum of the subdominant ultrametric distances S and of the sum of metric distances S for fractal and multifractal sets as a function of the number of points of the set. The scaling exponent is found to be the same for S and S in every case. A direct relation between the scaling exponent and the fractal dimension or dimensions of the set is obtained." @default.
• W347924419 created "2016-06-24" @default.
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• W347924419 date "1991-01-01" @default.
• W347924419 modified "2023-10-18" @default.
• W347924419 title "DEGREE OF ULTRAMETRICITY OF FRACTAL SETS" @default.
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• W347924419 doi "https://doi.org/10.1016/b978-0-444-88791-7.50020-x" @default.
• W347924419 hasPublicationYear "1991" @default.
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