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In the mid-1970s, Mandelbrot (Fractals, form, chance and dimension, W.H. Freeman and Co., San Francisco, 1977) introduced the concept of a fractal, a power-law statistical pattern between two random variables, and the last quarter of the last century was filled with articles on the results of searches for such patterns, the values of exponents were given, often without estimating them uncertainties and discussion of their nature and connection with the general laws of probability theory.

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Clouds and Turbulence, Self-similarity, and Peculiar Invariants

  • 章节

  • 发表日期：

    2025年

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  • Georgy Golitsyn,
  • Costas Varotsos

摘要

In the mid-1970s, Mandelbrot (Fractals, form, chance and dimension, W.H. Freeman and Co., San Francisco, 1977) introduced the concept of a fractal, a power-law statistical pattern between two random variables, and the last quarter of the last century was filled with articles on the results of searches for such patterns, the values of exponents were given, often without estimating them uncertainties and discussion of their nature and connection with the general laws of probability theory.