The probabilistic mechanism of formation of block structures

Abstract

Questions on the formation of block structures are considered. It is shown that the block structure is characteristic of bodies in a wide range of scales from microscopic to astronomic and from the bodies of nonliving nature to living organisms and communities. A scheme of the mechanism of the probabilistic formation of block structures is suggested. The characteristics general for structures of all scales are revealed. Evidence is presented that the hierarchical pattern of element sizes is characteristic of natural structures in which the ratio of linear sizes of elements neighboring by hierarchy is 2–5, while the characteristic scale coefficient is $\sqrt N$, where N is the total number of elements of which the system is formed. The block-probabilistic approach ensures knowledge of rare catastrophic events, including earthquakes, market crashes, floods, and industrial catastrophes, or creative events such as the formation of hypercomplex systems similar to organisms and communities. The statistics of rare events follows the power distribution (the distribution with a “heavy tail”) rather than the exponential one and especially the Poisson distribution, the Gaussian distribution, or the distributions with “light tails” close to them. The expression for the factor of increasing the formation probability of the systems, which is of many orders of magnitude even for the simplest systems, is acquired.