Generalized scaling and multifractal phase transition in some physical and astrophysical processes

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In our recent Letter [Phys. Lett. A 222 (1996) 375], it is shown (using data taken from the CfA2 catalogue) that there exists a phase transition from fractality to homogeneity in the large-scale universe. In the present Letter it is shown that this phenomenon is a consequence of a generalized scaling (some kind of self-similarity of random systems). It is also shown, by analysis of data obtained by different authors, that the generalized scaling and the multifractal phase transition to homogeneity occur in diffusive and growth processes as well as in percolation. Finally, recent data from the Perseus-Pisces survey are used to demonstrate universality of this phenomenon for the luminosity-space galaxy distributions of the large-scale universe.

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