Fractals in physics: applications and theoretical developments

L. Pietronero

Physica A: Statistical Mechanics and its Applications, 1992, vol. 191, issue 1, 85-94

Abstract: We report about the developments in two subjects in which we have been recently active. The first one refers to a reanalysis of the distribution of galaxies and clusters with the methods of modern statistical mechanics. Contrary to the usual picture of a relatively smooth distribution at large scale, we find that fractal and multifractal properties extend up to the observational limits. This result should have deep implications also in relation to the recently observed anisotropy of the microwave background radiation. The second subject concerns the attempts to develop a theory of fractal growth based on the new concept of the fixed scale transformation. We discuss the instructive example of the percolating cluster in which the FST program can be fully implemented. We then compare this example with the more complex cases of DLA and DBM for which the identification of the scale invariant growth rules is much more complex. In this respect the FST points to the key concept that is the scale invariance of screening and noise reduction. The state of the art and the main open problems will be critically discussed.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:191:y:1992:i:1:p:85-94

DOI: 10.1016/0378-4371(92)90510-W

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