Open AccessFinite-Size Scaling for Transient Similarity and Fractals
Author(s) -
M. Suzuki
Publication year - 1984
Publication title -
progress of theoretical physics
Language(s) - English
Resource type - Journals
eISSN - 1347-4081
pISSN - 0033-068X
DOI - 10.1143/ptp.71.1397
Subject(s) - fractal , transient (computer programming) , scaling , physics , statistical physics , scaling law , similarity (geometry) , dynamic scaling , mathematical physics , mathematical analysis , mechanics , geometry , mathematics , computer science , artificial intelligence , image (mathematics) , operating system
where V(:Fn)(S(:F n) or L(:Fn)) denotes the volume (surface or length) of :F n in units of bn . This definition is based on the infinitely smallscale similarity of the system. There are, however, many other interesting systems in which the similarity is valid only in some range of the scale factor bn , namely, we have "transient similarity". These systems may be called "transient fractals". As was already used by many authors,1),4)-7) a convenient definition of the transient fractal dimensionality is given by
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