The pλn fractal decomposition: Nontrivial partitions of conserved physical quantities

Vladimir García-Morales

Chaos, Solitons & Fractals, 2016, vol. 83, issue C, 27-37

Abstract: A mathematical method for constructing fractal curves and surfaces, termed the pλn fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal everywhere to the original function. Thus, the method is specially suited for constructing families of fractal objects arising from a conserved physical quantity, the decomposition yielding an exact partition of the quantity in question. Most prominent classes of examples are provided by Hamiltonians and partition functions of statistical ensembles: By using this method, any such function can be decomposed in the ordinary sum of a specified number of terms (generally fractal functions), the decomposition being both exact and valid everywhere on the domain of the function.

Keywords: Fractals; Cantor set; Statistical mechanics; Quantum mechanics (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:83:y:2016:i:c:p:27-37

DOI: 10.1016/j.chaos.2015.11.028

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