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EXPECTATIONS ON FRACTAL SETS

Bailey, David H. and Borwein, Jonathan M. and Crandall, Richard E. and Rose, Michael (2013) EXPECTATIONS ON FRACTAL SETS. Applied Mathematics and Computation, 220 . pp. 695-721.

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    Abstract

    Using fractal self-similarity and functional-expectation relations, the classical theory of box integrals (being expectations on unit hypercubes)is extended to a class of fractal string-generated Cantor sets" (SCSs) embedded in unit hypercubes of arbitrary dimension. Motivated by laboratory studies on the distribution of brain synapses, these SCSs were designed for dimensional freedom|a suitable choice of generating string allows for �ne-tuning the fractal dimension of the corresponding set. We also establish closed forms for certain statistical moments on SCSs, develop a precision algorithm for high embedding dimensions, and report various numerical results. The underlying numerical quadrature issues are in themselves quite challenging.

    Item Type: Article
    Subjects: 33-xx Special functions
    65-xx Numerical analysis
    Faculty: UNSPECIFIED
    Depositing User: Jonathan Borwein
    Date Deposited: 10 Nov 2012 08:40
    Last Modified: 28 Nov 2014 15:07
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1454

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