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Representing fractals by superoscillations

Research output: Contribution to journalArticle

Original languageEnglish
Article numberLT01
Number of pages7
JournalJournal of Physics A: Mathematical and Theoretical
Volume50
Issue number22
DOIs
DateAccepted/In press - 27 Apr 2017
DatePublished (current) - 9 May 2017

Abstract

Fractals provide an extreme test of representing fine detail in terms of band-limited functions, i.e. by superoscillations. We show that this is possible, using the example of the Weierstrass nondifferentiable fractal. If this is truncated at an arbitrarily fine scale, it can be expressed to any desired accuracy with a simple superoscillatory function. In illustrative simulations, fractals truncated with fastest frequency 216 are easily represented by superoscillations with fastest Fourier frequency 1.

    Research areas

  • Scaling, Approximation, Band-limited, Fourier

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via IOP Science at http://iopscience.iop.org/article/10.1088/1751-8121/aa6fba/meta;jsessionid=1C2CD0CECC3BB50EBF2678E41A6DC0D1.c3.iopscience.cld.iop.org. Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 678 KB, PDF-document

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