Representing fractals by superoscillations

Michael Berry, Sam Morley-Short

Research output: Contribution to journalArticle (Academic Journal)

6 Citations (Scopus)
218 Downloads (Pure)

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.
Original languageEnglish
Article numberLT01
Number of pages7
JournalJournal of Physics A: Mathematical and Theoretical
Volume50
Issue number22
DOIs
Publication statusPublished - 9 May 2017

Keywords

  • Scaling
  • Approximation
  • Band-limited
  • Fourier

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