Planar Substitutions to Lebesgue type Space-Filling Curves and Relatively Dense Fractal-like Sets in the Plane

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We present an algorithm for generating curves filling the unit square; i.e. space-filling curves, from any given planar substitution satisfying a mild condition. The proposed algorithm is mimicking construction steps of Lebesgue’s curve and is based on linear interpolation. Generated space-filling curves for some known substitutions are elucidated. Some of those substitutions further induce relatively dense fractal-like sets in the plane, whenever some additional assumptions are satisfied.
Original languageEnglish
Article number127654
Pages (from-to)1-25
Number of pages25
JournalJournal of mathematical analysis and applications
Volume530
Issue number2
Early online date18 Aug 2023
DOIs
Publication statusPublished - 15 Feb 2024

Keywords / Materials (for Non-textual outputs)

  • Space-filling curves
  • Lebesgue curve
  • Fractal-like set

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