Turtle graphics of morphic sequences

Research output: Contribution to journalArticleAcademicpeer-review

45 Downloads (Pure)

Abstract

The simplest infinite sequences that are not ultimately periodic are pure morphic sequences: fixed points of particular morphisms mapping single symbols to strings of symbols. A basic way to visualize a sequence is by a turtle curve: for every alphabet symbol fix an angle, and then consecutively for all sequence elements draw a unit segment and turn the drawing direction by the corresponding angle. This paper investigates turtle curves of pure morphic sequences. In particular, criteria are given for turtle curves being finite (consisting of finitely many segments), and for being fractal or self-similar: it contains an up-scaled copy of itself. Also space-filling turtle curves are considered, and a turtle curve that is dense in the plane. As a particular result we give an exact relationship between the Koch curve and a turtle curve for the Thue–Morse sequence, where until now for such a result only approximations were known.
Original languageEnglish
Article number1650009
Number of pages16
JournalFractals
Volume24
Issue number1
DOIs
Publication statusPublished - 2016

Fingerprint Dive into the research topics of 'Turtle graphics of morphic sequences'. Together they form a unique fingerprint.

  • Cite this