A characterization of connected self-affine fractals arising from collinear digits

King Shun LEUNG, Jun Jason LUO

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let A be an expanding integer matrix with characteristic polynomial f(x)=x²+px+q, and let D={0,1,…,|q|−2,|q|+m}v be a collinear digit set where m⩾0,v∈Z². It is well known that there exists a unique self-affine fractal T satisfying AT=T+D. In this paper, we give a complete characterization of connectedness of T. That generalizes the previous result for |q|=3. Copyright © 2017 Elsevier Inc.
Original languageEnglish
Pages (from-to)429-443
JournalJournal of Mathematical Analysis and Applications
Volume456
Issue number1
Early online dateJul 2017
DOIs
Publication statusPublished - Dec 2017

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Integer Matrix
Self-affine
Collinear
Connectedness
Characteristic polynomial
Digit
Fractals
Fractal
Polynomials
Generalise

Citation

Leung, K.-S., & Luo, J. J. (2017). A characterization of connected self-affine fractals arising from collinear digits. Journal of Mathematical Analysis and Applications, 456(1), 429-443.

Keywords

  • Connectedness
  • Self-affine fractal
  • Collinear digit
  • Radix expansion