Generalisations and randomisation of the plane Koch curve

A. Lakhtakia, V. K. Varadan, R. Messier, V. V. Varadan

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

The Koch curve evolves from a base equilateral triangle by the trisection of each side and the replication of the original triangle on the mid-section, the process being repeated ad infinitum by the addition of sets of successively smaller triangles. The process is generalised to replace the trisectioning by (2k+1)-sectioning. It is shown that a square is the only other regular polygon on which the (2k+1)-sectioning procedure can be implemented. The Koch curves thus generated are strictly self-similar, their fractal dimensions being similarity dimensions and enclose simply connected areas. Randomisation of the generating procedure is also discussed.

Original languageEnglish (US)
Article number052
Pages (from-to)3537-3541
Number of pages5
JournalJournal of Physics A: General Physics
Volume20
Issue number11
DOIs
StatePublished - Dec 1 1987

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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