Generalisations and randomisation of the plane Koch curve

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

Research output: Contribution to journalArticle

19 Citations (Scopus)

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 - 1987

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Plane Curve
Fractal dimension
Randomisation
triangles
Triangle
Regular polygon
Equilateral triangle
Curve
curves
Fractal Dimension
Replication
Strictly
polygons
fractals
Generalization
Similarity

All Science Journal Classification (ASJC) codes

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

Cite this

Lakhtakia, Akhlesh ; Varadan, V. K. ; Messier, R. ; Varadan, V. V. / Generalisations and randomisation of the plane Koch curve. In: Journal of Physics A: General Physics. 1987 ; Vol. 20, No. 11. pp. 3537-3541.
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Generalisations and randomisation of the plane Koch curve. / Lakhtakia, Akhlesh; Varadan, V. K.; Messier, R.; Varadan, V. V.

In: Journal of Physics A: General Physics, Vol. 20, No. 11, 052, 1987, p. 3537-3541.

Research output: Contribution to journalArticle

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