### 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 language | English (US) |
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Article number | 052 |

Pages (from-to) | 3537-3541 |

Number of pages | 5 |

Journal | Journal of Physics A: General Physics |

Volume | 20 |

Issue number | 11 |

DOIs | |

State | Published - Dec 1 1987 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*Journal of Physics A: General Physics*,

*20*(11), 3537-3541. [052]. https://doi.org/10.1088/0305-4470/20/11/052