COMMENT: Generalisations and randomisation of the plane Koch curve
COMMENT: Generalisations and randomisation of the plane Koch curve
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DOI：
10.1088/0305-4470/20/11/052
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发表时间：
1987-08
期刊：
影响因子：
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通讯作者：
A. Lakhtakia;V. Varadan;R. Messier;V. Varadan
中科院分区：
文献类型：
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作者：
A. Lakhtakia;V. Varadan;R. Messier;V. Varadan
科赫曲线从一个基本的等边三角形开始，通过每边的三分和中间部分原始三角形的复制而演变，这个过程通过添加一组连续更小的三角形而无限重复。该过程被推广到用（2k+1）-分段代替三分段。它表明，一个正方形是唯一的其他正多边形上的（2k+1）-剖分程序可以实现。由此产生的科赫曲线是严格自相似的，它们的分形维数是相似维数，并包含简单连通区域。随机化的生成过程也进行了讨论。
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.