What Type of Apollonian Circle Packing Will Appear?
What Type of Apollonian Circle Packing Will Appear?
复制标题
将会出现什么类型的阿波罗圆填料？
DOI：
10.1080/00029890.2021.1933834
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
J. E. Holly
中科院分区：
文献类型：
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作者：
J. E. Holly
摘要阿波罗圆包装是由三个成对相切的圆开始，添加两个圆或圆和线与前三个相切，然后通过连续添加新的圆和线与每一个新的相切的三个新的圆和/或线，永远重复这个过程。生成的填充是以下四种类型之一：有界（由其中一个圆包围）、半平面（有一条线）、条带（有两条线）或全平面。给定三个起始圆，会出现什么样的阿波罗圆包装？本文以图片的形式给出了答案，即，参数空间中起始圆的相对大小的图，指示填料的类型。结果是一个分形，然后进一步探索。
Abstract An Apollonian circle packing is created by starting with three pairwise tangent circles, adding the two circles—or circle and line—tangent to the first three, then repeating the process forever by successively adding new circles and lines tangent to every new tangent threesome of circles and/or lines. The resulting packing is one of four types: bounded (enclosed by one of the circles), half-plane (with one line), strip (with two lines), or full-plane. Given three starting circles, what type of Apollonian circle packing will appear? This article gives an answer in the form of a picture, i.e., a plot in the parameter space of relative sizes of the starting circles, indicating the types of packings. The result is a fractal, which is then further explored.