The Heighway Dragon Revisited
The Heighway Dragon Revisited
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DOI：
10.1007/s00454-003-0778-7
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发表时间：
2003-05
影响因子：
0.8
通讯作者：
Sze-Man Ngai;N. Nguyen
中科院分区：
文献类型：
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作者：
Sze-Man Ngai;N. Nguyen
我们证明海威龙是以线性顺序相交的几何相似的封闭圆盘状平面集合的可计数的联合：其中任何两个相交于不超过一个截点，并且对于任何三个圆盘，至少存在两个具有空交集。因此，海威龙的内部是不相交的开放圆盘状平面集合的可数并集。我们确定了龙的所有切割点，并表明，两个切割点之间的每个盘状子集是一个图自相似集定义的图定向迭代函数系统组成的四个种子集。我们的结果描述了一个相当完整的图片的拓扑和几何结构的Heighway龙。
We prove that the Heighway dragon is a countable union of closed geometrically similar disk-like planar sets which intersect each other in a linear order: any two of them intersect at no more than one cut point and for any three disks there exist at least two with an empty intersection. Consequently, the interior of the Heighway dragon is a countable union of disjoint open disk-like planar sets. We determine all the cut points of the dragon and show that each disk-like subset between two cut points is a graph self-similar set defined by a graph-directed iterated function system consisting of four seed sets. Our results describe a fairly complete picture of the topological and geometric structure of the Heighway dragon.