The Heighway Dragon Revisited |
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Authors: | Ngai Sze-Man Nguyen Nhu |
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Institution: | (1) Department of Mathematics and Computer Science, Georgia Southern University, Statesboro, GA 30460-8093, USA ngai@gsu.cs.gasou.edu, US;(2) Department of Mathematics, New Mexico State University, Las Cruces, NM 88003-8001, USA nnguyen@nmsu.edu, MX |
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Abstract: | 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. |
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