Name
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. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1007/s00454-003-0778-7 | Discrete & Computational Geometry |
Keywords | Field | DocType |
iterated function system,linear order | Cut-point,Topology,Iterated function system,Graph,Combinatorics,Disjoint sets,Countable set,Draco (constellation),Planar,Mathematics,The Intersect | Journal |
Volume | Issue | ISSN |
29 | 4 | 0179-5376 |
Citations | PageRank | References |
2 | 0.73 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sze-man Ngai | 1 | 3 | 1.16 |
| Nhu Nguyen | 2 | 29 | 5.65 |