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A Pit of Flowsnakes
Bradley Klee
Department of Physics
University of Arkansas
825 West Dickson Street
Fayetteville, AR, 72701, USA
Abstract
Vector replacement rules allow formulation of the flowsnake plane-filling curve as a bijection and as a surjection
. The
-function visits double and triple points predicted by Netto's theorem. Triple points belong to a relatively simple set, while double points resist easy classification. This paper formulates and analyzes the
-function. Methods applied to the flowsnake also apply to other plane-filling curves.