Complex Systems

A Pit of Flowsnakes Download PDF

Bradley Klee

Department of Physics
University of Arkansas
825 West Dickson Street
Fayetteville, AR, 72701, USA


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.