Complex Systems

A Pit of Flowsnakes Download PDF

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.