Mating, paper folding, and an endomorphism of PC²

2016/02/29 by Volodymyr Nekrashevych, Nekrashevych, Volodymyr
Mathematics · #37F15 #37F20 #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1603.00079

openalex publication_date 2016/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are studying topological properties of the Julia set of the map F(z, p)=((2z/(p+1)-1)², ((p-1)/(p+1))²) of the complex projective plane PC² to itself. We show a relation of this rational function with an uncountable family of "paper folding" plane filling curves.

Citations

• The Fractal Geometry of Nature

Related

• The Julia set of a post-critically finite endomorphism of PC²
• Julia sets and bifurcation loci
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• Filled Julia set of some class of Hénon-like map
• Quadratic matings and ray connections