Mating, paper folding, and an endomorphism of PC^2
  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 $PC^2$ to itself. We show a relation of this rational function with an uncountable family of "paper folding" plane filling curves. 
Volodymyr Nekrashevych
math.DS