MATING, PAPER FOLDING, AND AN ENDOMORPHISM OF PC2 Academic Article

We are studying topological properties of the Julia set of the map F ( z , p ) = ( ( 2 z p + 1 1 ) 2 , ( p 1 p + 1 ) 2 ) F(z, p)=left (left (frac {2z}{p+1}-1
ight )^2, left (frac {p-1}{p+1}
ight )^2
ight ) of the complex projective plane P C 2 mathbb {P}mathbb {C}^2 to itself. We show a relation between this rational function and an uncountable family of paper folding plane filling curves.