Julia subtyping: a rational reconstruction

Checkerboard Julia Sets for Rational Maps

In this paper, we consider the family of rational maps Fλ(z) = z n + λ zd , where n ≥ 2, d ≥ 1, and λ ∈ C. We consider the case where λ lies in the main cardioid of one of the n − 1 principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic. However, two such maps Fλ and Fμ are conjugate on these Julia sets only if the parameters at the center...

A Fast Algorithm for Julia Sets of Hyperbolic Rational Functions

Although numerous computer programs have been written to compute sets of points which claim to approximate Julia sets, no reliable high precision pictures of nontrivial Julia sets are currently known. Usually, no error estimates are added and even those algorithms which work reliable in theory, become unreliable in practice due to rounding errors and the use of fixed length floating point numbe...

Protos - a Rational Reconstruction

A Rational Reconstruction of Misbehavior

Classic social psychological research suggests that humans are more susceptible to social influence than they should be. This discrepancy between observed and normative behavior is often taken as the footprint of irrational reasoning. As much of the studied behavior is also socially undesirable, there is a dual verdict of irrationality and immorality. Using concepts and analytical tools from de...

Connectivity of Julia Sets for Singularly Perturbed Rational Maps

In this paper we consider the family of rational maps of the form F λ (z) = z n + λ/z n where n ≥ 2. It is known that there are two cases where the Julia sets of these maps are not connected. If the critical values of F λ lie in the basin of ∞, then the Julia set is a Cantor set. And if the critical values lie in the preimage of the basin surrounding the pole at 0, then the Julia set is a Canto...