This is a high-resolution version of Figure 2(b) from the paper "Hyperbolic entire functions with bounded Fatou components" by Bergweiler, Fagella and Rempe-Gillen (https://arxiv.org/abs/1404.0925). The Julia set is shown in dark tones of grey; the Fatou set is shown in white. The map is $f(z)=a\cos(z)+b$, with $a=4i/(1-\cosh4)$ and $b=4i-a$. There is a unique superattracting cycle consisting of the points 0 and 4i. Points in the Fatou set are coloured white and light grey depending on whether they take an even or odd number of iterations to reach the Fatou component containing $0$. Superattracting cycles are indicated by black filled circles; non-periodic critical points are marked with asterisks
Own work
L Rempe-Gillen