This is a high-resolution raster version of Figure 2(a) 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)=λ(1−cos⁡(z)){\displaystyle f(z)=\lambda (1-\cos(z))}, with λ=3/4{\displaystyle \lambda =3/4}. The superattracting fixed point at 0{\displaystyle 0} is the only attracting cycle; the second critical value λ{\displaystyle \lambda } belongs to the immediate attracting basin of this cycle. The Fatou component is unbounded, and the Julia set is not locally connected.
Own work
L Rempe-Gillen