File:Locally connected Julia set of a hyperbolic function in the complex cosine family with two attracting cycles.svg

English: This is a high-resolution version of Figure 2(d) 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 and light grey. The map is ${\displaystyle f(z)=\lambda (1-\cos(z))}$, with ${\displaystyle \lambda =2}$. There is a superattracting fixed point at $0$, whose basin is shown in white; the second critical value $\lambda$ belongs to the basin of a second attracting cycle of period 2. Every Fatou component is a quasidisc, and the Julia set is locally connected.