This is a high-resolution version of Figure 1(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 black. The map is f(z)=−z2e1−z2{\displaystyle f(z)=-z^{2}e^{1-z^{2}}}. Here there are superattracting fixed points at 0 and -1 (marked with filled circles), and 0 is an asymptotic value. The basin of 0 is coloured white and the basin of -1 is coloured grey. Every Fatou component is a Jordan domain, but all pre-periodic components of the basin of 0 are unbounded, and the Julia set is not locally connected. The non-periodic critical point 1 is marked by asterisks.
This file was derived from: Julia set of a hyperbolic entire function in the Laguerre-Polya class.svg:
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derivative work: Yomomo