I have been working on creating some pictures of (very roughly) Julia sets of Hénon maps. The aim is to use these to investigate some conjectures of Lipa. Below, the GIFs show a SaddleDrop output and the corresponding dynamical picture.

The above picture shows the "Julia set" of a Hénon map as we follow a hyperbolic component in parameter space. The SaddleDrop output was created by Sarah Koch. Each frame is a $c$-slice. The $c$ value for the Hénon map corresponds to the green dot. The Jacobian parameter is moving in a spiral through parameter space starting from $0$.

In the above picture we are travelling around a herd in parameter space (See Lipa's thesis).