I am looking for a geometric and topological way to make a visualization of higher dimensional berkovich spaces, starting with the berkovich plane. Of course, this is just a collection of bounded semi-norms, but the question remains: 
>Is there a visualization possible for $\mathbb A^2_{\text{Berk}}$ like the infinite branched tree for $\mathbb A^1_{\text{Berk}}$? 

(For $\mathbb A^1_{\text{Berk}}$ see for example Baker and Rumely's [Potential Theory and Dynamics on the Berkovich projective line]
[1], Chapters 1 - 2.)

I think you get a simplicial complex, but I don't know exactly how. On the one hand (reading Favre and Johnsson's [The valuative tree][2]), you have this list of valuations (thus, also of seminorms, allthough this book discusses seminorms on $\mathbb{C}^2$). On the other hand we have Berkovich's theory of Type I - Type IV points. I guess there just more Type I - Type IV points in a plane (i.e. more seminorms that occur as it were type I points), and some can be only represented by faces (two dimensional simplices), only I don't know how.

Are there any references on the visualization part?


  [1]: http://alpha.math.uga.edu/~rr/BerkPotDyn.pdf
  [2]: https://arxiv.org/abs/math/0210265