[isotropy]

I like this - nice playing around. We usually think of this kind of tree as having directed edges from parent to child, e.g. from set to element. In your graphs, you're erasing the direction of the edges, which uncovers a neat little symmetry that I never thought about before.

All the (non-limit) von Neumann ordinals are of the form X+1 = {X, {X}}, where X is the previous ordinal in the set. If you just look at trees of this form:

X+1: X <- node -> {X}, or X <- node -> node -> X

then you ignore the direction of the parent-child relation, you get this:

X+1: X -- node -- node -- X

So that's why your trees are symmetric as undirected graphs; and of course, every lower ordinal has its own version of this symmetry, which is also contained in the tree. All the large gaps between sections correspond to node--node edges of the larger ordinals. Kinda neat!