> I think a fair thing to ask is if the force-directed layout engine is uniquely responsible for the leaf-like structure and this has nothing to do with the Von

> I think a fair thing to ask is if the force-directed layout engine is uniquely responsible for the leaf-like structure and this has nothing to do with the Von Neumann ordinals themselves. > To check this I generated some Collatz trees and they ended up looking like microbes. I think it's safe to say the answer is no. "Uniquely responsible" seems to be doing too much work. These structures are reminiscent of dendritic fractals coming about from diffusion-limited aggregation in electrochemical deposition[1], which is a transitional phenomenon with a phase diagram (molar concentration of the electrolyte vs voltage) There is a sweet spot in the middle where you get intricate dendritic crystals: outside of that you get smooth layers or big blobs / spikes without much internal structure. I suspect it is primarily the modeling of the forces which is responsible for the behavior, with the topological structure of the tree somewhat indirectly corresponding to the chemical and electrical parameters. I am by no means an expert but it seems likely to me that these von Neumann dendrites vs the structure of Collatz trees is a fairly shallow relationship: lots of trees with similar graph-theoretic properties to the von Neumann trees would also demonstrate the leaf-like fractals, but with no meaningful relationship to the natural numbers. But it would be interesting to make this more precise. [1] https://en.wikipedia.org/wiki/Diffusion-limited_aggregation https://en.wikipedia.org/wiki/Diffusion-limited_aggregation