Fascinating breakdown of how numerical sequences produce geometric structures. The progression from the n=8 case to n=971 really shows how complexity emerges from simple rules, kinda reminds me of how fractals work. I had no idea the van der Corput sequence could map onto something as wild as the Chamanara surface with infinit handles, the whole Loch Ness monster analogy is perfect.
There are two sequences being considered: the Kronecker sequence, which is infinite, and the cycle of vertices in the graph, which is finite. The graph is formed by discarding all but the first n terms of the Kronecker sequence.
Fascinating breakdown of how numerical sequences produce geometric structures. The progression from the n=8 case to n=971 really shows how complexity emerges from simple rules, kinda reminds me of how fractals work. I had no idea the van der Corput sequence could map onto something as wild as the Chamanara surface with infinit handles, the whole Loch Ness monster analogy is perfect.
I’m probably missing something obvious, but can’t reconcile these two statements:
> The Kronecker sequence has no repeated entries precisely because the golden ratio is irrational.
> These vertices are connected in a cycle by black edges linking 0 to 1, 1 to 2, and so on…
With no repeated entries, how does a cycle arise?
There are two sequences being considered: the Kronecker sequence, which is infinite, and the cycle of vertices in the graph, which is finite. The graph is formed by discarding all but the first n terms of the Kronecker sequence.
Does that help?
Ah, yes, thank you.