[seqfan] Re: Anyone have a 3-D "Ulam" spiral?

Kevin Ryde user42_kevin at yahoo.com.au
Wed Apr 28 02:11:29 CEST 2021

primeness at borve.org (Neil Fernandez) writes:
> 3D Ulam spiral

Maybe similar thing expressed a different way?:  On a cube make a
horizontal spiral outwards on the top face, horizontal loops around to
traverse the sides, and a horizontal spiral inwards on the bottom face.
Then next layer by step down and spiral outwards on the bottom face, etc.

I think this needs at least 1 diagonal step in the loops so as to make
the spiral-inwards begin at a corner.  A diagonal step is unlike the 2D
spiral of course.  Could have every loop-around take a diagonal step at
its end so each loop begins on a corner.

Among self-similar curves, Peano gave a 3D form for filling a unit
cube which can be done in integers to fill one octant x,y,z>=0.
A couple of authors have thought about how Hilbert's curve might best
go in 3D, again in one octant unless you invent some sort of additional
reflections or something to go to negatives.

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