[seqfan] Re: A229215 Gosper Curve, major revision or new seq?

[Kevin Ryde]

bradklee at gmail.com (Brad Klee) writes:
>
> I'm not sure, but it looks like Yr computation uses an arbitrarily
> ordered list:
> 1,2,3,-1,-2,-3

Yes, A229215 directions

           3   2
            \ /
       -1 ---*--- 1
            / \
          -2   -3

but the curve rotates clockwise, so a(2)=-3.  Clockwise is the negation
-A062756(...).  Could reverse the vector instead 1,-3,-2,-1,3,2.

> And you get the asymmetrical sequence. If you use
>
> 1, -3, 2, -1, 3, -2
>
> You should get the periodic sign sequence.

Oh yes, curve turn +/- 60 degrees each time so however the direction is
encoded it's forward or backward one each time.

> I'm not sure I understand Terdragon connection, but it sounds
> interesting.

The usual terdragon is an unfold by 60 degrees.  A229215 is the same but
unfold by 120 degrees.  The bigger unfold means it doesn't touch itself.

        2-----3                  2-----3
    60   \                120   /
          \                    /
     0-----1            0-----1         (here spiralling anti-clockwise)

> when you encrypt a symbolic sequence such as these into numbers,
> depending on arbitrary choices it will / will not be easy for someone
> to decipher. I saw this problem on Sequences for Gosper curve and
> Hilbert curve: encoding of turns or vectors does not preserve symmetry
> and / or modulus arithmetic.

I agree with Joerg that say 0 to 5 would be more arithmetic.  That could
give net direction equal to sum of turns, modulo a full circle.  But the
motivation in A229214+A229215 is a little different, maybe, is it ...