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

[Brad Klee]

Hi Kevin,

Oh no! I'm just now realizing I did something like a spoonerism on the codes. It should be A229214 in the title. 

But the same arguments apply. 

Sign(A229215) is not periodic here, but it should be because vectors along the boundary alternate between "cosets".

I'm not sure, but it looks like Yr computation uses an arbitrarily ordered list:

1,2,3,-1,-2,-3

And you get the asymmetrical sequence. If you use

1, -3, 2, -1, 3, -2

You should get the periodic sign sequence. 

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

The bottom line: 

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. 




Thanks,

Brad




> On Aug 8, 2015, at 3:12 AM, Kevin Ryde <user42_kevin at yahoo.com.au> wrote:
> 
> bradklee at gmail.com (Brad Klee) writes:
>> 
>> First of all, Bos has done better than most at defining the function
>> using vector notation, which eliminates annoying + and - signs.
> 
> If I understand what it refers to, it'd also be from count ternary
> 1-digits per A062756.  (The middle digit of each rewriting rule advances
> by 1.)  Spot of pari,
> 
>    A229215(n) = [1,2,3,-1,-2,-3][(-A062756(n-1) % 6)+1];
> 
> n-1 is for offset 1 in A229215.  These replication things can go nicely
> with first segment counted as 0.  Wouldn't change A229215 now, but could
> consider for future similar.
> 
> The turn sequence (first differences, interpreted the right way) would
> be the terdragon A080846 as cross-referenced in A062756 (and variations
> of A080846).
> 
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