[seqfan] Re: Bear's paw sequence
Alonso Del Arte
alonso.delarte at gmail.com
Sun Aug 29 21:41:29 CEST 2010
Absolutely. With sequences like
A006874<http://www.research.att.com/~njas/sequences/A006874>
and A000740 <http://www.research.att.com/~njas/sequences/A000740> there is
certainly a place for sequences related to geometric designs, especially
when the design is as famous and familiar as the bear's paw (though I had no
idea that's what it meant to represent).
Would I be right in assuming you have already tried looking these sequences
up and going to Superseeker if that came up dry?
What I'd do if I were you, is see if any anthropological journals mention or
at least hint at the underlying mathematics of these patterns and go from
there.
Al
On Sun, Aug 29, 2010 at 1:34 PM, Jeremy Gardiner <
jeremy.gardiner at btinternet.com> wrote:
> Is there a place for sequences related to geometric designs in the OEIS?
>
> The following sequence was inspired by the traditional Bear's Paw quilt
> design:
>
> http://www.jeremy.gardiner.btinternet.co.uk/maths/bears_paw.gif
>
>
> 1,1,0,-1,1,1,0,-1,1,0,-1,-1,1,0,-1,-1,-5,0,-1,1,1,0,-1,1,1,0,0,1,1,-1,0,1,1,
>
> -1,0,-5,-1,-1,0,1,-1,-1,0,1,-1,0,1,1,-1,0,1,1,5,0,1,-1,-1,0,1,-1,-1,0,0,-1,-
> 1,1,0,-1,-1,1,0,5
>
> This geometric design is produced by drawing straight lines starting from
> the origin such that each pair of terms in the sequence gives successive
> differences in x and y coordinates.
>
> There is an interesting history of this design here:
>
> http://www.womenfolk.com/quilt_pattern_history/bearspaw.htm
>
> Changing the 5's in this sequence to 1's produces an octagonal cross
> design:
>
> http://www.jeremy.gardiner.btinternet.co.uk/maths/octagon_cross.gif
>
>
> 1,1,0,-1,1,1,0,-1,1,0,-1,-1,1,0,-1,-1,-1,0,-1,1,1,0,-1,1,1,0,0,1,1,-1,0,1,1,
>
> -1,0,-1,-1,-1,0,1,-1,-1,0,1,-1,0,1,1,-1,0,1,1,1,0,1,-1,-1,0,1,-1,-1,0,0,-1,-
> 1,1,0,-1,-1,1,0,1
>
> Alternative substitutions for 5's (and/or sign change) produces these other
> interesting designs:
>
> http://www.jeremy.gardiner.btinternet.co.uk/maths/diamond.gif
>
>
> 1,1,0,-1,1,1,0,-1,1,0,-1,-1,1,0,-1,-1,-0,0,-1,1,1,0,-1,1,1,0,0,1,1,-1,0,1,1,
>
> -1,0,0,-1,-1,0,1,-1,-1,0,1,-1,0,1,1,-1,0,1,1,0,0,1,-1,-1,0,1,-1,-1,0,0,-1,-1
> ,1,0,-1,-1,1,0,0
>
> http://www.jeremy.gardiner.btinternet.co.uk/maths/triangles.gif
>
>
> 1,1,0,-1,1,1,0,-1,1,0,-1,-1,1,0,-1,-1,1,0,-1,1,1,0,-1,1,1,0,0,1,1,-1,0,1,1,-
>
> 1,0,1,-1,-1,0,1,-1,-1,0,1,-1,0,1,1,-1,0,1,1,-1,0,1,-1,-1,0,1,-1,-1,0,0,-1,-1
> ,1,0,-1,-1,1,0,-1
>
> http://www.jeremy.gardiner.btinternet.co.uk/maths/bears_paw_cross.gif
>
>
> 1,1,0,-1,1,1,0,-1,1,0,-1,-1,1,0,-1,-1,5,0,-1,1,1,0,-1,1,1,0,0,1,1,-1,0,1,1,-
>
> 1,0,5,-1,-1,0,1,-1,-1,0,1,-1,0,1,1,-1,0,1,1,-5,0,1,-1,-1,0,1,-1,-1,0,0,-1,-1
> ,1,0,-1,-1,1,0,-5
>
> Doubtless these designs and the corresponding sequences have been studied
> before by someone - does anybody know of references to these?
>
> Jeremy
>
>
>
>
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