[seqfan] Re: OT: paper "Number representations and dragon curves"
Robert Munafo
mrob27 at gmail.com
Thu Jun 3 05:29:41 CEST 2010
Well, then again, maybe I *didn'*t read that Davis & Knuth paper. I just
checked my Knuth "Art of Computer Programming" vol. 2 "Seminumerical
Algorithms" (section 4.1) and there I find the discussion of base -1+i that
I remember, along with the picture of the dragon fractal (this is in the
1997 Third Edition of "Seminumerical Algorithms").
And, checking the OEIS, I see that your paper "Number Representations and
Dragon Curves" is cited only by one sequence (A106665), and by no other
sequence. Therefore I suspect you are investigating A106665.
So given that assumption, I suppose you're wondering what the "Alternate
paper-folding" is or means. It's pretty simple. Look at the Wikipedia
article, http://en.wikipedia.org/wiki/Dragon_curve and note the illustrated
description under the heading "[Un]Folding the Dragon" and note that the 1's
and 0's in the A106665 description correspond to the L and R folds in the
Wikipedia discussion.
On Wed, Jun 2, 2010 at 17:34, Robert Munafo <mrob27 at gmail.com> wrote:
> I'm pretty sure I read that back in my distant past.
>
> The content is essentially the same as in this article:
>
> William J. Gilbert,
> Fractal geometry derived from complex bases
> The Mathematical Intelligencer, Volume 4, Number 2 (June 1982), pp. 78-86
> (ISSN 0343-6993; DOI 10.1007/BF03023486)
>
> PDF available here:
>
> http://www.math.uwaterloo.ca/~wgilbert/Research/MathIntel.pdf
>
>
> On Wed, Jun 2, 2010 at 11:31, Joerg Arndt <arndt at jjj.de> wrote:
>
>> I cannot access in any way the paper:
>
>
>> Chandler Davis, Donald E.\ Knuth:
>
> {Number representations and dragon curves, I and II}
>
> Journal for Recreational Mathematics,
>
> vol.3, pp.61-81 and pp.133-149, (1970).
>
>
>> If anyone got an electronic copy of this one,
>
> kindly email it my way, thanks in advance!
>
>
--
Robert Munafo -- mrob.com
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