Quaternion Spiral

[Creighton Dement]

Dear Seqfans,

Plotting sequences
http://www.research.att.com/projects/OEIS?Anum=A108618
against http://www.research.att.com/projects/OEIS?Anum=A108619
also gives a (beautiful) spiral... which I decided to call “Gerald's
Spiral”.

Although he didn't set up this particular plot directly, he was the
first to notice the little “diamonds” with line segments parallel to the
x-axis in A108618 (these should rightfully be called “Gerald's
Diamonds”) in his plot of the first 32000 terms:
http://www.crowdog.de/Quad32000Ger.jpg
and this is information which might later become useful in the analysis
of the spirals.  

Important FAMP note: please do not download FAMP until later this
evening (German time) – possibly until tomorrow-  it's taking me a long
time update the interface (this has basically been done) and upload.  I
will label the new version “FAMP, ver. Moonlice 1.2 (Unix/Linux)”. It
may be able to run just as well on a Windows platform (perhaps with some
minor changes) as the program is written in Java,  but I haven't had
time to check this (the old version of FAMP should run o.k. on Windows).

Moreover, I know of at least two people who have thought about and/or
are trying to export bits and pieces of FAMP into other programming
languages. If you wish to do this you have my permission-  
the place to begin is with the file:
http://www.crowdog.de/MultiplyFlorets.html  it is really and truly the
heart of FAMP (and, if I remember correctly back to the beginning of
2004, it took me at 3 weeks of testing before I knew “without a doubt”
that  multiplication was being performed correctly) .
     
 

On a side note:
The answer to my Maple question has been answered (I've tested it and it
works- thanks Edwin Clark).

Sure, it would be a lot of fun to close the curtains in my room and
spend the next few weeks looking for 3dplots...(I will probably end up
doing just this) however, I am reminded of a saying I learned from
chess: “Don't go a huntin' when your house is burning down”.  Therefore,
I shall try to stick to updating FAMP for now.