[seqfan] Re: Floretions and related work of Creighton Dement

[Bob Lyons]

Hi Robert,

I'm not familiar with floretions.
But back in March, Neil and I discussed the FAMP programs and the fact that
there doesn't seem to be an easy way to run these programs.
Neil asked me to move all the FAMP programs from the PROG section to the
COMMENTS section.

Thanks,

Bob



On Fri, Apr 26, 2024 at 12:44 PM Robert Munafo <mrob27 at gmail.com> wrote:

> It's been a while since I had anything to do with this, but apparently
> Creighton K Dement (CKD) continues to work on "floretions", a rather
> elaborate and seemingly self-invented system that generates patterns
> including images, music, and integer sequences. The latest thing he
> just wrote me about uses a general definition based on binary
> representation of integers taken 3 bits at a time and then used to
> index into the basis elements of normal quaternions... or something.
>
> There are at least some pretty pictures, see e.g. the figure on page 2
> of the PDF
> https://github.com/Floretion-Inquisitor/floretions/blob/main/Floretions_and_D3_draft.pdf
>
> Has anyone gained any familiarity CKD's work more recently than 2010?
>
> Last time I checked, back in 2011 or so, the definition of
> "floretions" was completely different, a quasi ring-like algebraic
> system with 16 basis elements (but not normal sedenions). At the time
> there were many, many sequences in the OEIS based on these older
> "floretions" that lack a complete definition (as might be provided by
> a self-contained Mathematica program).
>
> I did a lot of work on this around 15 years ago, and corresponded with
> CKD, and at the time we concluded that most of the exact definitions
> were lost. The FAMP or "Floretion Algebra Multiplication Program"
> mentioned in many OEIS comments was Java that kept getting changed,
> and CKD forgot how to reproduce his earlier work. Others seem to have
> subsequently reverse-engineered some sequences by linear recurrences
> or generating functions, etc.
>
> The OEIS sequences that needed work (as of late 2009) were: A023554
> A038519 A049332 A059165 A085903 A090390 A094297 A096252 A097924
> A097947 A098111 A098212 A099163 A099256 A099867 A099868 A100212
> A100213 A100215 A100216 A100683 A100828 A100886 A100887 A100888
> A101348 A101386 A101463 A102129 A102214 A102239 A102285 A102296
> A102301 A102702 A102714 A102785 A102841 A102865 A102871 A103135
> A103145 A103177 A103196 A103644 A103645 A103646 A104004 A104005
> A104161 A104187 A104237 A104522 A104563 A104681 A104769 A104770
> A104771 A104934 A105058 A105077 A105082 A105163 A105225 A105343
> A105576 A105577 A105578 A105579 A105580 A105660 A105671 A105770
> A105951 A105963 A105964 A105966 A105968 A106157 A106603 A106664
> A106666 A106691 A107307 A107363 A107663 A107849 A107850 A107851
> A107852 A107853 A107854 A108051 A108057 A108306 A108390 A108391
> A108618 A108619 A108620 A108765 A108766 A108791 A108898 A108930
> A108931 A108946 A108985 A108986 A109164 A109165 A109249 A109340
> A109359 A109360 A109362 A109363 A109430 A109437 A109438 A109599
> A109609 A109610 A109620 A109731 A109765 A109781 A109782 A109784
> A109785 A109786 A109787 A109793 A109794 A109803 A110046 A110047
> A110048 A110050 A110051 A110052 A110062 A110063 A110064 A110151
> A110158 A110210 A110211 A110212 A110213 A110225 A110274 A110279
> A110280 A110281 A110282 A110283 A110293 A110294 A110307 A110308
> A110309 A110310 A110311 A110526 A110527 A110528 A110613 A110614
> A110679 A110683 A110684 A110685 A110686 A110687 A110688 A110689
> A110906 A111352 A111566 A111567 A111569 A111570 A111571 A111572
> A111573 A111574 A111587 A111639 A111640 A111641 A111642 A111643
> A111644 A111645 A111662 A111663 A111665 A111666 A111734 A111914
> A111915 A111926 A111954 A111955 A112533 A113066 A113067 A113224
> A113225 A113249 A114160 A114161 A114619 A114647 A114688 A114689
> A114696 A114697 A115032 A116483 A116484 A116698 A117153 A117154
> A119560 A119953 A119954 A120743 A126626 A129905 A131039 A131040
> A131041
>
> --
>   Robert Munafo, mrob27 at gmail.com
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>


-- 
Bob