[seqfan] Floretions and related work of Creighton Dement

[Robert Munafo]

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