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User:Creighton Dement
My main mathematical interest involves "floretions".
Floretions are hypercomplex algebraic objects built from words in the alphabet 1, 2, 4, 7 where the digits correspond to the quaternionic symbols i, j, k, e and are multiplied digit by digit with signs collected globally. They provide a coordinate system linking quaternion-like multiplication, finite group structure, integer sequences, and recursive triangular tilings. Most floretion-generated sequences currently at the OEIS come from order two floretions. If X is an order two floretion, then the sequence (X, X^2, X^3, ...) gives rise to 16 4th order linear recurrence sequences (one for each of the 16 base vectors). Note that the original notation with arrows over the base vectors has been "simplified" in recent work, e.g. X = .5'i + .5'ii' + .5'ij' + .5'ik' becomes X = 0.5ei + 0.5ii + 0.5ij + 0.5ik
Floretion link summary:
- FLORETION BASE VECTORS, TRIANGULAR TILINGS, AND DIGITWISE S3-ACTIONS
https://arxiv.org/html/2605.20265 (see appendix for hints on notational changes)
- Online Floretion Calculator
- "Main" OEIS definition
- Sequences related to “Floretion”
https://www.mrob.com/pub/seq/floretion.html
- STRUCTURE OF THE FLORETION GROUP
https://oeis.org/A173343/a173343.pdf (covers order 2 only)
- 7th order example
https://www.youtube.com/shorts/dsBdv_ZQppM (YouTube)
- Generating music with floretions
