When searching through the Oeis, I came across something called a floretion. Based on the context, it seems to be some sort of algebraic structure. I googled it and found nothing that explained their exact definition or motivation. Could someone explain its motivation and definition to me? A source would also be helpful if it explains the motivation.


The sequence is [A105163]: <http://oeis.org/A105163>



What is the motivation and purpose of the Floretion group?
A rather comprehensive collection of information on floretions, specifically in the context of Oeis, is [Sequences related to floretions.](http://www.mrob.com/pub/seq/floretion.html)



> 
> In essence, most of the "floretion" sequences come from an iterated
> function that begins with some initial value and produces one integer
> at each step of the iteration. The floretion algorithms operate on a
> 16-element quantity that can be thought of a a $4\times 4$
> matrix. Such a
> 16-element quantity is called a *floretion*. The name is deliberately
> similar to [quaternion](https://en.wikipedia.org/wiki/Quaternion), [octonion](https://en.wikipedia.org/wiki/Octonion) and [sedenion](https://en.wikipedia.org/wiki/Sedenion) because the
> operations performed with them are similar. (But why doesn't the floretion have its own Wikipedia page?)
> 
> 
> 


If you want to "hear" a floretion, [here you go.](https://web.archive.org/web/20160324053743/http://doku.floretions.fumba.eu/doku.php?id=start)


