Draft:Floretion

Floretion

Type	Theorem
Field	hypercomplex number
Conjectured by	Creighton Dement

Floretion (pronounced /ˈflɔːrɛtiɒn/) is a hypercomplex number system representing 16-dimensional quantities. Floretion, a hypercomplex number system representing 16-dimensional quantities, was developed by Creighton Dement as an extension of quaternions and octonions. These numbers are primarily utilized in iterative mathematical operations to generate complex, infinitely long integer sequences and patterns.

Definition and structure

Floretions are defined as algebraic expressions comprising real number coefficients and base vectors. These base vectors are constructed through the concatenation of digits from a designated four-element alphabet, Σ = {1, 2, 4, 7} Each digit in the alphabet serves as a coordinate index that maps directly to the classical units of quaternionic algebra (e, i, j, k). Each digit in the alphabet serves as a coordinate index mapping directly to the units of quaternionic algebra: (e), (i), (j), and (k). Standard mapping relates the digit 1 to the unit (e) (or 1), 2 to the imaginary unit (i), 4 to the imaginary unit (j), and 7 to the imaginary unit (k). Base vectors, are formed by concatenating these digits, such as (ii), (ij), or (ik). The total number of digits within a word determines the mathematical order of the floretion component.