Fractals and Chaos Related to Ising-Onsager-Zhang Lattices. Quaternary Approach vs. Ternary Approach

Continuing our idea (Int. J. Geom. Methods Mod. Phys.) of extending some aspects of Onsager (Phys Rev 65:117–149, 1944) crystal statistics to three dimensions taking into account binary and ternary crystal structures in connection with fractals and chaos related to Ising–Onsager–Zhang lattices, we (1) use the Galois extension structure of the nonion algebra, (2) analyze ternary and binary structures of $su\left(3\right)$ as well as (3) analyze the identification of the construction of the collection of two ternaries with the collection of three binaries, (4) observe that the approach is applicable to quarks and elementary particles including introduction of colors and, finally, (5) suggest an analysis of three quaternaries vs. four ternaries, involving duodevicenion and/or quindenion algebra.