Fractals and chaos related to Ising-Onsager lattices. Ternary approach versus binary approach

Abstract

In connection with several attempts to extend Onsager’s (1944) crystal statistics to three dimensions keeping the spirit of the original Ising’s (1925) model, we suggest to involve binary and ternary extension of triangles in connection with fractals and chaos, following the ideas of Kikuchi (1951). We apply ternary Clifford algebras in addition to the usual (binary) Clifford algebras and identify two ternaries with three ternaries with the help of noncommutative Galois extension. In some sense, the paper continues the ideas of Ławrynowicz, Marchiafava and Nowak-Kȩpczyk (2006), and Kerner and Suzuki (2012) published in this journal.