Standard Genetic Code and Golden Ratio Cubes

The well-known golden ratio and knowledge about genetic coding systems are useful for artificial intelligence systems, engineering, and education. The golden ratio has been recently suggested for an expansion to the field of probabilistic and artificial intelligence in Tanackov et al. (Tehni ki vjesnikc 18:641-647, 2011) [1], in brain research (Conte et al. in Chaos, Solitons Fractals 41:2790-2800, 2009; Pletzer et al. in Brain Res. 1335:91-102) [2, 3], and in human facial proportion (Mizumoto et al. in Am. J. Orthod. Dentofac. Orthop. 136:168-74; Petoukhov in Binary sub-alphabets of genetic language and problem of unification bases of biological languages. Dubna, Russia, p. 191, 2002) [4, 5]. In this paper, we consider the number of hydrogen bonds of genetic code matrix and establish a relation with golden ratio matrix. We construct three-dimensional cubes from two-dimensional matrices. Furthermore, we revealed some numerical patterns of golden ratios under basic addition operation. The relationship data about the genetic stochastic matrices/cubes associated with the genetic codes play important roles on our new understanding of genetic code systems and can lead to new effective algorithms of information processing for modeling mutual communication among different parts of the genetic ensemble.