Mapping Codons to the Complex Plane

The Tetrahedral Method by Paul Dan Cristea

Table of Symbolic Encoding Methods

Method Summary
2-bit binary representation Assigns a unique 2-bit binary sequence to each nucleotide (A = 00, C = 11, G = 10, T = 01)
4-bit binary encoding Assigns a unique 4-bit binary sequence to each nucleotide (A = 1000, C = 0010, G = 0001, T = 0100)
4-dimensional indicator sequence (Voss representation) Defines a four-dimensional space with a unique axis for each nucleotide
Use of a tetrahedron structure Represents the nucleotides in a three-dimensional tetrahedron model
Use of integer values Assigns a unique integer to each nucleotide, with different ranges used (e.g., 0 to 3, 1 to 4)
Use of real numbers Assigns a unique real number to each nucleotide (e.g., A = 21.5, T = 1.5, C = 0.5, G = 20.5, or A = 0.25, G = 0.5, C = 0.75, T = 1)
Complex number values Assigns a unique complex number to each nucleotide (e.g., A = 1zj, C={1zj, G= {1{j and T = 1{j)
Use of quaternions Represents nucleotides using quaternions, a form of complex number with four parts (e.g., A = izjzk,C= i{j{k,T={izjzk, and G = {i{jzk)

Source: Borrayo E, Mendizabal-Ruiz EG, Ve´lez-Pe´rez H, Romo-Va´zquez R, Mendizabal AP, et al. (2014). "Genomic Signal Processing Methods for Computation of Alignment-Free Distances from DNA Sequences." PLoS ONE 9(11): e110954. doi:10.1371/journal.pone.0110954