Download PDFRevised 13 June 2023
Accepted 28 June 2023
Available Online 12 July 2023
- DOI
- https://doi.org/10.55060/j.gandf.230712.001
- Keywords
- Genetic code equivalence
Fixed points
Julie sets
Mandelbrot sets
Golden ratio
Ring ratio
Unity ratio - Abstract
It is well known that a genetics system in biology delivers the biological organism’s self-reproduction in their generations. Similarly, the “golden ratio” in mathematics keeps its self-reproduction property in their iterations. The biological system divides the genetic four-letter alphabet (A, C, G, T/U) into various three pairs of letters. There are three kinds of genetic equivalences among these four-letter alphabets (A=C, G=U; A=G, C=U; A=U, C=G). In this paper, we investigate the geometric shapes and forms associated with these three kinds of genetic code equivalences. We show that each equivalence has its own geometric shape and form. These geometric properties include attracting fixed point, repelling fixed point, basin of attractions, Julia sets and corresponding Mandelbrot sets. We further study the golden ratio, ring ratio and unity ratio matrices associated with three kinds of genetic code equivalences.
- Copyright
- © 2023 The Author. Published by Athena International Publishing B.V.
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (https://creativecommons.org/licenses/by-nc/4.0/).
Cite This Article
TY - JOUR AU - Matthew He PY - 2023 DA - 2023/07/12 TI - Geometric Shapes and Forms Associated With Three Kinds of Genetic Code Equivalences JO - Growth and Form SP - 11 EP - 20 VL - 4 IS - 1-2 SN - 2589-8426 UR - https://doi.org/10.55060/j.gandf.230712.001 DO - https://doi.org/10.55060/j.gandf.230712.001 ID - He2023 ER -
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