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Published on: February 7, 2017
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p-Adic morphology, biomorphic structures and number theory.
1Independent Scholar, 125222, Moscow, Box#57, Russia.
Bio Systems
|March 31, 2021
Summary
This study links number theory and morphology, using p-adic arithmetic to model biological forms. New mathematical techniques reveal biomorphic structures and symmetries from number systems.
Area of Science:
- Number Theory
- Mathematical Morphology
- Computational Biology
Background:
- Traditional number theory and morphology lack a unified framework.
- Modeling complex biological forms requires advanced mathematical tools.
Purpose of the Study:
- To establish a link between number theory and morphology.
- To explore the use of p-adic arithmetic for modeling biological forms.
- To construct novel biomorphic structures using mathematical techniques.
Main Methods:
- Development of mathematical techniques based on locally compact abelian groups and p-adic spectrum.
- Application of these techniques to classical series and infinite products.
- Introduction of Ω-classes as a 2-adic analogue of modular arithmetic residual classes.
Main Results:
- Construction of biomorphic structures as continuous images of 2-adic balls in the complex plane.
- Demonstration of the connection between Ω-classes and discrete 2-adic diffusion.
- Identification of Ω-classes producing bilateral symmetry and multidimensional symmetries in natural numbers.
- Introduction of a cellular structure for natural numbers to construct 2-adic organisms.
Conclusions:
- P-adic arithmetic offers a novel framework for modeling biological morphogenesis.
- The developed mathematical techniques reveal new properties of number series and products.
- Ω-classes and cellular structures provide insights into generating complex biological forms from number theory.
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