This study presents and explores the “Metamorphosis Formula,” a theoretical framework designed for analyzing structural and morphological transformations in language, influenced by technological advancements and the demands of modern communication. A central component of the research is the development of algorithmic grammar theory, which utilizes mathematical formulas to analyze linguistic transformations, including changes induced by prefixes, infixes, and suffixes, as well as the use of chromatic algorithms to visually highlight grammatical information through color coding. The research integrates key concepts such as chromatic algorithms, the grammatical map, and the geometric architecture of information expression. It examines grammatical transformations at both national and international levels, focusing on the origin and adaptation of grammatical elements across various languages. The study analyzes the role of parentheses in grammatical structures and the adaptation of word roots in different linguistic contexts. Additionally, it develops advanced formulas, including the tone formula, the comparative formula, and the grammatical time formula, integrating grammatical correlations such as addition, elimination, fusion, and semantic flexion into a mathematical expression framework. The research explores the fusion and conjunction processes in grammatical elements, analyzing relationships such as determinant and determined, theme and rheme, and anaphoric and cataphoric elements. These relationships are mathematically defined and visually represented, offering new insights into linguistic structures. The study also examines information distribution processes within grammatical elements, addressing their morphological, syntactic, and phrasal values, and representing them through visual and mathematical models to enhance clarity. The findings emphasize the utility of color as a tool for facilitating the rapid comprehension of grammatical information, with significant implications for education and natural language processing. By connecting linguistic theory with mathematical and visual methodologies, this research contributes to a deeper understanding of linguistic evolution and offers practical applications for improving communication efficiency in academic and technological contexts.
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