A Periodic Macrostructural Extension Framework for Two-Dimensional Ternary Word Square Palindromes

This paper introduces a combinatorial scalability framework designed to extend a 5x5 ternary palindromic matrix template into a macrostructural 10x10 grid. By applying discrete axial reflections and mirroring techniques to four quadrant-aligned 5x5 sub-matrices, a highly symmetrical, periodic tiling system is generated. This framework preserves the fundamental phonotactic constraints—specifically the structural distribution of consonantal, vocalic, and nodal elements—on the micro-level, while establishing an invariant, multidirectional macro-palindrome on the 10x10 scale. The resulting composition demonstrates the exact structural scalability, translational symmetry, and iterative potential of the underlying ternary algorithm.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-21
DOI
https://doi.org/10.5281/zenodo.20332698
Primary Topic
Matrix Theory and Algorithms
Type
article
Field-Weighted Citation Impact
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article

A Periodic Macrostructural Extension Framework for Two-Dimensional Ternary Word Square Palindromes

Maik Eifler
Zenodo (CERN European Organization for Nuclear Research)
Matrix Theory and Algorithms
article

A Periodic Macrostructural Extension Framework for Two-Dimensional Ternary Word Square Palindromes

Maik Eifler
article en

Abstract

This paper introduces a combinatorial scalability framework designed to extend a 5x5 ternary palindromic matrix template into a macrostructural 10x10 grid. By applying discrete axial reflections and mirroring techniques to four quadrant-aligned 5x5 sub-matrices, a highly symmetrical, periodic tiling system is generated. This framework preserves the fundamental phonotactic constraints—specifically the structural distribution of consonantal, vocalic, and nodal elements—on the micro-level, while establishing an invariant, multidirectional macro-palindrome on the 10x10 scale. The resulting composition demonstrates the exact structural scalability, translational symmetry, and iterative potential of the underlying ternary algorithm.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 4%
Matrix Theory and Algorithms
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