A Generative Ternary Framework for Constructing Two-Dimensional Palindromic Word Squares

This paper introduces a generative blueprint for creating novel 5x5 palindromic word squares in any language. Based on a previously discovered ternary matrix representation of the historical Sator Square, this framework abstracts the structural constraints of language into three mathematical states (0, 1, 2). By using this matrix as a programmatic or manual template, creators can algorithmically generate flawless, multidirectional word-square palindromes without relying on trial-and-error linguistics.

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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.20330675
Primary Topic
semigroups and automata theory
Type
article
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article

A Generative Ternary Framework for Constructing Two-Dimensional Palindromic Word Squares

Maik Eifler
Zenodo (CERN European Organization for Nuclear Research)
semigroups and automata theory
article

A Generative Ternary Framework for Constructing Two-Dimensional Palindromic Word Squares

Maik Eifler
article en

Abstract

This paper introduces a generative blueprint for creating novel 5x5 palindromic word squares in any language. Based on a previously discovered ternary matrix representation of the historical Sator Square, this framework abstracts the structural constraints of language into three mathematical states (0, 1, 2). By using this matrix as a programmatic or manual template, creators can algorithmically generate flawless, multidirectional word-square palindromes without relying on trial-and-error linguistics.

Zenodo (CERN European Organization for Nuclear Research)
Quality Education
Openalex Percentile: Top 5%
semigroups and automata theory
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