Modeling Linguistic Complexity as a Multiscale Fractal-Information Structure via the Koch Snowflake (K) Paradigm

Human natural language has structural self-similarity and recursive informational scaling on an almost unlimited scale for many levels of hierarchy, from sub-lexical units to macro level discourse. The conventional linear and strictly context-free hierarchical models cannot account for both the interaction between bounded capacity and unbounded structural complexity. For the present paper, we present a unified model for linguistic complexity that offers us a perspective view of fractal-information of various scales from the perspective of the surface of the Koch Snowflake (). By introducing linguistic scales, phonemes/morphemes, words, syntax and discourse at discrete iterations in the snowflake boundary generator, we show that local context-sensitive insertion rules generate an infinite boundary length (structural capacity) within a strictly bounded Euclidean spatial measure (semantic domain). We combine Shannon information theory, algorithmic information theory (Kolmogorov complexity), and statistical physics (fractal dimension ) to measure information density, long-range correlation decay and structural entropy at linguistic levels. In addition, we investigate how contemporary deep learning architectures (such as Transformers) learn about this fractal geometry in high-dimensional embedding spaces. The paper provides empirical implications, open problems and future research outlooks.