The present paper introduces a novel object of study - a language fractal
structure. We hypothesize that a set of embeddings of all $n$-grams of a
natural language constitutes a representative sample of this fractal set. (We
use the term Hailonakea to refer to the sum total of all language fractal
structures, over all $n$). The paper estimates intrinsic (genuine) dimensions
of language fractal structures for the Russian and English languages. To this
end, we employ methods based on (1) topological data analysis and (2) a minimum
spanning tree of a data graph for a cloud of points considered (Steele
theorem). For both languages, for all $n$, the intrinsic dimensions appear to
be non-integer values (typical for fractal sets), close to 9 for both of the
Russian and English language.

该研究介绍了一种新的研究对象 - 语言分形结构，假设一个自然语言的所有 n-gram 嵌入构成了该分形集合的代表样本，通过使用基于拓扑数据分析和数据图的最小生成树方法估计俄语和英语语言分形结构的固有维度，结果发现对于俄语和英语语言，所有的 n 值的固有维度都是接近 9 的非整数值（典型的分形集合）。