Fractal Linguistics: Recursion, Scaling, and the Hidden Geometry of Language

Over the past few years, I’ve been playing around with an idea I call Fractal Linguistics—a way of understanding how language repeats its own structures at different scales of meaning and syntax. It began, as many linguistic discoveries do, with a puzzle: Persian complex predicates, those fascinating noun-verb or adjective-verb combinations like ranj keshidan (“to drag pain” meaning to suffer) or rang zadan (“to hit color” meaning to paint).

When I looked closely at these constructions, I noticed something remarkable. The same compositional logic that determines aspect and argument structure at the sentence level seems to reappear inside the predicate itself. It was as if each complex predicate was a miniature version of the verb phrase: a self-similar structure, recursively repeating the same syntactic and semantic relations that govern the larger clause.

That realization became the seed of what I now think of as Fractal Linguistics: the idea that language is not a hierarchy of discrete modules, but a scale-sensitive system, where the same structural patterns re-emerge at different linguistic magnitudes.

From Complex Predicates to Self-Similarity

In Persian, light verbs like zadan (“hit”), gereftan (“take”), or kardan (“do”) are often described as semantically “light,” but that term hides a deeper truth. They aren’t empty but rather underspecified, containing just enough structure to project an event template without fixing its content.

When these light verbs combine with a nonverbal element such as noun, adjective, or prepositional phrase, the result behaves like a full verb phrase: it projects arguments, defines event boundaries, and determines aspect. In other words, a complex predicate is a small-scale recursion of the verb phrase.

Scaling Meaning: How Aspect Emerges Twice

In event semantics, aspect (whether an event is bounded or ongoing) is determined compositionally by how verbs and their objects interact. The same principle holds within complex predicates: the boundedness of the nonverbal element and the underspecified structure of the light verb jointly determine lexical aspect.

At a larger scale, the verb phrase itself combines with complements and adverbials to produce clausal aspect. In both cases, boundedness and compositionality operate at different scales, producing parallel outcomes.

So, aspect is not a single-layer property of verbs—it’s a scaling phenomenon, emerging from recursive compositional structures across linguistic levels.

A Linguistic Mandelbrot Set

When you zoom in on a Persian complex predicate, you find the same geometry of relations that defines the entire clause: argument structure, aspect, telicity, and event delimitation. The small mirrors the large; the structure of the locatum rowqan zadan ("to hit oil" meaning to oil, to apply oil) reflects the logic of a full verb phrase. For specific examples and argumentation, see my presentation Recursion and Scaling in Complex Predicates: Light Verbs as Underspecified Regular Verbs.

This kind of self-similarity, where structural relations repeat at smaller or larger linguistic scales, is the hallmark of fractals. Just as coastlines or snowflakes reveal the same shape at every magnification, language seems to do the same. The syntax-semantics interface, in this sense, behaves fractal-like: scaling up or down doesn’t change its fundamental pattern.

Rethinking Lexical Categories

If this recursive structure holds, we may not need a separate “light verb” category at all. Instead, we can think of light verbs and full verbs as points on a continuum of structural specification. The difference between zadan as a light verb and zadan as a full verb isn’t categorical, it’s scalar. The same structural relations exist, but at different resolutions.

This scaling view dissolves the traditional boundary between lexical and phrasal formation, showing that the same syntactic architecture governs both. Complex predicates and full verb phrases are not different phenomena—they are the same structure, observed at different scales.

Everything is Compositional, Everywhere

As I presented in my earlier talk on this topic, the evidence points to one central insight:

“Everything is compositional. Eventive properties, aspect, argument structure, and interpretation are all derived by the contributions of each part, at every level of scale.”

In that sense, structure determines meaning, and recursion is not just a property of syntax—it’s the organizing principle of language itself.

Toward a Theory of Fractal Linguistics

This framework opens new directions for research. If linguistic composition is inherently scale-sensitive, we might model it using concepts from complex systems and fractal geometry, where patterns emerge through self-similar repetition.

It also connects naturally to AI: neural language models already encode multi-scale representations of syntax and meaning. Understanding language as fractal could bridge formal linguistics and machine representation, helping us explain why deep models capture linguistic regularities without explicit rules.

I’m currently developing these ideas further in a forthcoming paper, Fractional Dimensions in Language. For now, I think of Fractal Linguistics as an invitation: to look again at the familiar architectures of grammar and see them not as static trees, but as living, recursive structures—patterns that echo themselves from the lexicon to the clause.