Understanding Grammar as Fractal: Rhetorical effects and cultural implications, by MaryAnn Duffy


In science, the fractal is a relatively new discovery. The term comes from its Latin root, fractus, which means “to break” and alludes to the jagged, irregular-shaped edge. It is the term Benoit Mandelbrot, a linguist and mathematician, used in his 1982 book The Fractal Geometry of Nature to define the seemingly random shapes in nature that Euclidean-based geometry could not explain.

Euclidian geometry deals with more smoothly-shaped lines that produce circles, squares, triangles and rectangles. However, the edges produced by nature are not quite so tidy. Edges in nature —coastlines, shapes of leaves, a cauliflower—have extremely complex shapes and are difficult to measure. Measuring and mapping them for any patterns or consistency seemed to be a futile attempt at measuring nature’s randomness. Until Mandelbrot revealed the opposite. Many shapes in nature are actually recursive patterns. They start on the micro level and grow so as to render a self-same macro shape.


The edge of a coastline, as seen from an aerial view, is the same shape as any smaller part of that coastline’s whole. The cauliflower’s bloom is iterative self-same shapes. The silhouette of a tree, it turns out, mirrors its forest’s canopy. Given these fractal systems found all around us, it seems nature is not so random after all.



The fractal concept has not only captured the imagination of the scientific community, but popular culture as well. In 2010, the year Mandelbrot died, Wired magazine published a slideshow of different types of fractals found in nature, and that same year Time magazine ran a slide show to honor him. As recently as 2013, a website called Mother Nature Network ran a similar story.

Why is popular culture so enamored of this phenomena? Taken to its logical conclusion, it is captivating to think that fractals “subconsciously suggest that each of us is a microcosm, an image of the whole world, hence their strong appeal” (Mandelbrojt 98).

The fractal phenomena begs the question: How is it that nature, in its infinite complexity, is so deliberate as to dynamically repeat itself on such a grand scale? Even the staunchest atheist is bound to be dazzled by this phenomena. Is there an organizing entity at work, and what does this have to do with grammar?

If we look at the parameters of what a fractal is, a case can be made that grammar is also a fractal.

  1. [Fractals] are open and dynamic, as opposed to a static structure;
  2. include a very large number of interactive components/agents, as opposed to a hierarchical arrangement of types;
  3. show order from self-organization, as opposed to rule-bound relations;
  4. show nonlinear distribution of units, as opposed to random or statistically normal distribution; and
  5. have the property of scaling, as opposed to homogenous unity.  (Kretzschmar Jr. 272)

Dr. William Kretzschmar, Jr., creator of the Linguistic Atlas Project, writes about how the fractal phenomenon applies not to how language has variation, but how the complex systems of fractals account for language varieties. However, Kretzschmar discounts grammar as fractal, focusing solely on speech patterns of words based on rank and frequency.

Moreover, we do see self-organization from speech as we would expect from a complex system, in the form of geographical, social, and textual clustering of speech sounds and words. We recognize that sounds and words are not randomly distributed in speech interactions, but instead are associated in different ways with particular localities, particular social groups, and particular text types. Speech clearly meets these initial conditions for complex systems. . . . It seems clear, however, that linguistic rule structures as usually described in grammars, or in Bybee’s (2001) phonology, do not meet these criteria. By their nature, rule systems are static, hierarchical structures at low-energy equilibrium. [Emphasis added.] (Kretzschmar, Jr. 273)

If grammar is defined as man-made rules imposed on linguistic communities, the necessity of which is borne out of the need for standardization, Kretzschmar is correct; grammar is a static non-dynamic system. But is grammar an artificial man-made construction?


Grammar is not a set of rules imposed on us that we must follow in order to make written sense. Grammar is the emerging organic patterned orders of noun phrases, verb phrases and their attendant modifying phrases linguistic communities tend toward, bend, and even break to form new patterns as language evolves.

Which is to say, grammar is not prescriptive, it is descriptive.

If we look at grammar prescriptively—rules imposed on users—language as a fractal is simply a metaphor. But if we look at grammar descriptively, we see that it is a dynamic and changing system whose structural innovations make no sense one day, only to be considered cliché another.

It is in this sense, then, sentences in a text are smaller structural iterations of that text as a whole and create what we call style, and by extension, genre. When we take a tally of sentence structures in a text, how many and what type of verbal modifiers, prepositional phrases, dependent clauses, whether they tend toward adjectival or adverbial, and what syntactical orders are favored, grammar patterns emerge that signal a writer’s style.

For instance, in Jack Kerouac’s “October in the Railroad Earth,” he juxtaposes the grimy city-life of the poor and working class with the sublime sky, sea, and mountainous American landscape. In his rambling jazzy prose, Kerouac repeatedly uses Germanisms. He describes San Francisco as “‘ole Frisco with end of land sadness” and its commuters as “all these Millbrae and San Carlos neat-neck tied producers and commuters of America and Steel civilization.”

Additionally, Kerouac breaks sentence boundaries to create rhythms that go on for lines and lines. Assonances, alliterations and adjective-packed prose mimic the quintessential American art, jazz—particularly improvisation. The open-ended structure of his grammar alludes to the open-ended promise of the American dream. The structure lays the foundation for the overall effect and meaning of the text. The overall effect creates the genre. The genre reflects the culture.

Could it be that a text’s grammar really is a fractal of its whole, and that whole is a fractal of its genre, the genre a fractal of a culture?

Wai Chee Dimock, a Professor of English at Yale, in her article “Genre as World System: Epic and Novel on Four Continents,” asserts works are a fractal of their genre. She explores genre as an open, dynamic system, first explaining the traditional notion of what genre is: “Traditionally [genre] has been seen as a classifying principle, putting the many subsets of literature under the rule of normative sets” (85).

Alternatively, Dimock proffers a view of genre akin to looking at grammar descriptively and not prescriptively. She seeks to “invoke genre less as a law, a rigid taxonomic landscape, and more as a self-obsoleting system, a provisional set that will always be bent and pulled and stretched by its many subsets. . . a theory of interconnection” (86).

Dimock argues that the novel loops back temporally to mimic but then augments its own structure. She explains, “This is the most interesting implication of fractal geometry. It theorizes the novel as a linguistic sponge in its turn, picking up the poetic genre, inserting it into a different medium, and keeping it intact to some extent as grains and lumps” (96).

It is in the breaking of the rules, in experimenting and creating dissonant, jagged sentences that we reflect movement in our cultural aesthetic. Think of how new words and phrases are formed. We change nouns to verbs: “I google information.” We create new syntactical patterns and discard old ones: “Are you coming with?”

Even though there are standard forms and functions in language, the sentence remains highly plastic. Grammar is as variable as coastlines of continents. The complexity of choices of order, form, and function are so numerous, indeed infinite as they are broken and bent by evolving dialects and youthful expressions. But random, they are not.

This has far-reaching implications, in that how we describe things or write about them cannot be separated from our own understanding of the world. Cultural assumptions are reflected in language patterns. When we write about another culture, we necessarily use constructions that reflect our own experiences and understandings, which are connected to our place within our own culture, and our culture’s place among other cultures. That is why, to really understand another culture, one must know that culture’s language.

If we come from a culture that has a position of power, our writing will necessarily reflect that power position, rhetorically.

Literary theorist Edward Said approaches this from the idea of the West’s concept of Orientalism, specifically how the Middle East as portrayed in literature:

“. . .I have looked especially at cultural forms like the novel, which I believe were immensely important in the formation of imperial attitudes, references, and experiences. I do not mean that only the novel was important, but that I consider it the aesthetic object whose connection to the expanding societies of Britain and France is particularly interesting to study” (Said, Culture and Imperialism xiii).

Said defends his assertion of the novel as the creating and defining element of cultural assumptions because “stories are at the heart of what explorers and novelists say about strange regions of the world; they also become the method colonized people use to assert their own identity and the existence of their own history. . . . (Said, Culture. . . xiii).

Said echoes Dimock’s theory of genre as fractal when he explains how the suppressing of a people’s narratives produces “the threat of resurgent atavism” (Said, “Islam. . . ” 488). When a culture is oppressed and its customs and languages silenced, the backlash starts with a reach back to pre-colonial notions of itself so the culture can reassert itself, but also it must augment to fit the necessary defiance against the oppressor.

In Dimock’s words, this is when the novel temporally loops back to mimic but then augments. For Said, the augmentation for the colonized can often assert itself as nationalistic pride and morality. Said asserts that these new cultural structures are recursive of the mentalities from the Middle Ages and “accompany rigorous codes of intellectual and moral behavior” (“Islam”. . . ..xiii). He goes on to explain:

In time, culture comes to be associated often aggressively, with the nation or the state; this differentiates ‘us’ from ‘them,’ almost always with some degree of xenophobia. Culture in this sense is a source of identity, and a rather combative one at that, as we see in recent ‘returns’ to culture and traditions. These ‘returns’ accompany rigorous codes of intellectual and moral behavior that are opposed to the permissiveness associated with such relatively liberal philosophies as multiculturalism and hybridity. In the formerly colonized world, these ‘returns’ have produced varieties of religious and nationalist fundamentalists. (Said, Culture. . .xiii)

In this way, language as art is always political.

Interestingly, Toni Morrison, in her book Playing in the Dark: Whiteness and the Literary Imagination, sums up this phenomenon of how the oppressor’s notions of the oppressed come to be the accepted view. She is interested in “what makes intellectual domination possible; how knowledge is transformed from invasion and conquest to revelation and choice” (8).

More specifically, Morrison turns to the novel to trace notions of what it is to be white and/or black in America and echoes Said, though in an inverted way, when she proclaims:

“What Africanism became for, and how it functioned in, the literary imagination is of paramount interest because it may be possible to discover, through a close look at literary ‘blackness,’ the nature —even the cause—of literary ‘whiteness.’ What is it for?. . . . If such an inquiry ever comes to maturity, it may provide access to a deeper reading of American literature—a reading not completely available now. . . . ” (11)

Morrison is saying, there is no white without black. In portraying notions of black Americans, authors form notions of white Americans. Morrison’s focus is the effect of domination on the dominant culture.

To put it in a linguistic perspective, we can trace the effects of the melding of cultures through new grammars that emerge, particularly in the novel. Consequently, grammar reflects the organic shifts in cultural perceptions.

Grammar as fractal? We can look at grammar as it unfolds before us, or we can restrict our perception of it by the current trends we call rules. Rules, however, freeze us in time and in culture. Perceiving grammar as fractal allows for the bending of grammar rules and therefore helps us acknowledge the trends of our culture from its roots—from its narratives.

And now, as I have taken a break from Kerouac to write this blog, my son interrupts me to help him with writing his essay for his 7th grade class homework: “How do I write this, Mom?

“Write it like you would say it,” I say, “naturally.”


Works Cited

Dimock, Wai Chee. “Genre as World System: Epic and Novel on Four Continents.” Narrative, Vol. 14, No. 1, 2006.

Kerouac, Jack. “October in the Railroad Earth.”   Evergreen Review Reader, 1957-1967; A Ten-Year Anthology. Ed. Rosset, Barney. New York, Grove Press [1968]. n.p.: 1968.

Kretzschmar, Jr. William A. “Language Variation and Complex Systems.” University of Georgia, American Speech, Vol. 85, No. 3, Fall 2010. Web. 25 Jan. 2015. doi 10.1215/00031283-2010-016.

Mandelbrojt, Jacques. “Benoit Mandelbrot and Fractals in Art, Science and Technology.” Leonardo. 44.2 (2011): 98. Project MUSE. Web. 5 Nov. 2014. <http://muse.jhu.edu/>.

Mandelbrot, Benoit. The Fractal Geometry of Nature. New York: W.H. Freeman & Co, 1982. Web. 31 Jan. 2015. <http://is.muni.cz/el/1456/jaro2014/BPM_NUMA/The_Fractal_Geometry_of_Nature_-_B._Mandelbrot.pdf >.

Morrison, Toni. Playing in the Dark: Whiteness and the Literary Imagination. New York: Vintage, 1993. Print.

Plotnik, Arthur. Spunk and Bite. New York: Random House, 2007. Print.

Said, Edward. Culture and Imperialism. New York: Vintage, 1993. Print.

—— “Islam Through Western Eyes.” The Nation. 26 April 1980. 488-492. Web. 31 Jan. 2015.

Of Interest

TED talk with Mandelbrot explaining the concept and the math of fractals.

Nova’s documentary explaining this phenomenon.

Interview by Michael Silverblatt where David Foster Wallace talks about how he structured his novel Infinite Jest to mimic the Sierpinski Gasket fractal, or the Sierpinski Triangle.


About mem13

The world is a rare and colorful and unfathomable place. I hope to capture it here as it looks through the slant of my lens. This is a blog where I write about any- and everything I can think of. Mostly past and present stuff, although if you look closely you'll pick up some prophecies, too (prophecies void in Tennessee). Links to book reviews I've written elsewhere. Once I did a mixed media poem thing. That was cool. The two coolest people I’ve met were Ralph Nader & Chuck D. Chuck praised my threads. Can’t beat that.
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