The Eternal Fractal

Summer 2016, Uncategorized

by Moeko Noda

Fractal geometry showing Mandelbrot / setPASIEKA / SCIENCE PHOTO LIBRARY / Universal Images Group

Fractal geometry showing Mandelbrot / setPASIEKA / SCIENCE PHOTO LIBRARY / Universal Images Group

Some of the greatest literary works have in common a narrative structure of an interwoven set of fractals, according to a recent study carried out at the Institute of Nuclear Physics of the Polish Academy of Sciences. This news was taken up by science blogs, news sites, major newspapers such as the Guardian, and after a while by the online site of a literary magazine, thus reaching its way to me, a literature major who rarely reads science articles.

Ever since French Mathematician Benoît Mandelbrot introduced the idea to the world back in the 1960s, people have found this self-similar structure and pattern everywhere. In literature, in paintings, in the stock market, in vegetables, even in our heart beats, the infinitely complex patterns of a fractal reveal themselves, making it difficult for us to unsee them. Fractal is the rhythm that govern us all.

The term fractal was coined from the Latin adjective fractus, whose corresponding verb, frangere, means to break. It is a fitting word, for a fractal is an object that at first glance may seem broken, but on closer inspection reveals its distinctive “self-similarity”–no matter how the image is magnified or shrunk, one sees the same pattern. An often-used example of a fractal in nature, not coincidentally where the original search for fractals began, is the coastline of Britain. The island has a jagged coastline that, when its map is magnified, still shows a similar pattern of broken up lines that resembles the original coastline. Mandelbrot saw this pattern of co-existing roughness and simplicity everywhere in nature, and he set out to find a rule that governs it. His idea of encapsulating the order arising out of seemingly irregular patterns eventually culminated in his book, The Fractal Geometry of Nature. Clouds are not spheres,” he said, “mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

The appeal of a fractal lies not only in its mathematical innovation, but also in its beauty. The visualized form of the Mandelbrot set is considered a work of art, and an online search for “fractal art” will give a result of fractal images one after another, so mesmerizing in their complexity that the word “trippy” is suggested by Google autocomplete.

Fractals are not only artworks in themselves. Their patterns are also found in works of art which at first sight do not bear much similarity to these Google search images. The American painter Jackson Pollock’s paintings are one of these examples. In 2002, researchers Richard P. Taylor, Adam P. Micolich, and David Jonas published a paper titled “The Construction of Jackson Pollock’s Fractal Drip Paintings,” in which they statistically investigated the fractal features of his paintings. It’s not surprising that researchers found a similarity between Pollock’s dripped paintings and objects in nature, considering that critics often describe his painting “organic,” suggesting something akin to objects in nature found in these works. By running a statistical analysis of the self-similarity of Pollock’s works, the researchers found in them a pattern similar to a fractal.

The researchers fascinatingly suggest that it is human nature to “feel” fractals, that “the enduring popularity of Pollock’s Fractal Expressionism is based on an instinctive appreciation for Nature’s fractals shared by Pollock and his audience.”

A recent study of fractals in literature reached a similar conclusion. By analyzing the sentence length variation of more than 100 works of literature from around the world, researchers have found that “an overwhelming majority” of these works are written in “selfsimilar, cascade-like alternation” of various sentence lengths, creating fractal-like patterns similar to those of musical compositions or brain waves. What is more, they found that works in the genre of “stream of consciousness” show themselves to be multifractal, that is, a composed of a set of fractals irreducibly woven together. This result suggests that our thoughts cascade out in fractal patterns, which some authors, like Pollock has with his brushes, have managed to capture with their outstanding command of language.

Indeed, there is a literary genre called “fractal poetry” that is taught in a creative writing course at Colby-Sawyer College in New Hampshire. According to its syllabus, the course aims to teach how to appropriate fractals into poems by iterating certain linguistic elements within a poem or across a set of poems. Theater can also be fractal; the Japanese traditional theater of Noh is structured to reveal self-similarity in a Jo-Ha-Kyu pattern, Jo being the slow introduction, Ha being the acceleration, and Kyu being a fast close. This three-fold pattern is ideally found at all levels of the play such as line, dance move, scene, and the overall plot. Speaking of Asian culture, Mandelbrot was a fan of Hokusai’s paintings, which have fractal-like structures; Hokusai’s famous painting of a wave with Mount Fuji at the back took part in Mandelbrot’s 2010 TED talk  as one of the visual representations of a fractal in art.

Might fractals be the underlying principle of the universe? The infinitely intricate patterns of a fractal have always existed in the world, long before Benoît Mandelbrot “flipped on the switch” for the rest of us to see. Is the universe a completely determined structure with no uncertainty, infinitely complex but entirely settled, by the pattern of fractals? Well, I don’t know. But what at least seems clear is that the pattern of the fractal lurks beneath the complex phenomena in our everyday lives, its laws governing the breathtaking sceneries of nature, its rhythm reverberating within us and in so much that we create.

Moeko Noda is a rising senior at Swarthmore College in Pennsylvania, where she is studying comparative literature. This is her first published piece.

Photo credit: Fractal geometry showing Mandelbrot set. Photograph. Encyclopædia Britannica ImageQuest. Web. 15 Jun 2016.