# Dillard: fractal, like the creek

As a follow-up to our discussion of Dillard’s style of writing, I would argue that many of the characteristics (and especially the poetic-scientific hybrids we keep observing, perhaps inherited from Thoreau) can be categorized under the heading fractal. This is a mathematical concept that emerges, in fact, within a year or two of Pilgrim (mid-1970s). In fact, the mathematician (Mandelbrot) who coined the term ‘fractal’ recently died–his obit in the NYTimes provides a useful summary of what fractal means–a vision of a world that is not smooth–and intricate in its roughness; the classic examples are two of great interest to Dillard’s vision–a coastline and the shape of a leaf. Dillard’s version of the fractal: the frayed and fringed texture of the world that she focuses on in “Intricacy.”

The creator goes off on one wild, specific tangent after another, or millions simultaneously, with an exuberance that would seem to be unwarranted, and with an abandoned energy sprung from an unfathomable font. What is going on here? The point of the dragonfly’s terrible lip, the giant water bug, birdsong, or the beautiful dazzle and flash of sunlighted minnows, is not that it all fits together like clockwork–for it doesn’t, particuclarly, not even inside the goldfish bowl–but that it all flows so freely wild, like the creek, that it all surges in such a free, fringed tangle.

I see her writing as such a fringed tangle, replicating a kind of texture that she finds in the movement between her thinking and her observing, like the movement between creek-water and creek-bank. Fractal texture might be a word for this. Here is the definition of fractal from the OED–see if you hear anything of interest. The entire book as a fractal? One of the descriptions I have heard to describe a fractal helps me make sense of Dillard’s writing: the idea is that when you continually magnify an image of a border (coastline, or say the edge of a cloud), each successive larger/closer image will have a pattern something like the first one. So, reiteration without exact repetition; a loop that spirals; intricacy built upon a simplicity that is beautiful and unfathomable.

The OED entry for Fractal: **Etymology: **< French *fractal* (B. B. Mandelbrot 1975, in *Les Objets Fractals*), < Latin *fractus* , past participle of *frangĕre* to break

1977 B. B. Mandelbrot *Fractals* i. 1/2 Many important spatial patterns of Nature are either irregular or fragmented to such an extreme degree that..classical geometry..is hardly of any help in describing their form… I hope to show that it is possible in many cases to remedy this absence of geometric representation by using a family of shapes I propose to call fractals—or fractal sets.

My attitude has been totally different. I always saw a close kinship between the needs of “pure” mathematics and a certain hero of Greek mythology, Antaeus. The son of Earth, he had to touch the ground every so often in order to reestablish contact with his Mother; otherwise his strength waned. To strangle him, Hercules simply held him off the ground. Back to mathematics. Separation from any down-to-earth input could safely be complete for long periods — but not forever. In particular, the mathematical study of Brownian motion deserved a fresh contact with reality.

## What is a Fractal?

## The Border Between Chaos and Order

A fractal is defined by its properties. Two of the most important properties of all fractals are :-

1) self-similarity

2) fractional dimension

Self-similarity means that one part of the fractal is very similar to other parts of the same fractal. This can be seen in most fractal art . . . for example the fractal image above is a spiral made of smaller similar spirals, and each of those smaller spirals is itself made of similar smaller spirals, and so on, ad infinitum.

Start with a straight line . . . that has one dimension. Then make the line increasingly twisted in more and more complex ways . . . if the line was infinitely twisted it could fill an area and would thus be two-dimensional. Because of the principle of self-similarity (infinite complexity), a fractal line is part-way between one and two dimensions, so it is a fractal line that is on the way towards filling a space, because the wiggles on the line themselves have smaller wiggles, and those wiggles in turn have smaller wiggles and so on.

This might seem like mathematical abstraction but it has very practical results. For example, take the coastline of an island . . . look at it from far away and lay a piece of string along the coastline, and you will arrive at a length for that coastline. Then zoom in and you will see that where the coastline appeared to be a simple shape from far away, the line along the coast has a lot more detailed wiggles the closer you get. You could continue this increasing detail down to grains of sand along the coastline, and if you lay the piece of string around all the details, you get a LONGER measurement than you did from the initial far view!

“Ecological complexity refers to the complex interplay between all living systems and their environment, and emergent properties from such an intricate interplay. The concept of ecological complexity stresses the richness of ecological systems and their capacity for adaptation and self-organization. The complex, nonlinear interactions (behavioral, biological, chemical, ecological, environmental, physical, social, cultural) that affect, sustain, or are influenced by all living systems, including humans. It deals with questions at the interfaces of traditional disciplines and its goal is to enable us to explain and ultimately predict the outcome of such interactions. Ecological complexity can also be thought of as biocomplexity in the environment” (Li, 2004, editorial in Ecological Complexity).

Dillard extends her view of the intricacy/complexity of nature at the creek to that of the larger world when she associates Heisenberg’s Uncertainty Principle with the stalking of a muskrat: “the physicists are once again mystics” (206). Complexity, the scientists will tell you, has something to do with simplicity.

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