Dillard: on the fringe of fractal nature

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.


[a. F. fractal (B. B. Mandelbrot 1975, in Les Objets Fractals), f. L. fract-us, pa. pple. of frang{ebreve}re to break: see -AL1.]

A mathematically conceived curve such that any small part of it, enlarged, has the same statistical character as the original. Freq.attrib. or as adj.

1975Sci. Amer. Nov. 144/3 It seems that mountain relief, islands, lakes, the holes in Appenzeller and Ementhaler cheeses, the craters of the moon, the distribution of stars close to us in the galaxy and a good deal more can be described by the use of generalized Brownian motions and the idea of the fractal dimension. 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{em}or fractal sets. 1977Sci. News 20 Aug. 123 Sets and curves with the discordant dimensional behavior of fractals were introduced at the end of the 19th century by Georg Cantor and Karl Weierstrass.1978 [see snowflake curve s.v. SNOWFLAKE 7]. 1984Nature 4 Oct. 419/2 Parts of such patterns, when magnified, are indistinguishable from the whole. The patterns are characterized by a fractal dimension; the value log2 3 {appreq} 1·59 is the most common. 1985Ibid. 21 Feb. 671 Mandelbrot has argued that a wide range of natural objects and phenomena are fractals; examples of fractal trees include actual trees, plants such as a cauliflower, river systems and the cardiovascular system.
Other OED explorations to consider: fringe.
A fractal image: like Dillard’s sycamore tree vision? Or perhaps the creek, seen from space?
This site provides further discussion of Fractals, and the ways that many things in nature can be thought of as fractals: trees, the shore of a body of water, such as a river or a creek. A Nova video on Fractals, describing them as “one of nature’s biggest design secrets…The blinders came off and people could see forms that were there but formerly invisible.” We learn that a key to the discovery of the “fractal geometry of nature” (in contrast to traditional geometry) is to see things as rough/textured rather than smooth. Now who does that sound like?

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!

I think of the fractal’s vision of complexity through simplicity and order bordering chaos as something along the curve of Thoreau’s understanding of vision: “two views of the same,” where we can be beside ourselves in a sane sense.
Dillard extends her fractalized vision of the “frayed fringes of shore” (140) to a related scientific concept known as Complexity, the study of highly dynamical systems that emerges in the sciences, including biology and the study of ecosystems, as well as Chaos Theory–think Butterfly Effect.
“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.

Animated fractal mountain
Animated fractal mountain (Photo credit: Wikipedia)
This dynamic between simplicity and complexity, it would seem, is the mystery that Dillard has in view. As Dillard seems to think, in her whimsical way: you can’t make this stuff up.


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