Another Distraction: Fractals, Writing and Amusement

The visual mathematics of the fractal lends itself to metaphor. A fractal is a self-similar construct: the more you delve into it, the more it reveals itself, and what it reveals is more of the same, but complexly so, like a landscape.

bc coastTake the coastline, the incredibly rugged coastline, of British Columbia. From space, or from Google Earth, it’s already very jagged and detailed. Descend into it slowly, and each jag becomes progressively more intricate, taking on the appearance of the previous higher and wider level. Go deeper and the complexity does not diminish but shows itself even more so.

How long is the coastline? It depends on how closely you look.

What fractals are mathematically, or how the graphics are formed… I’m not going to try to attempt any of that, it’s been done much better, with more understanding, and in the requisite detail in a lot of places.

But I am interested in the metaphorical usefulness and the visual manifestations of fractals.

You wouldn’t think, off the top, that fractals could apply to writing. But it turns out to be a useful concept. Take a look at Randy Ingermanson’s article, How To Write A Novel: The Snowflake Method.

Flarium1

He counsels designing a novel similar to how a fractal might be constructed. Write a one sentence summary of your story. Expand that sentence into a paragraph into the major events of beginning, middle and end. For each major character, explore them for a page. Take the beginning, middle and end and break that up into smaller units. And so on.

Rudy Rucker, the computer scientist and sci-fi author, explores this same idea in his A Writer’s Toolkit:

“It really helps to think of the book you’re writing as a fractal. The levels are the novel as a whole, the novel’s parts, the chapters in the parts, the scenes in the chapters, the actions within a scene, the sentences describing the actions, the phrases in the sentences, and the words in the phrases. To write at the top of your form, you need to be effectively working each level, either consciously or with the unconscious craftsmanship that comes with practice.”

This blog post has an interesting, though short, discussion of the same idea: Fractal Stories?

In fact, blogging itself has been examined through the fractal metaphor. There’s something fractal about the Web…

Alice Fulton wrote an article in depth, Fractal Amplifications: Writing in Three Dimensions, about poetry and “fractility.”

Flarium2Screenwriters are not impervious to this meme of the fractal: Toward a Fractal Theory of Screenwriting is an example.

Take a look at this textual simulcra of a fractal at The Emotion Fractal. It is “a recursive space filling algorithm using English words describing the human condition.”

I can see this being useful for writing, perhaps in the development of characters, and just jogging your ideas about the emotional context you’re trying to develop. (The active area is the white on black at the top of the page. There is a short description below of how it works.)

The idea of the fractal has seeped into much wider domains of course. In cosmology, those theories of the universe, the fractal analogy denies the Big Bang theory and claims that the universe is of infinitely replicated fractal structure.

Following in this same vein, there’s an intriguing blog, Fractal Ontology, about “grasping and bridging the ruptures between cybernetics, language and society.”

The really distracting thing about fractals though for me is the siren call of playing with them visually. There are many programs, often free, out there which generate fractals. The best ones operate on three levels: 1) Generating a fractal such as the Mandelbrot within a flexible interface. 2) That graphical interface allows one to begin focussing into areas of graphical interest, and perhaps discovering some shape never found before. 3) The most sophisticated programs, such as Ultra Fractal, allow one to create fractal images that can be termed art.

What allows this artistic intervention into the generated fractals is the inventive use of layers, whether directly in software like Ultra Fractal, or in digital editing software such as Photoshop.

The idea that the composition of fractal images can be considered serious art is controversial in some quarters.

Before we go farther, here are a few lists of available fractal programs, whether freeware, open source, or commercial: Paul N. Lee’s website, Edwin Young’s list, and of course the Fractovia site.

Lately, I’ve been playing around a lot with the free flame fractal software Apophysis. (You can find the latest versions here.) Fractals in general and Apophysis in particular have large communities of interest out on the Web.

I’m more of a fractal finder at this stage, rather than a creator, but I’m slowly learning more how to use layers to build up an artful image. Here’s a few of my own discoveries in the world of Apophysis fractals.

March-080310-196

March-080312-115

 

 

 

 

 

 

 

March-080313-256

March-080315-50

 

 

 

 

 

 

There’s something seductively mysterious about these images, an order of nature and imagination mingled. There’s a quote by Francis Bacon that pertains:

“There is no excellent beauty which hath not some strangeness in the proportion.”

Mr. Bacon also said the purpose of art is to deepen the mystery. Fractals do that.

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4 Comments on “Another Distraction: Fractals, Writing and Amusement”


  1. I figure the universe is set up like a strand of dna and we cannot see past the point of the strand we are a small part of, what we think of as the universe. Hard to say just many such strands there are. I reckon quite a few. Fractality is a new concept on me but it sounds close to what I reckon is going on.

  2. fencer Says:

    Hi Mr. Beer

    Thanks for your comment…

    We are such a small part of things… we come up with these metaphors like DNA or fractals as aids trying to understand. But we’re probably more like those blind fellows standing around the elephant trying to describe it. (It’s like a thick rope… No, no it’s more like a fan… what’s with you guys, it’s like a tree trunk…)

    I was reading today about this guy, a surfer dude and snowboarder (who also happened to have earned a Ph.D. in physics) who’s shaken up the scientific world with a model which he calls the simple theory of everything. It’s based on the one of the most complicated mathematical shapes known which has 8 dimensions. Now there’s a model… we can’t even visualize that many dimensions. Or at least I can’t…

    Regards

  3. forestrat Says:

    Cool stuff. I really like the feathery green and orange one on the top right. It has that deep space image feel.

    MDW

  4. fencer Says:

    Thanks!

    You’ve got to look through a lot of candidates before finding something one likes, in that Apophysis program.

    Regards


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