Monday, 18 July 2011

Fractals and Poetry

"Fractals may be the most complex and the most subtle examples of patterns found in both mathematics and poetry ... When poets borrowed ideas from fractal geometry and applied them to the reading and writing of poetry, they made a remarkable intellectual leap" (M. Birken and A.C.Coon, "Discovering Patterns in Mathematics and Poetry", Rodopi, 2008, p.167).

So what are fractals? I only have a rough idea. Symmetry is when you can do something to a shape so that it matches itself - with rotational symmetry you rotate the shape; with reflection symmetry you reflect the shape. You can look upon fractals as another type of symmetry where instead of rotating or reflecting, you magnify. In real life you can get a rough idea of how this works by looking at a tree (the pattern of the boughs is like the pattern of twigs when you zoom in) or a coastline (the jaggedness of a coastline is similar whether you're looking at a satellite image or through a microscope) but pure fractals only exist in maths - it doesn't matter at what scale you look at certain mathematical objects, they'll always look the same.

It's unclear how this idea can apply to poetry, and in fact people seem to merge the fractal concept with ideas from complexity theory - "strange attractors", etc. The resulting poetry has been described using other, non-mathematical theories too, so the whole area's fraught with potential confusion. Whatever terms they use ("fractal" - Alice Fulton; "radical artifice" - Perloff) there seems to be fair agreement about the sort of poetry under discussion. Fulton's written extensively about it. Here are some quotes from Fractal Amplifications: Writing in Three Dimensions (Alice Fulton, Thumbscrew No 12 - Winter 1998/9

  • "During the last quarter of the twentieth century, science has turned away from regular and smooth systems in order to investigate more chaotic phenomena. Rather than being divided into the classical binaries of order and entropy, form now can be regarded as a continuum expressing varying degrees of the pattern and repetition that signal structure."
  • "Just as fractal science analysed the ground between chaos and Euclidean order, fractal poetics could explore the field between gibberish and traditional forms. "
  • "Over the past decade, scientists have come to view fractals as particular instances within the larger field of complexity theory. While retaining the term "fractal poetry", I hope to suggest ways in which complexity theory might amplify the possibilities of such a poetics. (A poem is not a complex adaptive system: the comparison is analogical, not literal.)"
  • "My tentative 1986 prospectus for post modern fractal poetry suggested that digression, interruption, fragmentation, and lack of continuity be regarded as formal functions rather than lapses into formlessness and that all shifts of rhythm be equally probable."
  • "On the ground between set forms and aimlessness a poem can be spontaneous and adaptive – free to think on its feet rather than fulfil a predetermined scheme. In a departure from Romantic ideals, fractal aesthetics suppose that "spontaneous" effects can be achieved through calculated as well as ad libitum means. Thus "spontaneity" does not refer to a method of composition but to linguistic gestures that feel improvisatory to the reader. Rifting and jamming, rough edge and raw silk – such wet-paint effects take the form of long asides, discursive meanderings, and sudden shifts in diction or tone. "
  • "Complex adaptive systems do not seek equilibrium or try to establish balance; they exist in unfolding and "never get there". As Holland says, "the space of possibilities is too vast; they have no practical way of finding the optimum." Like complex systems, fractal poetry exists within a vast array of potentialities: it is a maximalist aesthetic."
  • "Diction, surface textures, irregular metres, shifts of genre, and tonal variations take centre stage as defining formal elements. Function words (articles, conjunctions, prepositions) assume schematic importance."
  • " The poem plane is analogous to the picture plane in painting: a two-dimensional surface that can convey the illusion of spatial depth. Painters use perspective, colours, texture, and modelling to suggest three dimensions on the flat canvas. If objects are painted progressively smaller and closer together they will seem to recede. Space also can be suggested by juxtaposing oncoming warm colours with introverted cool ones. By alternating thickly-textured impasto with turpentine-thinned washes, the artist can create opaque areas of positive space and radiant glazes of negative space. Objects of the same scale can be modelled differently to create depth: a hard-edged rendering will appear nearer than a hazy one."
  • "Just as paint fosters illusions of proximity and distance on canvas, words can suggest spatial depth on paper. A fractal poem can do this by shifting its linguistic densities: the poem’s transparent, easy passages impart the sensation of negative space; they vanish into meaning when read rather than calling attention to their linguistic presence. More textured language, on the other hand, refuses to yield its mass immediately. The eye rests on top of the words, trying to gain access but is continually rebuffed. Such (relatively) opaque sections assume the solidity of positive space. By juxtaposing transparent with textured passages, fractal poetry constructs a linguistic screen that alternately dissolves and clouds."
  • "Rather than excise stale portmanteaus, fractal poetry might use empty rhetoric sardonically, as a means of splintering the "sincere" voice that was a modernist value. Abstractions are arguably the most rarified words because they have no relation to a specific physical object. In fractal poetics, abstractions are not forsworn as redundant explications of self-sufficient concrete symbols; rather the abstract becomes a valuable realm in itself"
  • "Fractal poetry likewise makes use of recurring cluster words, limbic lines, or canopy stanzas as a means of creating depth. (Cluster being an aggregation of stars with common properties; limbic connoting emotion and motivation; canopy casting a shade overall.) Unlike the villanelle or sestina’s recycling, fractal repetition does not appear at a predetermined place within a set scheme. The poem is more dynamic and turbulent because its repetitions have an element of ambush"
  • "As free verse broke the pentameter, fractal verse breaks the poem plane"

Many of these effects have been studied without recourse to complexity theory - they're what 20th century poetry (especially any erstwhile avant-garde works) use. Does this treatment offer any advantages over a more literary one? As Fulton says, it's only an analogy. The work of Jackson Pollock has been analysed to derive its fractal dimension, and experiments suggest that humans prefer fractal images with a dimensionality in the 1.3-1.5 range irrespective of whether the images are from maths, art or nature. I don't think similar work's been done with poetry, though I suspect "The Wasteland" is susceptible to such treatment.

For the moment I think I'll stick with the more literary descriptions, though the idea of measuring the different types of order appeals to me, as does the idea that some effects needn't be used as regularly or uniformly as they often are.


  1. I've invented a couple of fractal poem forms since the 1990s. (Being a geek as well as a poet, I do understand the math, and I've been following the developments in chaos theory and fractals since the 70s.) One of the most interesting concepts around fractals is order that emerges from chaos, smooth flow that emerges from turbulence. I've played with that idea in my own fractal poetry. The other main idea I've played with is self-similarity: when you zoom in or zoom out, you see the same kinds of patterns and shapes on several different scales. It was in fact the awareness that I was finding self-similarity on multiple scales in a poetic form I had invented and been writing with for some time, that made me realize that I was doing fractal poetry.

    What strikes me most about Fulton's descriptions of her variety of fractal poetry, on the other hand, is that, like LangPo, it's all about the surface effects. Even her descriptions of painting are all about superficial effects: the illusion of depth, for example. The literal repetitions of words, the obvious aspects of pattern and form. I have to say, I find her prescriptions to be fairly superficial and unconvincing, at least from these quotes.

    In other words, I agree with you that the whole thing is likely fraught with misunderstanding and misinterpretation. It seems pretty clear to me that Fulton's understanding of fractals is fairly superficial—which of course would account for her definitional results. In some ways, her prescriptions here are all too similar to various LangPo and "post-avant" manifestos, right down to exploring the interface between gibberish and form, as Fulton puts it. So what's new about this? Not much.

    The one comment Fulton makes here that I can support is that it makes for a maximalist poetry, a complex poetry, as opposed to a minimalist, reductive poetry. Complexity is indeed something essential here, I think. Too bad she didn't go deeper with that idea, though.

    1. although Alice is superficial in her analysis of fractal poetry, i think she is doing something in pioneering for what id like to call a new branch of poetry. you say that you'd developed some fractal poetry and that you have the understanding of what entails fractals; id recommend that you use these skills to make a change in the same rather than be critical or oppose the efforts being done thereof


  2. Thanks for the comments. I've only followed this topic at the Popular Science level. I'm glad to see that fractal poems are alive and well - your poems sound more purely fractal than the ones Fulton seems to be alluding to (which could be any fractured, partly repeating piece - hybrid, post-langpo). I may have misrepresented her - my post included a link to the full article, and she's published on the same theme elsewhere.

  3. Thanks in return. I've now read through the Fulton article you linked to, and I don't think you misrepresented her at all.

    You put your finger right on my objection to Fulton: she makes fractal poetry sound just like any other "fractured, partly repeating piece - hybrid, post-langpo" poetry. In other words, maybe she can't think outside that box that is her familiar ground. We all tend to judge the new by what is familiar to us, after all. (Jean Cocteau said that first, and it remains true.) So I give Fulton points for struggling with the issue, with trying to formulate something new. But her formulations, so far, are in fact nothing new. She's using the same language of the langpo and post-avant regarding poetic techniques that we've already heard in so many manifestos—and that is exactly why it doesn't convince me. It just doesn't seem any different. (Which of course is fine, is all they do is re-language what they're already doing. That's fine, it's just not NEW. LOL)

    Thanks for bringing this essay to our attention. It's interesting and provocative to think about. I might have to blog about it again soon.