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.