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. As architect Nigel Reading writes, "Pure Newtonian causality is an incorrect (finite) view, but then again, so is the aspect of complete uncertainty and (infinite) chance." The nature of reality now is "somewhere...in between" (‘Dynamical Symmetries’). It occurs to me that this shift in focus makes itself felt within literature as postmodernism. In any case, the poetry I am calling "fractal" shares many defining traits of that contested term: postmodern. Since other contemporary poetries show a greater allegiance to romantic, confessional, or formalist traditions, fractal aesthetics describe – or predict, if you will – only one feature of the topography. I say "predict" because I hope these remarks will suggest future vistas. When poets address aesthetics, their own work inevitably shades their views. I write from perceptions of where my poems have lately been and where they’re likely headed. I’ve provided few examples because I would prefer that readers locate (or build) the representative works themselves.
However, topological dimension behaves in quite unexpected ways on certain highly irregular sets such as fractals. For example, the Cantor set has topological dimension zero, but in some sense it behaves as a higher dimensional space. Hausdorff dimension gives another way to define dimension, which takes the metric into account.
Sierpinski triangle. A space with fractal dimension log2 3, which is approximately 1.585To define the Hausdorff dimension for a metric space X as a non-negative real number (that is a number in the half-closed infinite interval [0, 8)), we first consider the number N(r) of balls of radius at most r required to cover X completely. Clearly, as r gets smaller N(r) gets larger. Very roughly, if N(r) grows in the same way as 1/rd as r is squeezed down towards zero, then we say X has dimension d. In fact the rigorous definition of Hausdorff dimension is somewhat roundabout, as it allows the covering of X by balls of different sizes.
For many shapes that are often considered in mathematics, physics and other disciplines, the Hausdorff dimension is an integer. However, sets with non-integer Hausdorff dimension are important and prevalent. Benoît Mandelbrot, a popularizer of fractals, advocates that most shapes found in nature are fractals with non-integer dimension, explaining that "[c]louds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." [1]
There are various closely related notions of possibly fractional dimension. For example box-counting dimension, generalizes the idea of counting the squares of graph paper in which a point of X can be found, as the size of the squares is made smaller and smaller. (The box-counting dimension is also called the Minkowski-Bouligand dimension). The packing dimension is yet another notion of dimension admitting fractional values. These notions (packing dimension, Hausdorff dimension, Minkowski-Bouligand dimension) all give the same value for many shapes, but there are well documented exceptions.
THE HYPERCUBE The Fourth Dimension is portrayed geometrically by fractals and by the Hypercube. The Hypercube is the symbol used in mathematics to try and represent the fourth dimension in two dimensions (a drawing on a piece of paper - a plane).
From the center of the Hypercube through its 8 diagonals the Hypercube is related to everything in the Universe. The infinity in the Fourth Dimension lies in the infinity of relations. This can be expressed in terms of "fractal scaling", from the infinite small to the infinite big, perpendicular to the other dimensions and including the intervals or fractal dimensions between them. The meaning of fractal scaling is explained later in this Chapter, for now it is sufficient to understand this as scales of magnitude, as for instance from the size of the atom to the size of a galaxy. The Hypercube is cut by 4 diagonals constituting the central point. In consciousness this center point represents the identity or the Self. The number of the diagonals is 4 X 3 = 9, according to the Pythagorean theorem. The four diagonals are 1-5, 2-6, 3-7 and 4-0.
The Four Diagonals:
1-5 Matter
2-6 Consciousness
3-7 Energy
4-0 Self-Organization
So, what is a fractal?
An irregular geometric object with an infinite nesting of structure at all scales.
Why do we care about fractals?
Natural objects are fractals.
Chaotic trajectories (strange attractors) are fractals.
Assessing the fractal properties of an observed time series is informative
Just as fractal science analysed the ground between chaos and Euclidean order, fractal poetics could explore the field between gibberish and traditional forms. It could describe and make visible a third space: the nonbinary inbetween. Consider water. At low temperatures, it is fully ordered in the form of ice; at higher temperatures it becomes fluid and will not retain its shape. The stage between ice (order) and liquid (chaos) is called the transition temperature. Fractal poetics is interested in that point of metamorphosis, when structure is incipient, all threshold, a neither-nor. 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. Of course, disjunction also informed high modernist aesthetics. Postmodernism seems more an elaboration of that tradition than a wholly new formation. The new always contains aspects of the old: novation springs from the existent. Hand-me-downs are recombined and during the process freshness (a strange entity that might seem wrong or counterintuitive at first) seeps in. Perhaps it’s nothing new to say that newness is a composite. Rather than elide this truism, however, postmodernism rejects originality and stresses the inevitability of appropriation in creative work. The prefix "post" signals a foundational debt and an unabashedly reactive position that departs from a modernist make-it-new credo.
Common sense, moreover, suggests that contemporary work must be
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