In his 1982 book ‘The Fractal Geometry of Nature’ the mathematician Benoit Mandelbrot explored ‘irregular and fragmented patterns around us’ that ‘tend to be scaling, implying that the degree of their irregularity and/or fragmentation is identical at all scales.’
He called this family of shapes fractals, from the Latin adjective fractus, meaning fragmented or irregular. Such objects, Mandelbrot noted, are present in nature as well as in a wide range of fields.
Emily Grosholz has written a fine poetic tribute to Mandelbrot and his work.
Fractals are generally formed by a simple procedure, such as recursion. They tend to be self-similar (that is, they contain copies of themselves at different scales), with detail at every scale, and with an irregular structure that cannot readily be described in terms of traditional geometry. The Mathigon site has a good introductory guide to fractals.
Mandelbrot was the first to develop the field of fractal geometry and to study the occurrence of fractals in a wide range of applications. However, well before his time mathematicians had investigated some of the underlying concepts, including shapes that could not easily be described in standard geometrical terms. One such shape is the Cantor set, which is named after the German mathematician Georg Cantor (1845 – 1918) although it was first defined in 1874 in a paper by Henry John Stephen Smith (1886 – 1883), an Irish mathematician and professor at Oxford. The most common version of the set is formed by repeatedly removing the middle third section of a straight line.
The set’s linear structure lends itself to concrete poetry. Rodrigo Siquera’s poem ‘The Cantor Dust’ reflects on concepts of order and chaos, referencing the set in its layout. By contrast my own light-hearted poem ‘Cantor Dust‘ reflects on my antipathy to dusting!
The most iconic mathematically generated fractal is the Mandelbrot set, which is defined by a simple recursive rule in the complex plane. The set has an odd, dumpy shape with a ‘fuzzy’ boundary. Zooming in on the set’s boundary reveals its extraordinary beauty and intricacy in ever finer detail (you can try this out for yourself on the Mandelbrot Explorer website).
The Mandelbrot set has inspired artists, musicians and poets. American singer-songwriter Jonathan Coulton has composed a song entitled ‘Mandelbrot Set’; you can hear him perform the song here.
My poem ‘At the Edge’, from my pamphlet ‘Fractal Poems‘, is shaped by an image from the Mandelbrot set’s boundary:
At the Edge
The Cantor set and the Mandelbrot set are examples of mathematically constructed fractals. However, poetry can feature fractal characteristics without necessarily drawing explicitly on mathematical techniques or images.
In his 2006 collection Fractal Economies, Canadian experimental poet Derek Beaulieu has used iterative procedures to generate a series of fragmented concrete poems that challenge our perceptions of language.
Alice Fulton has written extensively on what she terms ‘fractal poetics’. She has described fractals as providing a framework for exploring ‘the hidden structures of free verse’, functioning as ‘a dynamic, turbulent form between perfect chaos and perfect order’. In this context, ‘Fractal poetry … makes use of recurring cluster words, limbic lines, or canopy stanzas as a means of creating depth’. Fulton’s poem ‘Industrial Lace‘, with its clusters of words and interwoven layers of imagery, exemplifies how she has applied these concepts in her own writing.
JoAnne Growney’s website Intersections – Poetry with Mathematics features several other examples of poems that contain fractal features in their structure.
Fractals in poetry can act as a teaching tool, a visual framework, a structural focus or provide a language in which to express the beauty and complexity of the natural world.
My pamphlet ‘Fractal Poems’ is available to purchase from Penteract Press.
My collection of essays ‘From Fibs to Fractals: exploring mathematical forms in poetry’, is available to purchase from Beir Bua Press.
Posted on 10th October 2021.