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The Islands of Benoît Mandelbrot:  Fractals, Chaos, and the Materiality of Thinking

by Nina Samuel, Editor
BGC/Yale University Press, New Haven and London, 2012
176 pp., illus. 160 col. Trade, £23.75
ISBN: 978-0-300-18643-7.

Reviewed by Edith Doove
Transtechnology Research, University of Plymouth


There are two things that spring to mind when reading this very informative book on Mandelbrot. One is René Daumal’s pataphysic, unfinished novel Mount Analogue and its account of a voyage to an imaginative island. Early on in his book the protagonist notes: “For a mountain to play the role of Mount analogue, its summit must be inaccessible, but its base accessible to human beings as nature made them. It must be unique and it must exist geographically. The gateway to the invisible must be visible” (32). The other is the recent news on Google’s Phantom Island, a non-existing island that somehow slipped into Google maps, images of which have more than a close resemblance to some of Mandelbrot’s constructions.

I will delve into these associations deeper elsewhere. For now it suffices possibly to state that although neither of these associations are mentioned in this book, what triggered them is the fact that Mandelbrot himself quite early on in his development of his fractal landscapes, makes the somewhat surprising connection of these (and their mountainous landscapes) to the science-fiction world of H.G. Well’s The Island of Dr. Moreau, thus alluding to a connection between the fictitious and the real. What this book successfully tries to demonstrate is how “images actively generate knowledge with their own particular logic”, more specifically in the work of Benoît Mandelbrot. It is published as the accompanying catalogue of the exhibition ‘The Islands of Benoît Mandelbrot – Fractals, Chaos, and the Materiality of Thinking, organized by Nina Samuel and others at the Bard Graduate Center at New York, running from 21 September 2012 till 27 January 2013. The researchers were able to make use of materials, images and objects, found in Mandelbrot’s office to which they had limited excess after his death in 2010 and that were previously unpublished.

Investigating in both book and exhibition, “the complex relationship between visual and scientific reasoning in fractal geometry and chaos theory, both of which are well-known for using digital scientific imagery”, one of the insights is the importance of images for generating knowledge rather than ‘just’ being illustrations. What is fascinating even more is the importance of hand drawing, especially in the early years of experimentation with computer graphics. As stated in an interview that Samuel held with him in 2005, Mandelbrot had a special talent for visualizing formula: “Once I heard a mathematical formula a shape came to my mind.” For him this was one of the explanations for his interdisciplinary approach.

Where this fascinating and rich book holds a specific interest is exactly in the link between art and science that is instigated through Mandelbrot’s work. Although Mandelbrot never pretended his images, hand-drawn or computer-printed, to be art there is a constant underlying interest in bridging the gap. He does that through his reference to Wells, in signing some of his drawings and prints, but even more explicitly in his article ‘Scalebound or scaling shapes: a useful distinction in the visual arts and the natural sciences’, published in Leonardo in 1981, and to which this book dedicates a whole chapter. In this article there is an attempt to apply his fractal sets to visual arts, indicated by author Juliet Koss as a possible “(…) draft for future analyses.” Although much more than a draft, the current book holds exactly that same promise.

Last Updated 1 January 2013

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