Fractals, Chaos, and the
Materiality of Thinking
Benoît Mandelbrot and
and Galaxies, series
of forty-five, 1974–77.
Role of Images in Scientific Thinking
Featuring never before exhibited works on
paper and objects including dynamic black
and white drawings, computer print-outs,
photographs, and computer-generated films
Focusing primarily on the work of one of the most
notable mathematicians of the twentieth century, The
from September 21, 2012 to January 27, 2013, explores
the role of images in the development of what has
become known as fractal geometry and chaos theory.
Nina Samuel, a visiting assistant professor at the BGC, is
the curator. Samuel, who received her PhD in art history
from the Humboldt University of Berlin, is also an asso-
ciate member of Das Technische Bild in Germany and a
former member of the Swiss national research program
eikones/NCRR Iconic Criticism.
For thousands of years, Western thought assumed
that fundamental geometry consisted of regular, ideal
forms, such as cubes, spheres, and cones, with straight
or evenly curved faces and edges. Benoît Mandelbrot
(1924–2010), however, explored mathematics as he
saw it— in all its untidiness and irregularity, devoting
himself to the study, for example, of the forms of the
coastlines of real islands, with all their unpredictable
inlets, creeks, and furrows.
Mandelbrot, in other words, looked at the world. In
so doing, he flouted what was in effect a prohibition
pervading much of mathematical thinking against the
use of visual representation. To reintroduce the visual,
Mandelbrot took the groundbreaking step of harnessing
the potential of computers, thereby transforming math-
ematics into an experimental science. The result was his
invention of fractal geometry, a geometry of actuality
rather than of abstraction, as exemplified in his classic
work, The Fractal Geometry of Nature (1982).
The notion of islands is central to Mandelbrot’s work,
associated in his thinking with both the inspiring and
the seductive role of images. They challenge his own
Benoît Mandelbrot and Sigmund
Handelman, programmer. “Carved
Fractal Mountain,” ca. 1975–76.
Metal object. Collection Aliette
Mandelbrot. Photo: Bruce M. White.
Benoît Mandelbrot and Mark Laff, programmer.
Investigations in the complex plane of cubic
polynomials, series of over 150, 1979. IBM.
Computer-generated print on photographic paper.
Collection Aliette Mandelbrot.
January 27, 2013
thetically compelling even if they are initially scientifical-
ly impenetrable. This constitutes another revelation of
the exhibition: the beauty of material thinking that can
be found in the visual detritus of scientific investigation.
trated book with essays by Professor Samuel and mem-
bers of the German research group Das Technische
Bild—Matthias Bruhn and Margarete Pratschke—as
well as scholars Wladimir Velminski, Jan von Brevern,
and Juliet Koss. Drawing new connections between
the material world and that of mathematical ideas, the
publication offers not only a rare glimpse at the arti-
factual terrain and graphic methodologies of Benoît
Mandelbrot and his contemporaries but also investigates
the role of scientific imagery in visual thinking across
diverse disciplines. Published with Yale University Press
(October 2012, paper, 160 color and b/w illustrations,
172 pages), it will be available for $40 in the BGC gallery
and through the Web site (bgc.bard.edu).
dictum that “seeing is believing” and point to the inter-
action between the hand and computer visualizations
to generate new ideas. Frequently, the computer alone
is unable to give an insight, and hand drawing becomes
necessary for transforming a confusing computer image
into a new idea or theory.
At his death in 2010, Mandelbrot left a mass of idio-
syncratically organized drawings, computer print-outs,
films, manuscript scribbles, objects, and polaroids in his
office in Cambridge, Massachusetts— an extraordinary
trove to which Mandelbrot’s wife, Aliette, generously
allowed Professor Samuel access. “To explore it was like
wandering through the mathematician’s brain,” said
Samuel. “It was like witnessing the ephemeral traces of
his very thought processes.” Selections from these mate-
rials form the core of the exhibition.
Along with this rare look into Mandelbrot’s working
process, sketches from his contemporaries—the French
mathematician Adrien Douady and the German bio-
chemist Otto E. Rössler—will also be publicly exhibited
for the first time. The work of the Massachusetts Insti-
tute of Technology meteorologist Edward N. Lorenz,
a pioneer of chaos theory, will be represented by loans
from the Library of Congress.
The Islands of Benoît Mandelbrot: Fractals, Chaos, and
the Materiality of Thinking allows the viewer to question
the idea that the illustration of a work must always be
secondary to the work itself. On the contrary, substantive
images often play generative roles in the scientific pro-
cess, constituting a kind of material thinking conducted
by producing and interpreting visual traces, such as
Alan Norton, program-
mer. Quaternion, 1980.
prints on photographic
paper. Collection Aliette
Benoît Mandelbrot. Computer-generated prints with
scribbles, undated. Collection Aliette Mandelbrot.
Drawing on the BGC’s academic and gallery programs,
the Focus Gallery presents small-scale exhibitions
primarily curated by faculty that embody ambitious
research and teaching. Each exhibition is part of an
academically innovative project that also includes gradu-
ate seminars, public programming, and publications
both in print and online. Graduate students and gallery
staff collaborate with faculty throughout the research,
planning and presentation stages. Envisaged as a kind
of laboratory, the Focus program promotes experimen-
tation in display, interpretation, and the use of digital
media, and reflects the BGC’s commitment to exhibi-
tions as integral to scholarly activity.
collaboration between the BGC and Das Technische
Bild, based at the Humboldt University of Berlin.
As part of the initiative, an English translation of the
text, Das Technische Bild (Akademie Verlag, 2008), is
being published in “Cultural Histories of the Material
World,” the BGC’s book series with the University of
Lectures, study days, gallery talks, and conversations
are offered in conjunction with the exhibition. For
more information, please call 212-501-3011 or e-mail
Guided tours for adult and school groups are offered
Tuesday through Friday between 11 a.m. and 4 p.m. and
on Thursdays until 7 p.m. Reservations are required for
all group visits. To schedule a tour, please call 212-501-
3013 or e-mail firstname.lastname@example.org.
Benoît Mandelbrot and
Alan Norton, programmer.
Quaternion, 1983. Computer-
generated prints on
photographic paper. Collection
The Bard Graduate Center Gallery is located in New
York City at 18 West 86th Street, between Central Park
West and Columbus Avenue. Gallery hours are Tuesday
through Sunday from 11 a.m. to 5 p.m. and Thursday
from 11 a.m. to 8 p.m. The admission fee is $7 general,
$5 senior and students (valid ID); admission is free
Thursday evenings after 5 p.m. For more information
about the Bard Graduate Center and upcoming
exhibitions, please visit bgc.bard.edu.
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