

Ulysses: Sand As Medium
Volume 7, Issue 3
1999
Sand animations:
As Time Goes By (2.9 MB)
Carpe Diem (2.8 MB)
Well Tempered (4.9 MB)
The
pictures included in this Graphics Gallery are an introduction to the relief
drawings traced in the sand by Ulysses, an installation which I built and displayed
at the Siggraph'99 Art Gallery. Ulysses renders mathematically inspired designs by
use of a computer driven magnet rolling a ball through a sand table.
Description of the Installation
Ulysses is mostly meant as a live installation, and is certainly at its best
when one can see its progress on the sand. The included illustrations are only
photographic stills of the sand tracings. They can only capture part of the aesthetics of
the project: what is missing is the surprise, the expectations, the feelings elicited by
the motion, the activity of the ball, the plasticity of the sand, the exacting development
of the tracing.
Ulysses is built
on a light wooden frame supporting a flat plate holding the sand. Underneath, a mechanical
table carrying a magnet is set in motion by two daisychained, brushless servo motors
connected to the computer by a serial cable. The Animatics "Smart" motors have
their own command language and interpreter. A driver translates the tracings geometry into
motor instructions, polls the motors' feedback, controls communications and provides a
graphical user interface. I wrote it in Tcl/Tk and it runs off an SGI O2, the same
computer that I use to develop my Mathematica designs on.
A digital camera is connected to the computer to survey the sand on demand and can be set
to interact with the process. As the ball moves through the sand from the magnet pull, it
rolls and does not slide. Its speed fluctuates as periodically the sand is first
compressed and then gives in, freeing the ball to jump ahead. The velocity may be set to
average from .5 to 5 cm/s.
The
problems of servo motors with very low speed, i.e., movements parallel to the axis, are
solved at the driver level. Scaling is also involved. An interesting difficulty, not
solved yet, is to correct at the path level the flexibility of the magnetic bind which
causes the ball to cut corners. David Bothman helped with engineering pointers and useful
conversations.
Following
the progress of a tracing for a full performance, or now and then observing a tracing from
different angles, and coming back for the surprise of a new design makes the Ulysses experience.
One can interact by direct sketching, wandering through mazes, playing with algorithms,
choosing patterns from a library, placing rocks, setting lights. Photographing for The
Mathematica Journal, I chose patterns from my collection saved on disk and let Ulysses
render them in the sand in a couple of hours or less.
The wildest functions can be fascinating, but the simplest lead to very quiet and
beautiful effects, with rendering bringing diversity and subtlety. With the basrelief
effects of sand, a function as simple as Sin[x+y+Sin[x]+Sin[y]] produces wonders.
Process
From conception to a sand trace, the process is as follows:
 The piece foreseen must be thought as one line: the ball can backtrack but not levitate
off the sand... yet. The inspiration for it can come from all the walks of life, art or
mathematics (see illustration captions).
 The geometry of the line is first coded in Mathematica, to produce a set of
coordinates. Packages by Alfred Gray, Tom WickhamJones, Roman Maeder and others were
useful, as were some of the published Mathematica literature and code. These were
also an inspiration to develop a full library of personal geometric extensions over the
years, allowing me now to compose designs rapidly and with a reasonable amount of effort.
 Mathematica is a convenient design language for dialogued geometric compositions.
My mind works well in the context of interpreter shells, scripting, and visual feedback.
As the sand tracings are concerned, the standard visualization tools need to be
complemented by imagination and practice: the sand is a very different and variable
medium, not controllable through PostScript alone.
 The driver is fed coordinate lists from disk. These in turn are either produced
directly, or by a filter which strips Mathematica
Graphics data
structures from extraneous information.
 Things have to be planned with the perspective of lights and shadows, a whole area for
which I have no software (although I have used Larry Gritz's Blue Moon Rendering Tools on
RenderMan output produced by Geomview, installed as
Graphics default
resource).
 There are interactive situations where one first places stones on the sand in the spirit
of the stone gardens. The camera image of the sand is first interpreted to find where the
stones are. The original line geometry is then altered to leave room for the stones and
have the ball slalom safely around them.
 Interestingly, the motors can be driven from position data, but also from speed or
acceleration. This opens possibilities for many nonintuitive explorations with Integrate and D.
Aesthetics
I have a taste for
quietness and beauty, for simplicity and depth, for rich effects of lights and matters
enjoyable from a wide range of distances and angles. I find that mathematics can create
the motifs, the compositions and the multiple depths of texture that allow these criteria
to be met. I find also that helped by natural elements like sand, water, light, shadow,
wood, and stone, our eyes and brain can be stimulated and satisfied to the extent of their
capacity, without the dryness and the bandwidth constraints of the digital world closing
in on us.
Hence my interest in blending mathematics and natural elements in my work. Nature
contributes to the work as it multiplies the effects of the simple instructions provided
to the ball for its movement. Better and faster than any computer, Nature can figure out
how to show the 10^10 grains of silica on Ulysses. Knowing all about gravity, soil
mechanics, and light propagation, Nature applies them in real time, with a shadow here, a
twinkle there.
Someone
once asked why these mathematical patterns imposed on natural materials have such sympathy
with shapes and surfaces that occur naturally. I guess I am lucky, or Nature read about
Ilya Prigogine and Benoit Mandelbrot. Seriously, in a simple regular pattern devoid of
human noise, Nature can express itself beautifully. It has a sympathy with mathematics.
A selection of works by other artists illustrates this interaction of mathematics and
natural elements in art:
 Mauro Annunziato: Chaos Revenge (Siggraph'99 Art Gallery): organic depth and
diversity.
 Carl Cheng: Friendship Acrobatic Troupe (SF Exploratorium): water and air
bubbles.
 Helaman Ferguson: Costa's Surface and Four Canoes: from transient snow to
billion year old granite.
 Haruo Ishi: Hyperscratch 9.0 (Siggraph'99 Art Gallery): sounds from chimes and
light.
 Yuki Sugihara: Water Display (Siggraph'99 Emerging Technologies): water veil.
Motivations
I was inspired to work in
"digital sand" by the traditional Japanese Zen gardens (Ryoanji, Daitokuji,
Ryosokuin, Daisenin, etc.), Tibetan mandalas, Navajo paintings and by more recent work by
Andy Goldsworthy and Michael Heizer, all who have found their expression in sand.
My interest in using computers for art is twofold. First, they answer my mathematical
inquiries, free my imagination, and express and evolve my designs. Second, they set
devices into motion in the physical world, which create or animate objects and images that
are my work. The latter extends my skills and thus empowered my mind can ask what my hands
alone could not do.
Although a computer is
involved in the creative process, this work is nothing but a tribute to and a continuation
of thousands of years of drawing, geometry, and fine arts by civilizations past. In fact,
computer as a tool fades entirely behind the aesthetic and spiritual concerns that art as
mathematics builds upon.
References
 "Concerning the Spiritual in Art" by Vassily Kandinsky (1912)
 "The Mathematical Approach in Contemporary Art" by Max Bill (1949)
(review "Werk" Nr.3, 1949, Winthertur) (available at http://www.solo.com/studio/am/tmacia.html)
 "Zen and the Fine Arts" by Shin'Ichi Hisimatsu (Kodansha, 1971)
 "The Ocean in the Sand  Japan: From Landscape To Garden" by Mark Holborn
(Shambhala, 1978)
 "Designing the Earth  The Human Impulse to Shape Nature" by David Bourdon
(Abrams, 1995)
About the author
JeanPierre Hébert studied engineering in Paris and is an independent
artist living in Santa Barbara, California. His interests range from
works on paper to mixed media and installations. His gallery on the
web is located at http://www.solo.com/sand/. He
can be reached at jp@mifu.solo.com.
Contents copyright 1999 © The Mathematica Journal and
JeanPierre Hébert
