In 2003, a serendipitous meeting at a Winston-Salem health food store between a dancer and a computer science professor was the beginning of an unexpected collaboration of artists and scientists. Since then, choreographer Karola Lüttringhaus of the alban elved dance company and Wake Forest professors Jennifer Burg and Yue-Ling Wong have been working together to create novel dance productions that weave together art and science. The goal of this collaboration is to introduce science and mathematics to dance lovers in a way they might appreciate; share the beauty of motion with those more likely to bury their noses in computers and math textbooks; and excite audiences in general with newideas and innovative choreography.  The role of Burg and Wong has been to suggest themes related to computer science and to weave digital imagery, sound, and poetry into modern dance performances.  The images and poetry are presented in digital form, projected on a large screen behind or beside the dancers. 

The Collaborators

The main dancer/scientist collaborators are:

Karola Lüttringhaus
Jennifer Burg
Yue-Ling Wong

Three other important participants in the 2003 and 2004 productions:

Below is a description of the 2003 and 2004 collaborations.

"Fibonacci and Phi," December 2003

Excerpt from "Fibonacci and Phi" program

The first production emerging from this collaboration was entitled "Fibonacci and Phi," staged in December 2003 at the Scales Fine Arts Auditorium, Wake Forest University.  This piece explored the intriguing ubiquity of the Fibonacci sequence and the Golden Ratio, Phi, in the beauty of natural and artistic creations. 

The poem "Phi" provided the thematic background for the performance. It was recited in short sections associated with different scenes during the dance performance .

Audio link to the poem Phi, read by Rhan Small

Phi, by Jennifer Burg

What are these haunting messages,
Coded in cryptic languages,
Through sights and sounds and senses
Speaking to us without words?

And how do we decipher
The beauty as it strikes us,
By saying it or counting it
Make it finally our own?

Who hears the golden music best,
Who sees with clearest vision?
And can they tell me what they see
And write down every note?

A child has eyes still bright and true,
An ear open to voices.
A child hears shouts of tiny “Whos”
On dust specks in the air.

A child knows worlds hold worlds inside,
Each world leads to another,
And angels dance on heads of pins
When you reach infinity.

But children don’t have words for this
And insufficient numbers,
And as we age we want to say
Or count what we have known.

The ancients mathematicians sought
A language most eternal
And found in pure proportions
A number timeless and divine.

The golden ratio they called it,
And Phi in Greek we named it.
And everywhere we find its mark
In nature and in art.

I see a message etched
In a ragged rocky coastline
And the pattern is repeated
In the ripples at my feet.

A fern unfurls its growing leaves
Like nature’s own fresh fractal,
So I paint a fractal of my own
To find the world inside.

I try to read a message
In the face of a sunflower
But I’m blinded by the spirals
Spinning left, and spinning right.

The spirals leave my dazzled grasp.
A galaxy is born
And sends to me through heaven’s time
A metaphor of stars.

A message whispers softly
In the angles of a seashell
And calls my soul to trace a curve
Down paths that never end.

I am told that these mute messages
All have Phi locked within them.
What is this magic number?
And what secrets does it hold?

We cannot write the number,
So irrational by nature.
Never ending, always changing
As it steps toward the sublime.

What would happen if we could
Know the endless perfection?
Say in words and in numbers
What we don’t yet understand?

If we mark the musical intervals
With infinite precision
Can we make a human symphony
From the harmony of the spheres?

If we trace the seashell’s spiral
Down endless perfect angles
Will we finally find the center
And meet the eye of God?

We cannot take the measure
Of Your exquisite beauty
Though it’s woven in the fabric
Of our world and our flesh.

We cannot say Your name
Though it’s written in the sky.
Still we silently rejoice to read
The messages You send.”

The production included eight digital media elements:

Montage of Digital Images

The opening digital movie was created by Annie Lausier and Victoria Strokanova, two Wake Forest students majoring in computer science and minoring in digital art. The movie captures the images – beautiful, disturbing, and provocative – that fill our every waking and sleeping moment.

Naomi’s Morning

The sunrise images for this scene were created from portions of a Mandelbrot fractal. In the dance, Naomi triggers the sunrise scene by moving through laser beams of light that send a MIDI-formatted message to a computer backstage, signaling it to display a new image. The movement-to-MIDI converter, designed for the company by Andy Turner, consists of a laser and photocell switch grid set up on stage. The laser beams are broken by the dancers’ movements, sending a message to a computer that can trigger either a musical sound or the display of an image or text. This allows the choreographer to interweave musical or visual output with dance. The imagery and MIDI-response for Naomi's dance were designed and implemented by Jennifer Burg.

The Mandelbrot Fractal Duet

The Mandelbrot Fractal Duet uses the classic Mandelbrot fractal as its backdrop. In the duet, the dancers again use the movement-to-MIDI converter to trigger the computer to zoom in on the fractal, as if they are navigating through its infinitely self-replicating space. Each time the dancers zoom in, the fractal’s pixel values are recomputed at a finer level of detail, covering a smaller portion of the complex number plane. Thus, the resolution and clarity of the image remain the same. The computation is done by in parallel by a Linux cluster.

The color palette, MIDI-to-computer interface, XWindows graphics display, and parallel computation of the fractal were designed and implemented by Jennifer Burg. The Fractal Duet was an interesting challenge in real-time parallel computation and an opportunity to test Wake Forest’s Linux cluster of parallel computers. Each time the dancers move through the movement-to-MIDI laser beam, a signal is sent to the cluster, physically located in downtown Winston-Salem. The parallel processors divide the work of the repetitive computation of pixel values and send the pixels back to a desktop computer backstage – for a resolution of 1024 columns by 768 rows of pixels. The real challenge was to be able to do this fast enough to animate the fractal with real-time computation. With a gigabit ethernet connection to the Linux cluster, myrinet network/switching technology within the cluster, and a desktop computer with a fast graphics video card, the time to redisplay the fractal was reduced to less than 1/10 of a second. This makes it possible for the dancers to create the illusion that they are driving through the fractal, in the end descending into one of its black holes.

The paper "Cluster Computation in Step with Real-Time Dance" by Jennifer Burg and Tim Miller, presented at the 17th International Conference on Parallel and Distributed Computing Systems, describes the technical aspects of the parallel fractal computation.

Dancing in Virtual Snow

This piece, created by Yue-Ling Wong, has the dancers “dancing in the virtual snow.” This scene incorporates anaglyphic 3D animation viewable by the audience through 3D glasses. The stereo visual effect makes the snow appear to be falling on, in front of, and behind the dancers, expanding the dimension of the performance space. Although most of the animated snowflakes are in the form of small snowballs, once in a while a special lacy one appears. These lacy snowflakes were adapted from the collection of Wilson A. Bentley, reported to be the first person to photograph a single snow crystal in 1885 by fitting his bellows camera with a microscope. During his lifetime, Bentley captured over 5000 snowflakes on photomicrographs.

Dancing with Mannequins

In "Dancing with Mannequins," two 3D mannequins lead a dance with human partners. Although the mannequins’ movements are based on “motion capture” data, their movements become original and unexpected during the performance by means of Yue-Ling Wong’s design. Taking a signal from dancers backstage who are operating a joystick and the computer keyboard, the upper and lower bodies of each mannequin can move independently of each other. Each of the upper and lower bodies can dance forward or backward in its own timeline and at its own speed. To make this truly a human-computer interaction, live dancers on stage try to keep up with the mannequins. This interactive dance explores the nonlinear re-creation of dance phrases by deconstructing and recombining pre-choreographed movements in real-time into new forms of expression.

Picnic Under the Fractal Tree

Trees are another example of a fractal structure found in nature. Again, you see the self-similarity in a tree — a twig growing from a branch resembles the branch itself, and both the twig and the branch resemble the shape of the whole tree. In "Picnic Under the Fractal Tree," a simple fractal tree is constructed beginning with one trunk, which then splits into a number of branches, each of which repeats the same process of splitting. During this scene, words become part of the tree's foliage. Each twig grows a word, a phrase, or a leaf. When the shedding of the foliage is triggered, the audience sees words start to fall off the twigs. As each person’s eyes jump from word to word and follow the words’ paths, the words combine to form a poem. Each audience member may construct a different poem by following different words in a different order. To involve the audience in the creative process, individuals were asked to contribute words and phrases for the fractal tree as they entered the theatre before the performance. Before the picnic scene, these words were input into the computer program. Each fractal tree randomly selected words from the collection for its foliage. The scene was created by Yue-Ling Wong.

The Logarithmic Spiral

Implicit in the logarithmic spiral are both the Fibonacci sequence and Phi. The size of the square through which the spiral is traced follows the Fibonacci sequence. The spiral can also be constructed by a succession of Golden Triangles – isosceles triangles in which the ratio of a side to the base is Phi. Because it is constructed upon the irrational number Phi, the logarithmic spiral spins infinitely to its center, never converging to a center point. The logarithmic spiral was created by computer science major Annie Lausier.

The Galaxy Fractal

The galaxy fractal for the final sequence was designed and programmed by Jennifer Burg and converted to a digital movie with the assistance of computer science major Jimmy Lin. The image is based on a Julia fractal, which differs from the Mandelbrot fractal computationally in the initial and constant values that are used in the equation. For the Galaxy Fractal, a spiral-shaped Julia fractal is set in motion to give the audience the feeling that they are traveling into it. Burg designed the fractal using Julia fractal calculations enhanced with a star-like effect. The digital movie was compiled from 2000 image files that were generated by a fractal computation program, imported into Adobe Premiere, and saved in QuickTime format.

The paper "Dancing with Fractals and Antique Snowflakes" by Burg and Wong gives more information on the "Fibonacci and Phi" performance.

"The Bridge," December 2004

The second collaboration of Lüttringhaus, Burg, and Wong was a two-part performance entitled "The Bridge," presented in December 2004 at Wake Forest University.  The first part, called "A Link with the Darkness," involved three-dimensional stereo projections created by Yue-Ling Wong. The second part, entitled "Une Journée Abstraite," explored concepts of languages -- both human and computer -- and the limits of what can be expressed and computed.  

Here is the program of "The Bridge."

The Making of "Une Journée Abstraite," as told by Jennifer Burg

Brainstorming for "Une Journée Abstraite" began in January 2004.  Our inspiration came from recognizing the multi-lingual nature of the dance troupe and collaborators – with speakers of German, Italian, Hebrew, French, Chinese, and English.  We decided to tackle the theme of human and computer languages and the related issues of computability and expressibility.  We even talked about Chomsky's hierarchy and Gödel's incompleteness theorem.  Was this really something that could translate into a dance production?

Innovations and Script

The alban elved dance company is known for its innovative choreography and daring experimentation with new modes of expression.  Each of their performances is distinctively different, stretching the limits of modern choreography, expression, and dancers' athleticism.  Tackling abstract concepts of computability as the theme of a dance production would be daring enough in itself.  To this, Karola added two more novel elements: spoken dialog; and a 15-foot tall steel structure on which the performers hang, climb, and dance.

the structure 

The spoken script of "Une Journée Abstraite" evolved from a number of sources:  pseudo-poetic lines I wrote for Karola in the form of questions submitted to a computer and the computer's responses, lines suggested by North Carolina School of the Arts professor Marty Rader; and paraphrases  from Albert Camus' The Fall.  Karola "deconstructed" my pseudo-poetic lines and reconstructed these lines, along with the other input, in the end creating dialog in the manner of the French "theatre of the absurd."  Dancers spoke alternately in French, Italian, Hebrew, and English.  The computer spoke in its own voice.

The Characters
The dancers played the parts of four characters.

Karola -- The liar; dynamic and enigmatic; played by Karola Lüttringhaus
Andrea -- Insecure, curious;  feels invisible to others; played by Andrea Lieske
Lena -- Interested in computers and abstractions; played by Lena Rose Polzonetti
Naomi -- Vulnerable,frightened,
whimsical; played by Naomi Greenberg

Computer Concepts and Digital Media Elements

Above all, "Une Journée Abstraite" was a dance performance – innovative, daring, dynamic, and powerful.  What I describe below, however, are the concepts of computer science that were interwoven in the performance, both thematically and visually. 

Introduction -- Reflections
The opening projection laid the thematic foundation with the abstract concepts of computability and expressibility, relieved with a little irony.  The concepts are explained in the voice of a computer.  

No explanation necessary here.  The computer speaks for itself.


"Reflections" (click image)

Ollie's World
"Ollie's World" offers another perspective on one of the production's main ideas.  On the one hand, computers are mindless manipulators of symbols.  They don't know what the symbols mean.  The symbols only have meaning in the minds of the humans who create the computer programs, who associate the symbols with their experience in the world.  On the other hand, "Ollie's World" asks us to consider how it might be to have a "thought" in some sense, but no ability to manipulate symbols.  "Ollie's World" went through several revisions.  In the first version, the projection showed an elderly man who had had a stroke and had lost his ability to use and understand simple words.  This version seemed too sad for the piece, so the elderly man was replaced with my dog, Ollie.  I thought about how Ollie must feel in a room of babbling voices, where only a few key words are understandable to him.

"Ollie's World" (click image)

Turing Machine Dance
Karola and I became intrigued with the idea of choreographing a dance with a Turing machine, so I created a Turing machine program that adds the binary numbers 11 plus 12, represented graphically with 3D states, an input tape, and a token moving from one state to another.  Karola choreographed the program as a duet, one of the dancers blindfolded.  Twelve states are necessary for the program.  Twelve chairs, which descend to the stage dangling from cords, become the twelve states for the dancers.  The computer voice recites the states, and the moves are displayed as the dance progresses.  Zeroes and ones, x's and y's, are expressed in a dynamic and precarious variety of dancers' poses – crouching, embracing, leaning, standing on chairs, and lying on the floor. 

"Turing Machine Dance" (click image)

The Poem "Day"

Aside from the pseudo-poetic dialog between computer and humans that I suggested for  "Une Journée Abstraite," I wrote two poems for the piece.  The first was entitled "Day."  The poem attempts to describe how beautiful my days seem to me.  I found that I couldn't do this, and the inadequacy of my words became the point of the poem and its companion poem, "Day, Reprise."  My original conception was to have "Day" recited in French, with the English translation offset in the audio.  In the final version of the piece, "Day" was recited by Naomi in a whimsical, off-hand way. 

Link to the poem "Day"

Day read in French and English

The Puzzle
To represent the "symbol-shuffling" nature of computers, I created a projection in the form of a hand-held puzzle where you slide the tiles around until you reach a recognizable picture or sequence of words.  This puzzle had two four-line verses expressing part of the theme of the piece.  In the end, we cut the puzzle down to one verse and incorporated it into the dance performance's conclusion, but here it is in its original form.

"A Puzzle" (click image)

Conclusion -- Day Reprise
We had a hard time with the conclusion of "Une Journée Abstraite."  The theme was difficult and abstract and perhaps not "audience friendly."  I had started out taking my computational theory seriously, but the script had evolved into theatre of the absurd.  While I was out taking pretty pictures and writing poetry about how inadequate computation and language are for expressing the beauty of this world, the dancers were turning Gödel's incompleteness theorem to Waiting for Godot.  Then I showed up at final rehearsals with sentimental nature imagery and a conclusion whose tone didn't match the rest of the piece.  How could this allfit together?

What seemed to pull everything together was a contrast between the computer's mindless shuffling of symbols and the human's attempt to express meaning by arranging symbols "in just the right way."  Maybe the poetry did fit, though not as the final note.  We needed to come full circle, and end in the voice of the computer.  This is the final version of the conclusion.

"Day Reprise, Conclusion of Une Journée Abstraite"
(click image)