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graph paper to make knitting patterns . I knitted the designs by hand and mounted them on padded boards. After several years of working with computer graphics, I wanted to make something tangible that I could hold in my hands while still working with computers. I also wanted to explore the beauty of fractal designs that had been made visible only after the invention of computers. Knitting with thick wools and light silks gave me the pleasure of touching the material and also reminded me of the textile origins ofcomputers with the Jacquard looms of the nineteenth century. By slowing down my hands, I was able to observe and think about the complexities of fractals and to make comparisons between the building of designs by stitches and of designs by pixels. Although the correspondence of pixel to stitch is not precise in these pieces, the experience of translating the design to knitted fabric gave me an understanding of the construction of computer images, and of the connection between discrete stitches and electric pulses. It also allowed me to ruminate on fractals as boundaries, the infinite self-replications inherent in fractal makeup, and the realization of an order that I originally perceived as chaos or at least as complexity beyond comprehension. The experience made me more visually aware, and I learned how to read fractals and other kinds of complex informationladen , pixel-built images. By knitting computer designs, I enjoyed reconnecting the discoveries of computer sciences with the gentle, ancient world of making cloth. INVISIBLE CITIES Michael McNabb, 120 Virginia St., San Francisco, CA 94110, U.S.A. E-mail: In 1985, the ballet Invisible Cities was realized as a collaboration between myself, choreographer Brenda Way and the Oberland Dance Company (ODC)/San Francisco Dance Company , and designer/engineer Gayle Curtis. Although most of the music is computer synthesized, there are also two live instrumental/electronic performers , including myself. This was a personal challenge, since I had been away from performing for a while. It was also an opportunity to try to raise the technical standards of music in dance performance, which I saw too often neglected. The music was funded by a grant from the (U.S.) National Endowment of the Arts and produced at the Center for Computer Research in Music and Acoustics, Stanford University. ltalo Calvino's novel Invisible Cities inspired us with its beauty, its original and concise structure, and its dreamlike imagery. It is an allegorical account of a meeting between the Venetian explorer Marco Polo and the Tatar Emperor Kublai Khan. Sensing the decline of his empire, the aged Kublai Khan summons the young foreigner Marco Polo to his garden to reassure him of the greatness of his realm. Marco Polo diverts the great Khan with tales of cities he has seen within the empire. As the barrier of their different languages is overcome, the images of the cities become increasingly vivid. Kublai Khan searches for a pattern among them, concluding finally that each description is of the same place and all are within him. The music contains both subtle and explicit stylistic elements of various popular and classical world musics, sections of pure musical fantasy , and various musical and digitally processed environmental sounds. In this way it conveys feelings and moods similar to those created by Calvino's weaving of hyper-realistic description and veiled, dreamlike fantasy. Conversely , the literary symbolism, characters and narrative of the book provided much of the inspiration for the choreographer and designers. However , rather than follow the book explicitly , we chose to adopt something of its form, then invented our own 'invisible cities' for each of the five major movements. At the time, Gayle Curtis was participating in work being done in machine choreography at the Veterans Administration Robotic Aid project. He wanted to see the concept carried further. For Invisible Cities, he directed the addition of a large robot arm as a visiting member of the ODC dance company. The powerful robot, transformed by the choreography of Way, Margo Apostolos, and Curtis, performed the role of Kublai Khan. I further enhanced its persona by amplifying the sounds of its motors and digitally processing these sounds into...


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