There was a long hiatus of a hundred years where drawing did not play any role in mathematics because hand and pencil and ruler were exhausted. They were well understood and no longer in the forefront. And the computer did not exist…

One had to create intuition from scratch. Intuition, as it was trained by the usual tools — the hand, the pencil and the ruler — found these shapes quite monstrous and pathological. The old intuition was misleading … I’ve trained my intuition to accept as obvious shapes which were initially rejected as absurd, and I find everyone else can do the same.

— Benoit Mandelbrot

Fractals are mathematical representations of the workings of the universe. Their geometry is the result of iterative algorithms that change over time. They describe what is considered randomness with mathematical accuracy.

Twenty years ago, in his seminal work The Fractal Geometry of Nature, Mathematician Benoit Mandelbrot derived the term “fractal” from the Latin verb frangere, meaning to break or fragment. Each fragment (or fractal) is self-similar, meaning that each part contains the basic structure of the whole.

My use of fractal imagery plays on the idea of representation in art (especially in painting), while simultaneously figuring within the realm of the abstract. Even the physical act of painting is abstracted, subsumed by an artistic process in a Duchampian tradition. However, my pronouncement of these digital ready-mades does not imply finality, as the nature of these images is Nature itself – ever changing.

Play consists of three paintings that have been rendered digitally, from the initial conception to their final execution as giclée prints on canvas. Play is preceded by Foreplay, a series of three 12 x 12 pixel excerpts from the larger images. Foreplay employs silkscreening techniques whose slight imperfections can be conceived of as obliterated by the mathematical threshold and scale of the Play series that follows it.

The visibility of the halftoning process speaks of the nature of print and draws on the pop art tradition of Warhol and Liechtenstein. It also underscores the plastic nature of the images by exposing the processes by which they were composed in order to be perceived by the human eye. Their pixelized origin is apparent and further deconstructed into four halftone screens: cyan, magenta, yellow and black.

These images are a transposition of media; the remaining PLAY evokes their video past. A video signal fed into a computer returned the fractal images to their source media, but in new form (and with it new meaning). The mathematical expression of the fractals is no longer a dynamic function – they have become art-objects/picture-files. They form narratives reminiscent of time-based media’s, yet the image pixelization in Play affords rectilinear stability and brackets a reading of individual images transgressing freeze-frame “nature.”

The next transposition of media attempted here is photographic. Nile, like Play, was conceived digitally, but began as a mathematical formula on my computer.From the visualized equation, a digital negative was generated, then used to create a print on photographic paper; nowhere was a camera used in the process. I have counted on Photography’s strong bond to realism and landscape to faithfully reproduce Nile, while contributing its random grain structure so unlike the pixel. Nile is the first of an ongoing series of formulae/photographic landscapes. Paired with this photograph is another print, degenerated from Nile’s digital file. By modifying the file encoding, the pixels in the resulting image find themselves shuffled and regrouped. Again, the grain interferes/compliments the underlying geometry.

Photorealism is oft thought of as the logical conclusion of representational painting. Yet, Fredric Jameson cites photorealistic painting as a copy not of reality, but of a photograph, which is already a copy of the original. Play copies an original, yet realism, photography (or any technologically driven process of recording images) and painting take on a new configuration as the original is in itself a mathematical abstraction.

The seventeenth century philosophy of René Descartes separated the I from the world, inspiring a new scientific ideal: a mechanistic, fragmented model of the universe. This fragmentation of nature finds a contemporary manifestation as the pixel, the atomic equivalent of a grain of sand.

“In the Mind’s eye, a fractal is a way of seeing infinity,” says author James Gleick. Conversely, the biological eye receives images increasingly moderated by technology and its reductive codification of objective reality. Simulations of reality are prevalent in the video games and cinematic effects that substitute for the immersive space once offered exclusively by painting. As mental landscapes adjust themselves to these new realities, painting offers a visual language established through historical precedent that can adequately maintain the viewer’s interest to provoke contemplation.
Andrew Mallis
May 2002

Select Bibliography

• Art&Design: Painting in the Age of Artificial Intelligence, David Moos, Ed. London: Academy Group Ltd., 1996
• Fredric Jameson, “Postmodernism, or the Cultural Logic of Late Capitalism,” in New Left Review, no. 146 (July-August 1984)
• Gleik, James. Chaos. New York: Penguin Books, 1988
• Hales, N. Katherine. The Seductions of Cyberspace in Rethinking Technologies, Verena Andermatt Conley, Ed. Minneapolis: University of Minnesota Press, 1993. Pp 173-191.
• Hales, N. Katherine. Narratives of Artificial Life in FutureNatural: nature, science, culture, George Robinson, Ed. New York: Routledge, 1996.
• Kapra, Fritjof. The Tao of Physics. Boston: Shambhala Publications, Inc., 1991
• Mandelbrot B., Benoit. The Fractal Geometry of Nature. New York: Freeman, 1983
• Margulis, Dan. Professional Photoshop: The Classic Guide to Color Correction, 4th Ed. New York: Wiley Publishing, Inc., 2002
• Michael Field and Martin Golubitsky. Symmetry in Chaos. New York: Oxford University Press, 1995

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