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Science is always searching for predictability. For example, when will the next solar eclipse occur? Science can predict the exact time and also tell us where on earth is the best place to view it. Scientific theory relies on whether predictions are supported by observation. These theories rely on relationships that are deterministic; given a present condition, a future event can be determined.

Much in our environment can not be predicted. The arrangement of molecules in our brain does not determine our behavior. Each cloud is different, even if they are at the same altitude and under the same climatic conditions. We are also evolving as our earthly environment changes in ways we can not predict.

Then we come to what has been dubbed the butterfly effect. Is it possible for a butterfly flapping its wings in Brazil to set off tornadoes in Texas? Even though the weather is governed by the atmosphere, and the atmosphere obeys deterministic physical laws, long range accurate weather reporting still has much to be improved, even though we now have great amounts of observations and incredible computer resources for analysis and simulation.

Unpredictable behavior of deterministic systems has been called chaos, a term introduced 1975. Strange attractors, first appeared in 1971 related to the nature of turbulence and the patterns that were produced.

Chaotic processes are not random; they follow rules, but even very simple rules can produce extreme complexity. This complexity can be expressed as a series of equations or visualized and rendered when the element of time is introduced into its interpretation. The mathematics of chaos provide the tools for creating and displaying such phenomenon.

Scientific phenomenon has an artistic aesthetic that transcends its ability to attempt to explain the world around us.

Resulting images are seemingly inspired from natural forces such as, wind and water, or earthen formations. One explores the possible subsurface patterns in nature that are not visible to us; another smoldering smoke, others; folding, bending, twisting draping and crumpling of identifiable materials or organisms.

In the rendering of strange attractors a number of methods are outlined how the element of time can be developed. Time can be represented as the number of times a mapped location is selected or when the location is selected. A variety of coloring schemes based on the concept of time are also discussed. The other aspect time serves is the ability to visually suggest three-dimensional surfaces within two-dimensional strange attractors. This last effect enables strange attractors to be artistically presented in a manner that adds dynamic properties and ghostly interiors to static images. The added third dimension suggests surfaces that visually want to be logically followed but can never be.

The presentation will begin with an introduction to chaos followed by a description of the basic mathematics behind the generation of strange attractors and how computer software can be written to develop them. A series of pieces developing the time concept will be displayed, how a search of attractors was conducted, and a final series of current images. Time and density, time and points, expanding time, and unfolding time are concepts that will be discussed.

Biography

Robert J. Krawczyk is an Assistant Professor in the College of Architecture at the Illinois Institute of Technology in Chicago focusing on digital craftsmanship. His digital art and designs have been presented internationally including SIGGRAPH 2001 and the upcoming 2003 Art Gallery. Digital art can be found at: www.netcom.com/~bitart