Weird Fields Make Wonderful Art

By Ken Kostel|Thursday, July 15, 2004

 Most of us have seen the cyclonic swirl of water running down a drain, but what about the turbulent rush of the jet stream or the dance of an electromagnetic field? John Belcher and colleagues at the MIT Center for Educational

Courtesy of the Center for Educational Computing Initiatives

Computer Initiatives developed a computer program that turns the mathematical descriptions of these phenomena, technically known as vector fields, into visual patterns showing the fields frozen in time. Then he took the program a step further, allowing students in his introductory-level class on electricity and magnetism to design their own field patterns. Belcher judged the results based on both their aesthetic appeal and the elegance of the math used to create them. Top honors in the Weird Fields contest went to undergraduate Nicki Lehrer. Her image, shown at right, bears a title only a physicist could appreciate: g(x,y) = (ln(sin(x)))^3*(tan(y)), h(x,y) = (ln(cos(y)))^3*(tan(x)). But the result is both beautiful and mathematically challenging, Belcher says. “It’s hard to come up with an analytical function that creates right angles.”

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