This figure shows an algebraic surface that resembles the Cloud Gate sculpture, created by Anish Kapoor, in Chicago's Millenium Park. The sculpture is also known to local residents as the Chicago Bean.
Cloud Gate, which has a shiny metallic surface, is said to have been inspired by liquid mercury. (Click here to see a Wikipedia article that contains a daytime photo of the sculpture.) I have not managed to find specific documentation about mathematical equations that might have guided the design of the sculpture, although the book Anish Kapoor: Past Present Future (MIT Press,2008) says that computer modeling was essential to the process of analyzing the complex form.
I am not the only person to attempt a "reverse engineering" approach to representing Cloud Gate by mathematical equations. Indeed, a Google search on "Cloud Gate math" will produce several online articles about this topic. When I first saw the sculpture, I realized that many of its vertical cross sections resemble a certain type of 4th degree plane curve. Rotating this curve around a vertical axis is a first step in constructing the surface; this is followed by stretching it in one of the horizontal directions. The top and bottom are parametrized separately; additional "deformation factors" are introduced to lift portions of the edge.
In addition to the Wikipedia article, a Google search of images produced some photos posted on Tumblr that show the sculpture under different light conditions. Since I have not been able to reproduce the shiny daytime surface, I tried to imagine how sunset colors might be reflected.
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The Java files used in this page were downloaded from the
Geometry Center webpage.
I generated the geometric data for this figure in November 2012 and May 2013.
Updates completed on June 5, 2013.
Prof. Joel Roberts
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
Office: 351 Vincent Hall
Phone: (612) 625-1076
Dept. FAX: (612) 626-2017
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