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November 6, 2000–A Mathematica image by computer graphic artist Michael Trott has been selected for exhibition in the Eighth New York Digital Salon. The digital print, entitled Extruded Hilbert Curve over a Charged Hexagonal Truchet Pattern, is a colorful, composite image of a complex fractal overlaying a randomly generated pattern. However, this description does not begin to convey the vibrancy and complexity of the resulting design.
The image was created using Mathematica and is reliant upon that program’s deep understanding of symbolic and numerical mathematics for its intricacy and intrinsic beauty. A Hilbert curve is a plane-filling curve, meaning that at its limit the generated curve approaches every point in a specified plane arbitrarily close. In Trott’s design, the entire curve was then extruded into a third dimension and rounded outwards through the midsection to achieve the desired result.
In contrast to the complicated nature of a Hilbert curve, a Truchet pattern is based on a very simple premise. If you take a square and draw two quarter circles around diagonally opposing vertices, only two unique orientations exist. When multiple such squares with randomly selected orientations are combined into a tiling pattern, a unique, organic pattern that is random and yet retains an underlying structure is created. This same principle can be applied using hexagons instead, as Trott did here, to introduce additional possible orientations and a more intricate pattern. The resulting hexagonal Truchet lines are then “electrically charged,” and the resulting equipotential lines are shown in the background graphics.
The New York Digital Salon exhibit opened today and will run through December 9 in the Visual Arts Museum in New York City. It will also be shown internationally beginning in January 2001 in both physical and lecture form. Last year’s exhibit traveled to Spain, England, Italy, China, and Japan and received extensive media coverage. The physical exhibit is accompanied by a website and a show catalog, which include scheduling information, artwork images, artists’ statements, and selected essays. The catalog is a special edition of Leonardo, the leading journal to address the application of contemporary science and technology to the arts.
Extruded Hilbert Curve is also a featured image in the Graphica book series. Graphica, released last year, is a two-volume collection of unique and unusual color illustrations created using Mathematica by Trott and fellow artist Igor Bakshee. In conjunction with the Digital Salon exhibit, the series is currently on sale as a special promotion through the Graphica web site.
This is not the first time Trott’s work has received widespread exposure. In March, the Director of Art Programming for the city of West Hollywood contacted Trott and Bakshee about using the Graphica images as part of a public service announcement on a digital billboard over Hollywood’s Sunset Strip. The City Commissioner thought the artwork was “simply beautiful” and approximately 30 Graphica images have now been on display as brief animations since August of last year.