Limited edition Giclee print in each of small, medium and large formats, 19"
x 16" (small), 2007, based on a pen plotter drawing circa 1985
In Greek geometry, the word "gnomon" meant: That which is left over after removing a self-similar part. Robert Ammann discovered a variety of golden-ratio-based, aperiodic tilings. One tile, when removed from its bounding rectangle, leaves a gnomon having the same shape as the bounding rectangle, creating "self-gnomicity". Playing with this idea after meeting Ammann, I first drew this piece in 1985, as a plotter drawing. Both the geometry and a mysterious "tie-die" texture/structure emerges when our visual system integrates myriad tiny details. To the discerning, the Fibonacci numbers evince themselves also.
Douglas McKenna, Freelance Artist, Software Developer, President, Mathemaesthetics, Inc.
"Since childhood, I have been enamored of the textures and structures evinced by recursive subdivisions, hierarchical tilings, self-referential designs, and space-filling curves, all formed by algorithmically traversing trees of linear or other transformations. Even before I helped illustrate the geometric fractal portions of Mandelbrot's "The Fractal Geometry of Nature", I was drawing them by hand, or using primitive 1970s-era computer graphics. In mathematical art, the balance between platonic and aesthetic beauty is difficult to achieve. Symmetry represents a loss (or compression) of information, and is rarely the basis of good art. Yet in math, symmetry is considered essentially beautiful. To me, a tension between symmetry and asymmetry seems integral to notions of visual beauty. My pieces, some of which rely on my own space-filling curve results, are intended not only to illustrate a mathematical principle, but also to please the eye with structural or textural intrigue. "
Other works by the artist