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. "
http://www.mathemaesthetics.com/MathArtPrints.html
Other works by the artist