Paul Gailiunas

Statement

I am interested in all types of mathematical art, and have attended every Bridges conference since 2000, submitting work for the exhibitions since 2007. I work in both 2-D and 3-D, although often the three-dimensional ideas exist only as electronic images. My creative thinking seems to gravitate towards tilings and polyhedra, with a preference for images and objects that allow multiple interpretations, typically figure/ground relationships, although that is not an exclusive interest. For example at Bridges in 2008 I presented a family of visually interesting surfaces related to the lemniscate. Bookbinding takes up a significant amount of my time and I presented some bindings based on knot designs at Bridges London in 2006, and I exhibited my binding of an edition of The Hunting of the Snark at Leeuwarden in 2008. Other examples of my work can be seen in the gallery at www.societyofbookbinders.com.

Artworks

The design is based on a thousand year-old cross base found on the island of Anglesey, Wales. The underlying structure is related to the Cesaro fractal and the box fractal. In the original Celtic design the arrow-heads must occur in several different shapes for the pattern to work, but by using square approximations to logarithmic spirals it becomes possible to have a single shape of arrow-head.

The underlying structure of the Anglesey Arrow images allows recursion to any depth. This image is generated by carrying out one further iteration beyond that implied by the Celtic original.