Mountain Laurel is one of three recently completed sculptures now on display in the Schow Science Library at Williams College. They show an area of three-dimensional Penrose tiling that continues to infinity in all directions. This ongoing series is a collaboration with my friend computer scientist Duane Bailey who has spent 30+ years investigating Penrose tiling. Our exhibition is called a.periodicity a mathematical term for this curious symmetry.
The sculptures are structurally identical -all precisely the same size and shape. But each is coloured differently according to some aspect of the mathematics. Mountain Laurel provides insight into the relationship between 2D and 3D versions of Penrose tiling.
In two-dimensions Penrose tiling requires two different shapes to construct; a fat rhombus and a skinny rhombus. Although each tile in the sculpture is identical, Mountain Laurel codes them according to the shadow they would project onto a flat surface. Green tiles would project the shadow of a skinny rhombus in 2D. Pink tiles would create the shadow of a fat rhombus in 2D.
In all three sculptures, colour enables us to see unexpected shapes and patterns when the sculpture is viewed from different angles. Mountain Laurel is built from identical rhombi -the tiles are all the same shape – but the composition yields marvelously irregular patterns. Shapes and rhythms appear and disintegrate as you move around the sculpture.
The back of the sculpture provided its title Mountain Laurel. Here’s work in progress with binder clips and reverse-engineered clothes pins.
Aperiodic tilings are mathematical models for quasicrystals, physical solids that were discovered in 1982 by Dan Shechtman who subsequently won the Nobel prize for his work in 2011. I’ve also built them in stained glass, with mathematical rules encoded into the surface pattern.