Jack Criddle
This video shows three mathematically precise sculptures built by
artist-geometer Debora Coombs and computer scientist Duane Bailey.
The sculptures show a small patch of an infinite surface made from a
single shape, a rhombus repeated hundreds of times, tilted at
different angles. The sculptures have exactly the same structure.
Each has a unique color palette that emphasizes a feature of the
underlying mathematics. If this geometry were projected onto a
two-dimensional surface it would form a Penrose tiling. A tiny pink
and green seed may be seen toward the end of the video. If you were
to begin building a sculpture with this cluster of six rhombs you
could predict the location of all dark rhombs to infinity. The
locations of lighter colored rhombs cannot be predicted.
Furthermore, repositioning just one of these lighter colored rhombs
will cause others to flip at distant unknowable locations. In
Nature, this quasi-crystalline pattern has only been found in
meteorites.