Edmund Harriss

"Nautilis and Conch"

Laser Cut wooden tiles, within 12" X 12" the tiles need to lie flat on the table and can be positioned in many ways, 2006.

These two tiles represent a break- through in the study of Rauzy fractals. These are certain shapes related to substitution rules using letters. There is an extensive theory in the case where the scaling of the substitution rule was a PV (sometimes called Pisot) number, these are real algebraic numbers greater than one all of whose algebraic conjugates have absolute value less than one. These tiles and their associated tilings were the first example of a dual using a non-PV number. They were discovered by the artist in conjunction with Pierre Arnoux, Maki Furukado and Shunji Ito.

"Ammann Squares"

Printed on canvas, 2' X 2', 2006.




The Ammann-Beenker tiling is the eight-fold sibling of the more famous, five-fold Penrose rhomb tiling. It was discovered independently by R. Ammann and F. Beenker.Like the Penrose tiling, the Ammann-Beenker can be constructed by both a substitution rule and as a slice of a higher dimensional lattice. This picture and Ammann Squares try to explore these two methods in a visual manner. In this picture the scaling symmetry given by the substitution rule is considered.

"Ammann Scaling"

Printed on canvas, 2' X 2', 2006.



The Ammann-Beenker tiling is the eight-fold sibling of the more famous, five-fold Penrose rhomb tiling. It was discovered independently by R. Ammann and F. Beenker.Like the Penrose tiling, the Ammann-Beenker can be constructed by both a substitution rule and as a slice of a higher dimensional lattice. This picture and Ammann Scaling try to explore these two methods in a visual manner. In this picture the joined lines of tiles, that show the higher dimensional origins are considered.