The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.

Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.

Click on the thumbnails to see larger image and share.

"Two Squares (2006)," by Edmund Harriss (University of Leicester)Printed on Canvas 36" x 36". This is based on the Ammann-Beenker Tiling. Along with Ammann Squares this work explores the extension of the work of Raymond Brownell (www.raymondbrownell.com) to more complicated geometry. 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 two particular methods. The first method is uses the substitution rule, and the second method is to construct the tiling as a planar slice of a four dimensional lattice (in much the same way that a computer draws a line using the pixels of its screen) and then project this to the plane.
See more information at www.mathematicians.org.uk/eoh/Art/Ammann_Text.pdf.

--- Edmund Harriss

"Octagonal Gasket (2006)," by Edmund Harriss (University of Leicester)Printed on Canvas 36" x 36". This image is based on a version of the Sierpinski Gasket with octagons rather than triangles. --- Edmund Harris

Sculpture System No. 5 (2009)" by Richard Grimes (www.richardgrimes.net) and Edmund Harriss (University of Leicester)Deltahedra are polyhedra where all the faces are regular triangles. Sculpture system 5 is a system to build any deltahedron using triangular shapes that hinge together. A huge variety of polyhedra can be made using just twenty of these shapes. The actual sculpture was built by a group of volunteers who also designed the final shape that was actually built. --- Edmund Harris

"CurveTile (2004)," by Edmund Harriss (University of Leicester)A pattern built of just four images (two up to rotation). You can make some some patterns yourself at www.mathematicians.org.uk/eoh/Curvetile/Curvetile.html. --- Edmund Harriss

"Ammann Scaling (2006)," by Edmund Harriss (University of Leicester)Printed on Canvas 24" x 24". 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 two particular methods. The first method is uses the substitution rule, and the second method is to construct the tiling as a planar slice of a four dimensional lattice (in much the same way that a computer draws a line using the pixels of its screen) and then project this to the plane. See more information at www.mathematicians.org.uk/eoh/Art/Ammann_Text.pdf. This was a commission for the School of Mathematical Sciences at Queen Mary. It is one of a pair with Ammann Squares, exploring aspects of the Ammann-Beenker Tiling. It appeared in the June 2007 issue of Notices of the AMS. --- Edmund Harriss

"Sculpture System No. 5 (2009)" by Richard Grimes (www.richardgrimes.net) and Edmund Harriss (University Of Leicester)Deltahedra are polyhedra where all the faces are regular triangles. Sculpture system 5 is a system to build any deltahedron using a triangular shapes that hinge together. Using just twenty of these shapes a huge variety of polyhedra can be made. The actual sculpture was built by a group of volunteers who also able to design the final shape that was actually built. --- Edmund Harriss