Dallas Clement

Artist, Programs Facilitator
Winnipeg Art Gallery
Winnipeg, Canada

These works are part of a project where the subject of the artwork is a mathematical group. The art highlights mathematical properties of the group, as an experiment into the visual and aesthetic qualities of these abstract concepts. A visual analysis of the works can result in several different insights, but it is the goal that no matter the viewer, the work is visually interesting. Artistically, the subject matter is uniquely and absolutely defined, but the number of possible presentations is enormous. The artist's goal is to explore this space to find a successful artistic and mathematical interpretation. The project has included a variety of media, including video and digital prints, broadening the artistic and expository possibilities.

10 x 18 inches

A six by six grid is initialized with the letters A,R,T in alphabetic order at each location in the grid. Each row and each column is assigned a specific permutation. The row permutation is performed first, and then the column permutation, at each location on the grid. The video shows the permutations occurring, one grid location at a time, until the entire grid has been permuted three times. If, after both the row and column operation, the letters

form the word ART, the grid in that location forms a darker grey. By using letters to display the permutation group on three elements, certain permutations will create words. In this case, half of the permutations are easily recognizable words: ART, RAT, and TAR.

Alt 4 Klein 4 Cyclic 3
22 x 22 inches
Archival Print Digital Image

A visual representation of the Cayley table for the A4 group, the elements of which are the even permutations on four elements. Each group element is associated to a specific color. The colors and order of the elements are chosen so that the Klein four subgroup as well as the quotient group are visible. The print is hung on a diagonal so as to emphasize the abelian or non-abelian nature of the groups.