2025 Joint Mathematics Meetings

Doug Dunham, Lisa M. Shier

Artists

Doug Dunham

Professor Emeritus of Computer Science

Dept. of Computer Science, University of Minnesota Duluth

Duluth, Minnesota, USA

ddunham@d.umn.edu

https://www.d.umn.edu/~ddunham/

Lisa M. Shier

Adjunct Professor

University of Maryland Global Campus

New Market, Alabama, USA

kwajshier@yahoo.com

Statement

Our goal is to create aesthetic tessellating patterns on hyperbolic surfaces such as the Poincaré disc model. Many of our designs have been inspired by Euclidean patterns of M.C.Escher, which then had to be modified to fit into the hyperbolic plane. Once we have designed a pattern, we implement it using computer controlled embroidery sewing machine. We have successfully done this with two previous, but simpler patterns. Proper digitization of the pattern requires about 150 hours of hand work and the use of specialized software. The choice of materials is critical to the quality and aesthetic appeal of the the final result, especially the type of thread and choice of colors.

Artworks

Image for entry 'An Embroidered Pattern of Shells'

An Embroidered Pattern of Shells

450.0 x 450.0 cm

Computer-guided Embroidery

2024

To create this pattern, we were inspired by M.C Escher's Regular Division Drawing 42, which is mathematically interesting since the apparent 4-fold rotation centers of scallop shells only have 2-fold rotational symmetry, and there are two kinds of 4-fold rotations at the meeting points of conchs. So Escher's pattern has symmetry group p4, or 442 in orbifold notation. Our hyperbolic version preserves the 2-fold scallop meeting points and has two kinds of 5-fold conch rotation centers, yielding the symmetry group 552 in orbifold notation. The implementation was done in two steps: 1) creating an input file understood by the machine, and 2) the actual stitch-out which involved changing colors of thread and moving