2024 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 circle model or on triply periodic polyhedra. Once we have designed a pattern, we proceed to implement it using computer controlled crafting devices such as a paper plotter/cutter or an embroidery sewing machine. Proper digitization of the pattern requires over 100 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. Sewing out the design requires a computer controlled top of the line embroidery machine and 20 hours of supervised operation.

Artworks

Image for entry 'Hyperbolic Embroidered Butterflies'

Hyperbolic Embroidered Butterflies

35.0 x 35.0 cm

Machine Embroidery

2023

This is a tessellation of the Poincaré circle model of hyperbolic geometry by Escher-inspired butterflies. The pattern's symmetry group is [7,3]+, with color group being the simple group of order 168. It was implemented using embroidery to capture many, but not all, of the details of the original image. Stitches have a long dimension, allowing us to add information not present in an image. The butterfly stitches follow the orientation of the butterflies and the spots have stitches perpendicular to the underlying butterfly. We stopped the butterfly pattern about 7/8 of the way to the edge of the bounding circle because the butterflies were becoming too small to implement with finite thickness thread and filled the rest with gray.