Travels in Hyperbolic Space


Session Title:

  • Art and the Algorithm

Presentation Title:

  • Travels in Hyperbolic Space



  • Although working with different representations of space may seem like one of the natural domains of artists, few have had exposure to work involving geometries other than our familiar Euclidean construction of space. As certain branches of mathematics become increasingly visual, computers are being used to view and explore spaces which have previously been described primarily through abstraction. Familiarity and perhaps involvement with these theories may afford the artist who works with new technologies a greater opportunity to explore and influence our conception of how our world is constructed. Delle Maxwell and Charlie Gunn worked together (with the help of many others) to create a video called Not Knot. Not Knot tells the story of one way that mathematicians understand, SF knots. The project was initiated to visualise some of the exciting results in three dimensional topology made by mathematicians working with the Geometry Center in Minneapolis, Minnesota — particularly the results of William Thurston in the classification of three-dimensional spaces.

    His deep geometric intuition was suited to the medium of computer visualisation. Group members brought together skills from mathematics, computer animation, art, design, and computer science. We chose to feature hyperbolic space because it has great appeal to both mathematical and non-mathematical audiences. It allows people to experience the concept of curved space for the first time in a realistic way, a concept which is of central importance in many physical theories of natural science. After a brief introduction, we will show this video tape and will then discuss and illustrate via animation other strange visual characteristics of such spaces. Although the tape was not created as a work of art, it is meant to be a visual experience. As such, we believe it can serve as a catalyst for artists wishing to explore other geometries and to gain more insight into the theories that are shaping our understanding of the space around us.