Boundary Functions (1998)

We think of personal space as something that belongs entirely to ourselves. However, Boundary Functions shows us that personal space exists only in relation to others and changes without our control.

Boundary Functions is a set of lines projected from overhead onto the floor, dividing people in the gallery from one another. When there is one person on its floor, there is no response. When two are present, a single line cuts between them bisecting the floor and dynamically changing as they move. With more than two people, the floor divides into cellular regions, each with the quality that all space within it is closer to the person inside than any one else.

The regions surrounding each person are referred to as Voronoi diagrams. These diagrams are widely used in diverse fields and spontaneously occur at all scales of nature. In anthropology and geography they describe patterns of human settlement; in biology, the patterns of animal dominance and plant competition; in chemistry the packing of atoms into crystals; in astronomy the influence of gravity on stars; in marketing the strategic placement of chain stores; in robotics path planning; and in computer science the solution to closest-point problems. The diagrams represent as strong a connection between mathematics and nature as the constants e or pi.

By projecting the diagram, the invisible relationships between individuals and the space between them become visible and dynamic. The intangible notion of personal space and the line that always exists between you and another becomes concrete. The installation doesn’t function at all with one person, as it requires a physical relationship to someone else. In this way Boundary Functions is a reversal of the lonely self-reflection of virtual reality, or the frustration of virtual communities: here is a virtual space that can only exist with more than one person, in physical space.

The title, Boundary Functions, refers to Theodore Kaczynski's 1967 University of Michigan PhD thesis. Better known as the Unabomber, Kaczynski is a pathological example of the conflict between the individual and society: engaging with an imperfect world versus an individual solitude uncompromised by the presence of others. The thesis itself is an example of the implicit antisocial quality of some scientific discourse, mired in language and symbols that are impenetrable to the vast majority of society. In this installation, a mathematical abstraction is made instantly knowable by dynamic visual representation.

Exhibition History

Ars Electronica 1998 (prize), Linz, Austria
The Tech Museum. San Jose, California, 1998
Interaction '99, Gifu, Japan
NTT Intercommunications Center (ICC), Tokyo, Japan, 1999 
Transmediale 2000, Berlin, Germany
Foro Artistico, Hanover, Germany, 2001
The Exploratorium, San Francisco, 2001
Shinzuoka Arts Center, Tokyo, Japan, 2002
The Kitchen, New York City, 2002
Toki Messe. Nigata, Japan. April 2003
MAIS: Exposition d'Installations Interactives. Brussels, Belgium, 2004
Le Channel, scène nationale de Calais. France. September, 2004
Nabi Arts Center, Seoul, South Korea, 2004
Phaeno Science Center, Wolfsburg, Germany, 2004
Tilt. Perpignan, France. February, 2005
Artefact. Belgium. February, 2005
Tokyo Intercommunications Center. May, 2006
Kitakyushu Innovation Gallery, Kitakyusu City, Japan, 2007
Miró Foundation, Mallorca, Spain, October 2007
Milwaukee Art Museum. October, 2008

Technical Realization

The installation consists of an overhead camera and projector aimed at the floor through a mirror. The camera and projector are connected to a computer, which performs tracking of the moving people on the floor by processing the video image using custom software. The software then generates the Voronoi diagram, which is projected back onto the floor.

By kind permission of Jonathan Shewchuk, Boundary Functions uses the Triangle library.