The Sculpture Manifold: A Band from a Surface, a Surface from a Band

Bernd Krauskopf, Hinke M. Osinga and and Benjamin Storch
Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture (2008)
Pages 9–14


The steel sculpture Manifold consists of an 8 cm wide closed band of stainless steel that winds around in an intricate way, curving and coming very close to itself. It is based on a complicated mathematical surface, known as the Lorenz manifold, which has an important role in organising the chaotic dynamics of the well-known Lorenz equations. Namely, this surface consists of all points that, under the force field generated by the Lorenz equations, end up at the origin of the three-dimensional phase space. This is special because all other points go to the famous Lorenz butterfly attractor. The Lorenz manifold can be found and represented numerically by a set of smooth closed curves consisting of points that lie at the same geodesic distance (given by the length of the shortest path on the surface) from the origin. Any band between two such curves illustrates an aspect of the geometry of the surface. As is explained in this paper, the sculpture Manifold represents a choice of band that is motivated by aesthetic, practical and mathematical considerations. The goal was to create an element of dynamicism while only hinting at the underlying surface.