Level surfaces of complicated smooth functions.
No. 141, 1974
(Geometry of manifolds and singular points of smooth functions)
India ink and pencil on paper, 31.5 x 44 cm.
Hanging in the sky, smooth forms spin and twist like weather patterns, as if a tornado is reaching down into a chasm in the earth, probing the many levels below. On the surface, bulbous sculptures dot the landscape. At the lowest depth, shoes line up along a strata of a subterranean horizon. This image seeks to depict graphically the successive level surfaces of a function defined for the entire three-dimensional space, a level surface being a set of points whose value is constant. Indeed, the topology of a level surface can change along with the value of a function as it crosses a critical value. Here, critical points of the function appear on the corresponding level surface. At some singular points, separatrix disks drop down from one level surface to another. To a large extent, the structuring of the various level surfaces determines the topology of the entire manifold.
