A contour of a function f(x,y,z) is obtained by setting w = k constant where w = f(x,y,z).
The resulting surface f(x,y,z) = k is a contour in the domain of f.
A set of contours in either the two or three variable case is called a level set. Level sets that have singularities are especially interesting since the hypersurface has critical points at these values of k.
This demo shows some contour surfaces of the four-dimensional graph of the function f(x,y,z) = -x4 + 2x2 - y4 + 2y2 - z4 + 2z2 .
Use the tapedeck controllers to analyze the different level sets of the function f. What can you say about critical points of the hypersurface f(x,y,z)?