What Should a Surface in 4-Space Look Like?

We wish to investigate spaces of dimension greater than three and in particular surfaces in 4-dimensional space. Such surfaces can be knotted. Our explorations include mathematical and visualization tools.Mathematically we focus on a particular example of visualization of the result of an energy flow of a knotted surface. In terms of visualization, we use sound, texture, and a slicing technique of “splayed slabs”, in addition to more traditional tools.Basic issues of the mathematical visualization process are discussed.