As far as I understand it follows from the work of M. Freedman that there exist locally flat embeddings of two dimensional surfaces in $\mathbb R^4$ that can not be smoothed in the class of locally flat embedding. (For definition of locally flat see http://en.wikipedia.org/wiki/Local_flatness)
I am curious if one can draw a realistic picture of such a surface. At least is it possible to draw an intersection of such a surface with a (linear) hyperplane in $\mathbb R^4$? Is the Hausdorff dimension of such an intersection equals $1$?