Smooth Mountains

Multivariable calculus students can see that the height function is everywhere differentiable and that it has many local maxima, local minima, and a variety of saddle points. Since every small neighborhood of a point on the surface resembles the tangent plane at the point, the picture is really not a fractal.

The image was generated by the bicubic spline interpolation, which was applied on an ordinary fractal to tame and smooth its chaotic ups-and-downs (the numbers of iterations at various points).