  The level curves of an analytic function germ almost always have bumps at
unexpected points near the singularity. This profound discovery of N. A'Campo
is fully explored in this paper for $f(z,w)\in \C\{z,w\}$, using the
Newton-Puiseux infinitesimals and the notion of gradient canyon. Equally
unexpected is the Dirac phenomenon: as $c\ra 0$, the total Gaussian curvature
of $f(z,w)=c$ accumulates in the gradient canyons.
