  In this paper we study an experimentally-observed connection between two
seemingly unrelated processes, one from computational geometry and the other
from differential geometry. The first one (which we call "grid peeling") is the
convex-layer decomposition of subsets $G\subset \mathbb Z^2$ of the integer
grid, previously studied for the particular case $G=\{1,\ldots,m\}^2$ by
Har-Peled and Lidick\'y (2013). The second one is the affine curve-shortening
flow (ACSF), first studied by Alvarez et al. (1993) and Sapiro and Tannenbaum
(1993). We present empirical evidence that, in a certain well-defined sense,
grid peeling behaves at the limit like ACSF on convex curves. We offer some
theoretical arguments in favor of this conjecture.
  We also pay closer attention to the simple case where $G=\mathbb N^2$ is a
quarter-infinite grid. This case corresponds to ACSF starting with an infinite
L-shaped curve, which when transformed using the ACSF becomes a hyperbola for
all times $t>0$. We prove that, in the grid peeling of $\mathbb N^2$, (1) the
number of grid points removed up to iteration $n$ is $\Theta(n^{3/2}\log n)$;
and (2) the boundary at iteration $n$ is sandwiched between two hyperbolas that
are separated from each other by a constant factor.
