  Tropical sandpile model (or linearized sandpile model) is the only known
continuous geometric model exhibiting self-organised criticality. This model
represents the scaling limit behavior of a small perturbation of the maximal
stable sandpile state on a big subset of $\mathbb Z^2$. Given a set $P$ of
points in a compact convex domain $\Omega\subset \mathbb R^2$ this linearized
model produces a tropical polynomial $G_P{\bf 0}_\Omega$.
  Here we present some quantitative statistical characteristics of this model
and some speculative explanations. Namely, we study the dependence between the
number $n$ of randomly dropped points
$P=\{p_1,\dots,p_n\}\subset[0,1]^2=\Omega$ and the degree of the tropical
polynomial $G_{P}{\bf 0}_\Omega$. We also study the distributions of the
coefficients of $G_{P}{\bf 0}_\Omega$ and the correlation between them. This
paper's main (experimental) result is that the tropical curve $C(G_{P}{\bf
0}_\Omega)$ defined by $G_{P}{\bf 0}_\Omega$ is a small perturbation of the
standard square grid lines. This explains a previously known fact that most of
the edges of the tropical curve $C(G_{P}{\bf 0}_\Omega)$ are of directions
$(1,0),(0,1),(1,1),(-1,1)$.
  The main theoretical result is that $C(G_{P}{\bf 0}_\Omega)\setminus (P\cap
\partial\Omega)$, i.e. the tropical curve in $\Omega^\circ$ with marked points
$P$ removed, is a tree.
