  Emergence is a concept that is easy to exhibit, but very hard to formally
handle. This paper is about cubic sand grains moving around on nicely packed
columns in one dimension (the physical sandpile is two dimensional, but the
support of sand columns is one dimensional). The Kadanoff Sandpile Model is a
discrete dynamical system describing the evolution of a finite number of
stacked grains --as they would fall from an hourglass-- to a stable
configuration (fixed point). Grains move according to the repeated application
of a simple local rule until reaching a fixed point. The main interest of the
model relies in the difficulty of understanding its behavior, despite the
simplicity of the rule. In this paper we prove the emergence of wave patterns
periodically repeated on fixed points. Remarkably, those regular patterns do
not cover the entire fixed point, but eventually emerge from a seemingly highly
disordered segment. The proof technique we set up associates arguments of
linear algebra and combinatorics, which interestingly allow to formally state
the emergence of regular patterns without requiring a precise understanding of
the chaotic initial segment's dynamic.
