  I study the time-evolution of a particle prepared in the ground state of an
infinite well after the latter is suddenly expanded. It turns out that the
probability density $|\Psi(x, t)|^{2}$ shows up quite a surprising behaviour:
for definite times, {\it plateaux} appear for which $|\Psi(x, t)|^{2}$ is
constant on finite intervals for $x$. Elements of theoretical explanation are
given by analyzing the singular component of the second derivative
$\partial_{xx}\Psi(x, t)$. Analytical closed expressions are obtained for some
specific times, which easily allow to show that, at these times, the density
organizes itself into regular patterns provided the size of the box in large
enough; more, above some critical time-dependent size, the density patterns are
independent of the expansion parameter. It is seen how the density at these
times simply results from a construction game with definite rules acting on the
pieces of the initial density.
