  Quasi-crystals are aperiodic structures that present crystallographic
properties which are not compatible with that of a single unit cell. Their
revolutionary discovery in a metallic alloy, less than three decades ago, has
required a full reconsideration of what we defined as a crystal structure.
Surprisingly, quasi-crystalline structures have been discovered also at much
larger length scales in different microscopic systems for which the size of
elementary building blocks ranges between the nanometric to the micrometric
scale. Here, we report the first experimental observation of spontaneous
quasi-crystal self-assembly at the millimetric scale. This result is obtained
in a fully athermal system of macroscopic spherical grains vibrated on a
substrate. Starting from a liquid-like disordered phase, the grains begin to
locally arrange into three types of squared and triangular tiles that
eventually align, forming 8-fold symmetric quasi-crystal that has been
predicted in simulation but not yet observed experimentally in non-atomic
systems. These results are not only the proof of a novel route to spontaneously
assemble quasi-crystals but are of fundamental interest for the connection
between equilibrium and non-equilibrium statistical physics.
