  Continued advances in quantum technologies rely on producing nanometer-scale
wires. Although several state-of-the-art nanolithographic technologies and
bottom-up synthesis processes have been used to engineer such wires, critical
challenges remain in growing uniform atomic-scale crystalline wires and
constructing their network structures. Here we discover a simple method to
fabricate atomic-scale wires with various arrangements, including stripes, X-,
Y-junctions, and nanorings. Single-crystalline atomic-scale wires of a Mott
insulator, whose band gap is comparable to those of wide-gap semiconductors,
are spontaneously grown on graphite substrates \DEL{and epitaxial monolayer
graphene on SiC }by pulsed-laser deposition. These wires are
one-unit-cell-thick and have an exact width of two- and four-unit-cells (1.4
and 2.8\,nm) and lengths up to a few $\mu m$. We show that the non-equilibrium
reaction-diffusion processes may play an essential role in atomic pattern
formation. Our findings offer a new perspective on the non-equilibrium
self-organization phenomena on an atomic scale, paving a unique way for the
quantum architecture of nano-network.
