The Bose-Hubbard model describes bosons on a lattice with competing kinetic energy (hopping J) and on-site repulsion (U). At integer filling and small J/U, bosons are Mott localized: each site has exactly n bosons and tunneling is energetically forbidden — an incompressible insulator. As J/U increases past a critical value (J/U)_c ≈ 0.034/z (z = coordination number), the system undergoes a quantum phase transition to a superfluid: bosons delocalize into a coherent condensate, phases lock across sites. The simulation shows occupation numbers per site (dot size) and phase coherence (colors). In the superfluid, all phases align; in the Mott phase, phases are random but occupation is fixed.