  We interpret experimentally known B-Mg-Ru crystals as quasicrystal
approximants. These approximant structures imply a deterministic decoration of
tiles by atoms that can be extended quasiperiodically. Experimentally observed
structural disorder corresponds to phason (tile flip) fluctuations.
First-principles total energy calculations reveal that many distinct tilings
lie close to stability at low temperatures. Transfer matrix calculations based
on these energies suggest a phase transition from a crystalline state at low
temperatures to a high temperature state characterized by tile fluctuations. We
predict B$_{38}$Mg$_{17}$Ru$_{45}$ forms a decagonal quasicrystal that is
metastable at low temperatures and may be thermodynamically stable at high
temperatures.
