  We introduce a general method for designing tailored lattices of magnetic
microtraps for ultracold atoms, on the basis of patterned permanently
magnetized films. A fast numerical algorithm is used to automatically generate
patterns which provide optimal atom confinement while respecting desired
lattice symmetries and trap parameters. The algorithm can produce finite and
infinite lattices of any plane symmetry; we focus specifically on square and
triangular lattices which are of interest to future experiments. Typical trap
parameters are discussed as well as the impact of realistic imperfections such
as finite lithographic resolution and magnetic inhomogeneity. The presented
designer lattices open new avenues for quantum simulation and quantum
information processing with ultracold atoms on atom chips.
