Microdevices containing a predetermined preferential axis of magnetization are disposed in an array having discreet regions. Under influence of a magnetic field, the microdevices can have at least twelve discrete orientations, and can advantageously be flipped upside down in place. Microdevices can be coded in a manner that supports a coding space of at least 102, 103, 106 or even 1010 or more choices, and can include one or more chemically reactive sites. The regions can be defined by long and short bars, in which microdevices span gaps between the longer bars, and the shorter bars measure less than 60% of such gaps. Preferred embodiments are also provided to produce microfabricated microdevices for magnetic assembly-based arraying.