A model involving head motion is given for self-consistently computing magnetic recording medium magnetization patterns. The reduction in demagnetizing field due to the presence of the high-permeability head structure is included, as is record head removal, read head replacement, and computation of the readback voltage. The model is capable of handling an arbitrary record current waveform. Optimum record-current amplitude for nonreturn to zero (NRZ) digital recording is first determined, and then single-, double-, and quadruple-transition computations are performed using two different values of hysteresis loop squareness and both linear and exponential current reversals. Results are primarily for the Karlquist fringe field, but the recording properties of a head exhibiting regions in which the fringe field reverses sign are also briefly investigated.