Numerical calculations reveal that the target and spiral growth patterns in spherulites can be generated from the time-dependent Ginzburg-Landau equations (model C) by coupling a conserved compositional order parameter and a nonconserved crystal ordering parameter. Of particular interest is that the periodic concentric rings (target) or the spirals at the spherulitic core remain stationary in both the crystal (orientational) ordering field and the concentration field. Another intriguing observation is that the growth of target and spiral spherulites occurs in a stepwise fashion in synchronism with the rhythmic energy dissipation during crystallization.