The formation of segregation patterns in initially homogeneous, fluidized, binary mixtures of particles has been studied. The adjustment of the bed depends on the proportions of fine and coarse particles in the mixture and the gas flow rate relative to the minimum fluidization velocities of the two components. The particles are immobile until the gas flow rate is sufficiently large to fluidize the mixture of particles. When the gas flow rate exceeds this critical value, alternating vertical bands of coarse and fine particles form. At a second critical gas velocity this pattern breaks down and the more familiar pattern of a mixed horizontal band on top of a layer of coarse particles forms. A phase diagram, constructed from experimental observations, shows the conditions for which each of these regimes exists. Its structure is explained in terms of the fluidization and consequent mobility of the mixture components. When horizontal bands are present, the thickness of the lower layer of coarse particles decreases with increasing gas flow rate depending on the proportion of fine particles in the bed. This, and its development, can be understood by analogy with the sedimentation of particles through a turbulent fluid. The experiments imply that the efficiency of mixing by the bubbles in the fluidized bed is very much less than that expected from gas bubbles in a liquid.