We study the general phenomenon of random organization using a vortex system. When a periodic shear with a small shear amplitude dinp is applied to many-particle (vortex) assemblies with a random distribution, the particles (vortices) gradually self-organize to avoid future collisions and transform into an organized configuration. This is detected from the time-evolution of the voltage V ( t ) (average velocity) that increases towards a steady-state value. From the subsequent readout measurements of V ( t ) using various shear amplitudes, we find that the information of the input shear amplitude dinp is memorized in the configuration of the vortex distributions in the transient as well as the steady state, and that it is readable. We also find that the transient vortex configuration formed during random organization is not microscopically homogeneous but consists of disordered and organized regions.