Self-organization is a phenomenon found in biomolecular self-assembly by which proteins are spontaneously driven to assemble and attain various functionalities. This study reports on self-organized behavior in which distributed centimeter-sized modules stochastically aggregate and exhibit a translational wheeling motion. The system consists of two types of centimeter-sized water-floating modules: a triangular-shaped module that is equipped with a vibration motor and a permanent magnet (termed the active module), which can quasi-randomly rove around; and circular modules that are equipped with permanent magnets (termed passive modules). In its quasi-random movement in water, the active module picks up passive modules through magnetic attraction. The contacts between the modules induce a torque transfer from the active module to the passive modules. This results in rotational motion of the passive modules. As a consequence of the shape difference between the triangular module and the circular module, the passive modules rotate like wheels, being kept on the same edges as the active module. The motion of the active module is examined, as well as the characteristics and behavior of the self-organization process.