We acquire symbols based on the time sequence data obtained from our environments, and take the symbol manipulation for the data processing and generation, which is one of the higher functions of our intelligence. For the realization of the robot intelligence, it will be a fast way to design the symbol manipulation system. The scalability and spatio-temporal continuousness are important foci of the information processing system for the real world robot to process a large amount of information. In this paper, we design the spatially continuous symbol space using the dynamics based information processing system by putting the dynamics in the functional space. The utilization of the dynamics connects the continuous sensor signal and the discrete symbols, the allocation of the dynamics in the symbol space causes the spatially continuousness and the selection of the appropriate bases holds the scalability of the system.