A pneumatic system includes a fluidic switching module, an air connection inlet configured for connection to a source of pressurized air, a plurality of air connection outlets each in fluid communication with the air connection inlet, a first cascading subsystem downstream from and in fluid communication with the air connection inlet and configured to receive a pressurized airflow from the air connection inlet, a second cascading subsystem downstream from and in fluid communication with the first cascading subsystem, and a third cascading subsystem downstream from and in fluid communication with the first cascading subsystem. The fluidic switching module is configured to cyclically and sequentially direct the pressurized airflow between the plurality of air connection outlets without any moving parts or external controls.