Applicants have discovered a novel apparatus and method to aggregate and displace a plurality of magneto-responsive entities (steerable self-propelled entities or SSPEs) in three dimensions using time-multiplexing. The apparatus for controlling aggregation of SSPEs in a body comprises at least three sets of magnetic field sources arranged in three axes for generating a controlled magnetic field and a controller connected to at least one of said magnetic field sources to create a three dimensional convergence point. The method for aggregating the entities can comprise using a first set and a second set of said magnetic field sources to generate opposed magnetic field gradients in each said set to cause aggregation of said magneto-responsive entities in two axes and wherein the controller is configured to reverse a direction of said magnetic field gradient in a third set of magnetic field sources in a third axis according to a first predetermined program.
