A machine that is capable of assembling a copy of itself from a feedstock of parts is described. The machine operates on a lattice or grid on which it is able to move and from which it receives power and control signals. The machine (assembler) is composed of modules that each perform some functionality. In the simplest case, only three module types are needed: a linear step module, a gripper, and an anchor. The linear step module is capable of moving from one lattice location to the next, the gripper module is capable of gripping other modules, and the anchor module is capable of attaching the machine to the grid. With these three primitives it is possible for this simple machine to move on the grid using inchworm-like motions, pick up other modules, and assemble a copy of itself.