In exemplary embodiments of this invention, a programmable surface comprises an array of cells. Each of the cells can communicate electronically with adjacent cells in the array, can compute, and can generate either normal thrust or shear thrust. Distributed computing is employed. The programmable surface may cover all or part of the exterior of a craft, such as an aircraft or marine vessel. Or, instead, the programmable surface may comprise the craft itself, which may, for example, take the form of a "flying carpet" or "flying sphere". The thrust generated by the programmable surface can be employed directly to provide lift. Or it can be used to control the orientation of the craft, by varying the relative amount of thrust outputted by the respective cells. The number of cells employed may be changed on a mission-by-mission basis, to achieve "span on demand". Each cell may carry its own payload.