We demonstrate the fabrication of horizontally aligned carbon nanotube (HA-CNT) networks by spatially programmable folding, which is induced by self-directed liquid infiltration of vertical CNTs. Folding is caused by a capillary buckling instability and is predicted by the elastocapillary buckling height, which scales with the wall thickness as t(3/2). The folding direction is controlled by incorporating folding initiators at the ends of the CNT walls, and the initiators cause a tilt during densification which precedes buckling. By patterning these initiators and specifying the wall geometry, we control the dimensions of HA-CNT patches over 2 orders of magnitude and realize multilayered and multidirectional assemblies. Multidirectional HA-CNT patterns are building blocks for custom design of nanotextured surfaces and flexible circuits.