In exemplary implementations of this invention, a digital material comprising many discrete units is used to fabricate a sparse structure. The units are reversibly joined by elastic connections. Each unit comprises fiber-reinforced composite material. Each unit is small compared to the sparse structure as a whole. Likewise, in a sparse structure made from this digital material, the number of types of units is small compared to the total number of units. The digital material is anisotropic. This anisotropy may be due to different fiber orientations within each unit. Furthermore, different units in a single sparse structure may be oriented in different directions and in different, non-parallel planes. In some cases, the digital material is reinforced with carbon fibers, and connections between units are stronger than the units themselves. The small discrete units may be assembled into a strong, lightweight sparse structure, such as an airframe.