A radical departure from generally accepted concepts in construction robotics is proposed in this paper. A new process derived from the emerging field of additive manufacturing processes is investigated for its potential effectiveness in construction automation. In essence, complex assemblies of large construction components are substituted with a large number of elemental component assemblies. The massive complexity of information processing required in construction is replaced with a large number of simple elemental operations which lend themselves easily to computer control. This exploratory work is illustrated with sample masonry structures that cannot be obtained by casting. They are manufactured by an incremental deposition of sand and Portland cement akin to Navajo sand painting. A thin layer of sand is deposited, followed by the deposition of a patterned layer of cement. Steam is then applied to the layer to obtain rapid curing. A characterization of the resulting material properties shows rather novel anisotropic properties for mortar. Finally, the potential of this approach for solid freeform fabrication of large structures is assessed.