A method and apparatus for constructing building structures of various desired geometric patterns comprising the steps of establishing a mold controllable in successive steps along a path corresponding to the desired geometric pattern, the mold having a surface shape corresponding to a segment of the desired geometric pattern; applying a building construction material in liquid or atomized form in abutment with said surface to which said building material solidifies to establish a segment of the building structure; temporarily retaining said mold in abutment with the applied construction material to support the applied construction material for a time period sufficient to permit said applied material to solidify sufficiently to be self sustaining; and repositioning the mold in successive positions along the geometric pattern and adjacent to a previously cured segment and applying said building material in abutment with said mold at each position.