A memory device includes a planar substrate, a plurality of horizontal conductive planes above the planar substrate, and a plurality of horizontal insulating layers interleaved with the plurality of horizontal conductive planes. An array of vertical conductive columns, perpendicular to the pluralities of conductive planes and insulating layers, passes through apertures in the pluralities of conductive planes and insulating layers. The memory device includes a plurality of programmable memory elements, each of which couples one of the horizontal conductive planes to a respective vertical conductive column.