A slatted horizontal blinds system has separate positional controls for distinct subsets of slats. Odd and even slats can be moved relative to each other both horizontally and vertically. With a scalloped upper and lower edge, overlapping slats can produce a variety of light allowing and esthetic modes. Some versions only support up and down movement and some slats are rectangular. This is caused by hiding and exposing of slat portions and voids between slats by the relative movement of odd and even slats. Slats may have translucent colored portions, apertures or printed designs. The absolute movement may only be of one subset of slats while other slats stay in position. In other cases all slats can move simultaneously in relation to each other. Mechanisms include screw drive with “lost motion” operation and movement latches. Also slidable carriages, end-cams, and linear motors can be used. In some cases the bottom rail has mechanisms as well as the head rail.