A self-scanning flat display having a light active matrix in the form of a set of periodic lines which include light-reflecting, light-transparent, or light-emitting elements. These elements are controlled by current or a charge generated by a scan raster device. The raster device is made in the form of a streamers produced from nanostructured active material, in which there is induced and propagates a soliton, i.e., a maintained running electronic wave. The soliton controls the light active matrix. The nanostructured material includes clusters with tunnel-transparent coatings. The clusters have the sizes, at which the resonant features of the electron are manifested. The sizes are determined by the circular radius of the electron wave. The cluster size is set within the range r.sub.0-4r.sub.0, i.e., 7.2517 nm.ltoreq.r.ltoreq.29.0068 nm. The width of the tunnel-transparent gap is not more than r.sub.0=7.2517 nm.