Abstract: Hats such as baseball-type caps and sun visors which have a brim projecting from the forward part of the hat, or sailor hats or Stetson-type (or cowboy-type or fedora-type) hats that have a brim extending about the periphery of the hat are provided with a device on or forming the brim that presents two or more composite graphic images or sets of images. The hat brim includes at least two interleaved series or sets of sections are arranged in a wave-like manner that each present a composite image or a set of images. The sections of each series of interleaved sections generally face in a common direction so that images or parts of images displayed by the sections of a same series are viewable together, and the sections of different series face in different directions. An observer can view a first image or set of images on the brim from a first direction and second image or set of images on the brim from a second direction.