Two infinite families of self-similar tilings are described which have apparently not been reported before. Each tiling is based on a single prototile that is a segment of a regular polygon. Each tiling is also edge to edge and bounded in the Euclidean plane, by means of the tiles being reduced in size. by a fixed scaling factor. This results in self similarity. Tilings are constructed from these prototiles that are of a rich visual complexity, and an example is given of an Escher-like design based on one of these tilings.