1. An image processing apparatus, which combines, with original image data that is image data of an original image, superimposed image data that is image data of an image to be superimposed on the original image, the image processing apparatus comprising: at least one of (i) a self-similar image storing section that stores one or more patterns of self-similar images and (ii) a self-similar image detecting section that detects a pattern of a self-similar image that is combined with the original image data; a superimposed image data generating section that generates the superimposed image data from a self-similar image, based on the pattern of the self-similar image; an image combining section that generates composite image data by combining the original image data with the superimposed image data; and a size determining section that determines a draw size of the original image in a case where the original image is drawn, the superimposed image data generating section generating the superimposed image data by adjusting the pattern of the self-similar image so that a size of the superimposed image corresponds to the draw size.