An image processing apparatus generates a sub-self-similar set F, which is a subset of a self-similar set A with respect to contraction maps f1, . . . , fn and forms an image expressing the sub-self-similar set F. The apparatus includes a base-address-set designating section, a generation-rule acquiring section and a sub-self-similar set generating section. The base-address-set designating section selects m addresses each of which formed of infinite sequence of {1, . . . , n} and generates a base address set M including the selected addresses. The generation-rule acquiring section acquires a rule of generating a hypothetical sub-self-similar set G, which is a subset of a hypothetical self-similar set B with respect to n hypothetical contraction maps g1, . . . , gn, by using the generated base address set M. The sub-self-similar set generating section generates a sub-self-similar set F, which is a subset of the self-similar set A.