1. An image processing apparatus for generating a sub-self-similar set F, which is a subset of a self-similar set A with respect to a plurality of contraction maps f 1 ,. .. , f n where n is a natural number and larger than 1, and for forming an image expressing the sub-self-similar set F, the apparatus including a processor, the processor comprising: a base-address-set designating section that selects m addresses each of which are formed of finite sequence {1,. .. , n} and generates a base address set M including the selected m addresses; a generation-rule acquiring section that 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 g 1 ,. .. , g n , by using the generated base address set M; and a sub-self-similar set generating section that generates a sub-self-similar set F, which is a subset of the self-similar set A, by applying the acquired generation rule to the plurality of contraction maps f 1 ,. .. , f n .