Some fractal number sets take some animal shape and 3D self-similar structures, as the result of the single function operation. This paper makes tests of a composite function iteration to determine a number set. These double-function number sets take shapes of neither a union or an intersection of two single-function sets, nor a form of geometry synthesis, but resemble a hybridization of number sets as in biological phenomena. The double-function number sets keep some characteristics of related single-function number sets, but with differences and take their own unique shapes. It is revealed that not only the functions but also the composite order of two iteration functions determine the shape of double-function number sets, which bring about the appearance of binate fractal number sets. And the iteration functions satisfy matching conditions for advanced double-function number sets. The symmetric double-function number set requires symmetric single-function number sets and the self-similar double-function number set requires self-similar single-function number sets. This paper presents 5 iteration functions and 31 pictures which show 3D images of 11 number sets and their self-similar sub-sets. Comparing the double-function number sets with the phenomena of animal hybridization, it is discovered that they are similar. It may be inferred that in the combination of animal genes, we have the order principle and the information of biological genes may be recorded not only in genes but also in orders of genes.