此前分形数集已经出现了动物形模样和三维自相似形态,那还只是单个函数的运算结果.这里进行的是两个函数复合迭代运算共同确定一个数集的试验.这种双函数集的形体模样既不是两单函数集的集合交并,也不是它们形体的几何合成,更像是与生物现象类似的数集杂交.双函数集的形态会传承其两单函数集的某些特征,又不同其单函数集而有自己的独特性.发现不仅两函数是而且两函数的复合迭代顺序也是双函数集形态的决定因素,表明分形数集存在同函异序双生子.高级双函数集的函数还有配型条件,对称双函数集的产生须要两函数的单函数集是同类对称数集,自相似双函数集的产生须要两函数的单函数集是同类自相似数集.文中提供了5个具有代表性的迭代函数,附图31幅展示了11个数集及自相似子集的三维形象.通过比对发现双函数集成形与动物杂交现象在多方面都有惊人的一致.推测动物基因结合有类似的顺序原理,生物基因信息不仅记录在基因中而且会记录在基因顺序中.

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.