通过将整数同余的概念推广到实数范围，定义了实数“局部”的概念。即通过某种方式（例如进制分解或连分式分解）将实数表示成无限序列，称无限序列中包含的有限序列为实数的“局部”，具有相同局部的实数称为“同局”。考察实值函数函数值的局部，有如下结论：函数值同局的点组成的集合构成二值分形，构成规则图形是特例；对函数取局部得到新的函数，它的图象是多值分形，构成规则图象则是特例。这种分形复杂性的根源是数的无限性，其规律性的根源是它受到某个指定函数的控制。与传统的分形生成方法不同，文中提出的分形生成方法勿需迭代过程。更进一

By extending the concept congruence from integer to real number field, this paper defines a concept named ‘part’ of real number. A real number can be represented as an infinite sequence, a finite sequence of it is called 'part'. If two real numbers have the same part, then they are called isopart. By Studying the part of a real value function, we have the conclusion as following: the set which includes all the isopart points is normally a binary fractals, The image of the new function generated by taking the part of the given function is multi-value fractals. The infinity of real number leads to the complexity of this kind of fractals, and the given function leads to the regularity. The method does not need iterative operations which are essential for traditional fractal generation methods. In addition, it makes the connection between numbers and fractals.