说明：  被誉为大自然的几何学的分形( fractal) 理论是现代数学的一个新分支。分形的概念最早是由美籍数学家曼德布罗特( B. B. Mandelbort) 提出 ， 分形是指部分与整体以某种方式相似的形体。自相似原则和迭代生成原则是分形理论的重要原则。它表征分形在通常的几何变换下具有不变性， 即标度无关性。分形维数是分形理论中的主要参数， 分形维数反映了复杂形体占有空间的有效性， 它是复杂形体不规则性的量度。
(The fractal (fractal) theory, which is known as the geometry of nature, is a new branch of modern mathematics. The concept of fractal was first proposed by the American mathematician, Mandelbrot (B. B. Mandelbort), which refers to a form that is similar in some way to the whole. The principle of self similarity and the principle of iterative generation are the important principles of the fractal theory. It characterizes the invariance of the fractal under the usual geometric transformation, namely the scale independence. Fractal dimension is the main parameter in fractal theory. Fractal dimension reflects the validity of the occupied space of complex form, and it is the measurement of the irregularity of complex shape.)