本文从斐波那契数列的通项公式出发，得到光滑的斐波那契振荡函数.再经过解析延拓至复平面，发现函数的零点排列在一条直线上.斐波那契函数将复平面上的直线映射为黄金螺旋线，呈现出自相似的特点.我们进一步由金属分割数定义金属函数,对其性质进行了初步的探讨.

This paper starts from the Fibonacci sequence to obtain a smooth oscillating Fibonacci function. The function is extended to complex plane via analytical continuation. We find that all the zeros of the function lie on a line. The Fibonacci function map strait lines on the complex plane to golden spirals, which exhibits self-similarity characteristics. We further extend the metal ratios to define metal functions and preliminarily explore their properties.