Vertical Scaling Factor Variable Fractal Interpolation Function

In fractal theory, fractal interpolation is a fitting method and it palys an important role. It is the successful application of the theory of iterated function systems in the area of function interpolation. Firstly, the appearance, devel-opment and main theory of fractal interpolation function are proposed in this paper. Secondly, in the context of general fractal interpolation function, we in-troduce a kind of fractal interpolation function whose vertical scaling factors are not constant. Then, we consider the integral of these functions.The condition for such functions remaining within a given rectangle with vertical scaling factor is obtained. Finally we give a brief introduction of bilinear fractal interpolation function.