Construction and box dimension of the composite fractal interpolation function

In this paper, we construct the composite fractal interpolation function and prove that the compositeness of two general fractal interpolation functions is still a fractal interpolation function. And its generating iterated function system is obtained from given iterated function systems. Finally, the box dimension of the composite fractal interpolation function is discussed. We give an inequality estimate of the upper and lower box dimensions of the composite fractal interpolation function.

Automated summary

In this paper, we construct a composite fractal interpolation function and prove that the composition of two general fractal interpolation functions is also a fractal interpolation function. The generating iterated function system of the composite function is obtained from given iterated function systems. Finally, we discuss the box dimension of the composite fractal interpolation function and provide an inequality estimate for the upper and lower box dimensions.