Some Properties Of Fractal Interpolation Surface

A new method of approximation of experiment data of fractal interpolation is introduced. Some properties of fractal interpolation surface on the rectangular grids are discussed. These properties including the dimension, Holder continuity and the indefinite integral of binary fractal interpolation function are studied. The indefinite integral of binary interpolation function generated by iterated function system (IFS) is proved, and its IFS are given. At the same time, the sufficient and necessary condition for 2-th-order partial derivative of binary fractal interpolation function equaling itself is obtained, and the sufficient and necessary condition is extended to 2N-th-order partial derivative. In addition, some results about integration, moment and integration of fractal interpolation surface function on various scales are discussed. In the end, some properties of multivariate fractal interpolation surface function such as box-dimension, the expression with series, the relations between the moment and the coefficient are discussed. These properties have obtained some valuable results. These both have in theory and the practical application two aspects the vital significance, and are beneficial consummation and supplement for fractal theory. It can provide corresponding theory basis with both studying rock section plane and the fault surface and other application of fractal geometry.