The mathematical model of binary fractal interpolation is introduced. Based on the statistical self-similarity of rock fracture surface

the concept of improved self-affine fractal interpolation is put forward. By using the method of the improved self-affine fractal interpolation

the rock fracture surface is simulated with the measured data from the rock fracture surface. Compared the surfaces simulated with different number of given data to the practical fracture surface

the simulated precision is obtained. The relationship between the number of given data and the simulated precision obtained and shows the power function law. This means that we not only can obtain the simulated result in the interpolation

but also can get the estimation precision of the simulated result. Using a little amount of given data to simulate unknown surface gives the simulating method from the parts to the whole. This is useful for studying

simulating and displaying the shape of complicated objects intuitively with some little information

such as the topographty

the fault surface and the fracture surface of materials.