A NEW NONLINEAR BIVARIATE FRACTAL INTERPOLATION FUNCTION

In this paper, we present a new nonlinear bivariate fractal interpolation function (FIF) by using the Matkowski’s fixed point theorem and the Rakotch contraction. In particular, we give a new nonlinear fractal interpolation surface (FIS) on a rectangular grid. Our technique is different from the methods presented in the literature.

A NEW CONSTRUCTION OF THE FRACTAL INTERPOLATION SURFACE

In this paper, we introduce a new construction of the fractal interpolation surface (FIS) using an even more general iterated function systems (IFS) which can generate self-affine and non self-affine fractal surfaces. Here we present the general types of fractal surfaces that are based on nonlinear IFSs.

Research on a Class of Multi Parameter Fractal Interpolation Curved Surface Based on Iterative Function Image Generating Method

This paper extends the polynomial function to double logarithmic function, constructing a class of multi parameters iterative function, and uses this function to calculate the fractal interpolated surface for given interpolation points, and establishes the iterative function mathematical model of multi parameters fractal interpolation. In order to verify the effectiveness and reliability of this proposed model algorithm, this paper uses MATLAB numerical simulation method to calculate, and programs the Newton iterative function of multi parameters fractal interpolation surface, finally gets calculation nephogram of multi parameters fractal interpolation curved surface through calculating. Finally, using iterative method reduces the surface grid size, increasing the smoothness of the surface, so the surface is closer to the actual surface. It provides a new computer method research of fractal interpolation function.

SURFACE FITTING AND ERROR ANALYSIS USING FRACTAL INTERPOLATION

The fitting of a given continuous surface defined on a rectangular region in ℝ2 is studied by using a fractal interpolation surface, and the error analysis of fitting is made in this paper. The fractal interpolation functions used in surface fitting are generated by a special class of iterated function systems. Some properties of such fractal interpolation functions are discussed. Moreover, the error problems of fitting are investigated by using an operator defined on the space of continuous functions, and the upper estimates of errors are obtained in the sense of two kinds of metrics. Finally, a specific numerical example to illustrate the application of the procedure is also described.

Fuzzy Fractal Interpolation Surface and its Applications

Tackling of uncertain data is a major problem in analysis, modeling and simulation. Fractal interpolation surface and fuzzy set method are employed to solve the issue of uncertainty in modeling irregular surface. Initial interpolation data grid point is used as the kernel of Gaussian fuzzy membership function and its fuzzy numbers can be calculated by specifying λ of λ-cut set. These fuzzy numbers are used as uncertain data, which are the boundaries of the fluctuation of initial grid, and defined as a new kind of fuzzy interpolation grids. With these interpolation grids fractal interpolation surface algorithm is applied to act on. By these definitions, experimental data for modeling rock surface is illustrated to show that how the interpolation scheme proposed in this paper enhances the controllability for manipulating uncertain data.

Fractal Study on Blank Residue of Mould Cavity

A mathematical model of fractal interpolation surface is introuduced in this paper. A calculation to fractal dimension of the messy point data is proposed and used to get appropriate vertical scale factor to construct precise blank residue model. Fractal dimensions of different fractal interpolation surfaces with different vertical scale factor are different. The relationship between vertical scale factor and fractal dimension is obtained through calculating fractal dimensions of tested surfaces which are created by fractal interpolation with different vertical scale factor.