Some Properties Of A Fractal Interpolation Function

Fractal interpolation is a new method of approximation of experimental data, It can provide nature deterministic approximation of complex phenomena. Thus, fractal interpolation curve can simulate the shape of material object distinctly. Firstly, the appearance, development of fractal geometry and recent study are proposed. Secondly, fundamental theory of fractal geometry, fractal interpolation function (FIF) and its properties are summarized, including two definitions of dimension, iterated function system (IFS), continuity, stability of FIF. On this basis, according to the theory FIF depend on vertical scaling factors, a construction of a kind of FIF are obtained, conditions of linear property and smooth property of this FIF on some intervals are given. In addition, the relation between Minkowski dimension and Hausdorff dimension is discussed, its Minkowski dimension is absolutely larger than its Hausdorff dimension. Different properties of two FIF according to their IFS are discussed, the selection of scaling factors is important to the FIF is proved. These conclusions have vital significance in theory and the practical application two aspects, and are beneficial consummation and supplement for fractal theory. It can provide corresponding theory basis for other application of fractal geometry.