A Contribution to Fractal Interpolation Techniques and their Properties

Abstract

In applied mathematics, interpolation by polynomials is rather an old technique. The newlineapproach of fractal interpolation gives a new direction to demonstrate the smooth and nonsmooth bodies. Over the past three decades, theory of fractal interpolation has been one of the newlinedominant research matters among fractal group. It is a modern method to analyze the newlinescientific data. Traditional interpolation schemes have great limitations for irregular shape newlinekind of data. So, for this we describe the irregular shapes by using the fractal interpolation newlineschemes. The unsmooth items such as clouds, coastlines, woodland skyline etc are newlinerepresented by the fractal interpolation functions. Fractal interpolation is one of the newlineapplication parts of the IFS theory which is a generalization of classical interpolation that is newlineused as a new approach to represent complex phenomena and is used in many fields like newlinecomputer graphics, astrophysics, medical, biological sciences, image compression, signal newlineprocessing, data analysis, financial series, complex dynamics, telecommunication, and pattern newlinerecognition. In the application part of computer graphics, this method provides an option for newlinecatching the data in self-similarity designs at any dimension of magnification. The majority newlineuse of fractals in computer science is the fractal image compression. Fractal image newlinecompression gives more compression ratio than usual schemes (e.g. JPEG or GIF file newlineformats). In telecommunication, fractal antennae reduce greatly the size and weight of the newlineantennae. In physics, fractals are used to describe the roughness of surfaces. This thesis newlineentitled with A contribution to fractal interpolation techniques and their properties . In newline