Abstract
This chapter discusses fractal interpolation functions. The fractal dimension of the graphs of Euclidean functions is always 1; these elementary Euclidean functions are useful not only because of their geometrical content but also because they can be expressed by simple formulas. Moreover, elementary functions are used extensively in scientific computation, computer-aided design, and data analysis because they can be stored in small files and computed by fast algorithms. The graphs of these functions can be used to approximate image components; rather than treating the image component as arising from a random assemblage of objects, it can be well defined using fractal interpolation functions. Fractal interpolation functions also provide a new means for fitting experimental data. Fractal interpolation functions share with elementary functions that they are of a geometrical character, that they can be represented succinctly by formulas, and that they can be computed rapidly. The main difference is their fractal character.
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