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On the Parameter Identification Problem in the Plane and the Polar Fractal Interpolation Functions

โœ Scribed by L. Dalla; V. Drakopoulos

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
200 KB
Volume
101
Category
Article
ISSN
0021-9045

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โœฆ Synopsis

Fractal interpolation functions provide a new means for fitting experimental data and their graphs can be used to approximate natural scenes. We first determine the conditions that a vertical scaling factor must obey to model effectively an arbitrary function. We then introduce polar fractal interpolation functions as one fractal interpolation method of a non-affine character. Thus, this method may be suitable for a wider range of applications than that of the affine case. The interpolation takes place in polar coordinates and then with an inverse non-affine transformation a simple closed curve arises as an attractor which interpolates the data in the usual plane coordinates. Finally, we prove that this attractor has the same Hausdorff dimension as the polar one.

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