Hidden variable bivariate fractal interpolation surfaces. (English) Zbl 1046.28004
Summary: We construct hidden variable bivariate fractal interpolation surfaces (FIS). The vector-valued iterated function system (IFS) is constructed in \(\mathbb R^4\) and its projection in \(\mathbb R^3\) is taken. The extra degree of freedom coming from \(\mathbb R^4\) provides hidden variable, which is an important factor for flexibility and diversity in the interpolated surface. In the present paper, we construct an IFS that generates both self-similar and non-self-similar FIS simultaneously and show that the hidden variable fractal surface may be self-similar under certain conditions.
MSC:
| 28A80 | Fractals |
Keywords:
bivariate fractal; fractal dimension; FIF; IFS; surface generation; self-similar surface; iterated function systemReferences:
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