Abstract
In this paper, we give the fractal interpolation curves generated on the Koch curve by Hölder continuous functions and function vertical scaling factors, and at the same time, we present the estimation method of box dimensions of curves of R3 through the estimation of lower and upper box dimensions of obtained curves, where a remarkable fact is that the box dimensions are dependent not only on function vertical scaling factors but also on Hölder exponent of harmonic functions on the Koch curve.
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