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BOX DIMENSION OF BILINEAR FRACTAL INTERPOLATION SURFACES

Published online by Cambridge University Press:  30 May 2018

QING-GE KONG
Affiliation:
School of Mathematical Science, Zhejiang University, Hangzhou 310027, China email kongqingge@163.com
HUO-JUN RUAN*
Affiliation:
School of Mathematical Science, Zhejiang University, Hangzhou 310027, China email ruanhj@zju.edu.cn
SHENG ZHANG
Affiliation:
School of Mathematical Science, Zhejiang University, Hangzhou 310027, China Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA email zhan2694@purdue.edu

Abstract

Bilinear fractal interpolation surfaces were introduced by Ruan and Xu in 2015. In this paper, we present the formula for their box dimension under certain constraint conditions.

Type
Research Article
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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Footnotes

The research was supported in part by the NSFC grants 11271327, 11771391 and by ZJNSFC grant LR14A010001.

References

Barnsley, M. F., ‘Fractal functions and interpolation’, Constr. Approx. 2 (1986), 303329.CrossRefGoogle Scholar
Barnsley, M. F., Elton, J., Hardin, D. and Massopust, P. R., ‘Hidden variable fractal interpolation functions’, SIAM J. Math. Anal. 20 (1989), 12181242.CrossRefGoogle Scholar
Barnsley, M. F. and Massopust, P. R., ‘Bilinear fractal interpolation and box dimension’, J. Approx. Theory 192 (2015), 362378.CrossRefGoogle Scholar
Bouboulis, P. and Dalla, L., ‘A general construction of fractal interpolation functions on grids of ℝ n ’, Eur. J. Appl. Math. 18 (2007), 449476.CrossRefGoogle Scholar
Falconer, K. J., Fractal Geometry: Mathematical Foundation and Applications (Wiley, New York, NY, 1990).Google Scholar
Feng, Z., ‘Variation and Minkowski dimension of fractal interpolation surfaces’, J. Math. Anal. Appl. 345 (2008), 322334.CrossRefGoogle Scholar
Geronimo, J. S. and Hardin, D., ‘Fractal interpolation surfaces and a related 2-D multiresolution analysis’, J. Math. Anal. Appl. 176 (1993), 561586.CrossRefGoogle Scholar
Hardin, D. P. and Massopust, P. R., ‘The capacity of a class of fractal functions’, Commun. Math. Phys. 105 (1986), 455460.CrossRefGoogle Scholar
Małysz, R., ‘The Minkowski dimension of the bivariate fractal interpolation surfaces’, Chaos Solitons Fractals 27 (2006), 11471156.CrossRefGoogle Scholar
Massopust, P. R., ‘Fractal surfaces’, J. Math. Anal. Appl. 151 (1990), 275290.CrossRefGoogle Scholar
Mazel, D. S. and Hayes, M. H., ‘Using iterated function systems to model discrete sequences’, IEEE Trans. Signal Process. 40 (1992), 17241734.CrossRefGoogle Scholar
Metzler, W. and Yun, C. H., ‘Construction of fractal interpolation surfaces on rectangular grids’, Internat. J. Bifur. Chaos 20 (2010), 40794086.CrossRefGoogle Scholar
Ruan, H.-J. and Xu, Q., ‘Fractal interpolation surfaces on rectangular grids’, Bull. Aust. Math. Soc. 91 (2015), 435446.CrossRefGoogle Scholar
Ruan, H.-J., Su, W.-Y. and Yao, K., ‘Box dimension and fractional integral of linear fractal interpolation functions’, J. Approx. Theory 161 (2009), 187197.CrossRefGoogle Scholar
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