Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-24T01:21:12.706Z Has data issue: false hasContentIssue false
  • English
  • Français

BOX DIMENSION OF BILINEAR FRACTAL INTERPOLATION SURFACES

Part of: Classical measure theory Approximations and expansions

Published online by Cambridge University Press:  30 May 2018

QING-GE KONG Open the ORCID record for QING-GE KONG [Opens in a new window] ,
HUO-JUN RUAN Open the ORCID record for HUO-JUN RUAN [Opens in a new window]  and
SHENG ZHANG Open the ORCID record for SHENG ZHANG [Opens in a new window]
QING-GE KONG
Affiliation:
School of Mathematical Science, Zhejiang University, Hangzhou 310027, China email [email protected]
HUO-JUN RUAN*
Affiliation:
School of Mathematical Science, Zhejiang University, Hangzhou 310027, China email [email protected]
SHENG ZHANG
Affiliation:
School of Mathematical Science, Zhejiang University, Hangzhou 310027, China Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

bilinear fractal interpolation surfacesbox dimensioniterated function systemsvertical scaling factors

MSC classification

Primary: 28A80: Fractals
Secondary: 41A30: Approximation by other special function classes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 113 - 121
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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), 303–329.Google Scholar
Barnsley, M. F., Elton, J., Hardin, D. and Massopust, P. R., ‘Hidden variable fractal interpolation functions’, SIAM J. Math. Anal. 20 (1989), 1218–1242.Google Scholar
Barnsley, M. F. and Massopust, P. R., ‘Bilinear fractal interpolation and box dimension’, J. Approx. Theory 192 (2015), 362–378.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), 449–476.Google 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), 322–334.Google Scholar
Geronimo, J. S. and Hardin, D., ‘Fractal interpolation surfaces and a related 2-D multiresolution analysis’, J. Math. Anal. Appl. 176 (1993), 561–586.CrossRefGoogle Scholar
Hardin, D. P. and Massopust, P. R., ‘The capacity of a class of fractal functions’, Commun. Math. Phys. 105 (1986), 455–460.CrossRefGoogle Scholar
Małysz, R., ‘The Minkowski dimension of the bivariate fractal interpolation surfaces’, Chaos Solitons Fractals 27 (2006), 1147–1156.CrossRefGoogle Scholar
Massopust, P. R., ‘Fractal surfaces’, J. Math. Anal. Appl. 151 (1990), 275–290.Google Scholar
Mazel, D. S. and Hayes, M. H., ‘Using iterated function systems to model discrete sequences’, IEEE Trans. Signal Process. 40 (1992), 1724–1734.Google Scholar
Metzler, W. and Yun, C. H., ‘Construction of fractal interpolation surfaces on rectangular grids’, Internat. J. Bifur. Chaos 20 (2010), 4079–4086.CrossRefGoogle Scholar
Ruan, H.-J. and Xu, Q., ‘Fractal interpolation surfaces on rectangular grids’, Bull. Aust. Math. Soc. 91 (2015), 435–446.Google 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), 187–197.Google Scholar