Table of Contents
SRX Mathematics
Volume 2010 (2010), Article ID 432521, 10 pages
http://dx.doi.org/10.3814/2010/432521
Research Article

Construction of Fractal Surfaces via Solutions of Partial Differential Equations

Department of Informatics and Telecommunications, Telecommunications and Signal Processing, University of Athens, Panepistimiopolis, 157 84 Athens, Greece

Received 31 July 2009; Revised 23 September 2009; Accepted 13 October 2009

Copyright © 2010 P. Bouboulis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. F. Barnsley and S. Demko, “Iterated function systems and the global construction of fractals,” Proceedings of the Royal Society of London A, vol. 399, pp. 243–275, 1985. View at Google Scholar
  2. P. R. Massopust, “Fractal surfaces,” The Journal of Mathematical Analysis and Applications, vol. 151, no. 1, pp. 275–290, 1990. View at Google Scholar
  3. P. R. Massopust, Fractal Functions, Fractal Surfaces and Wavelets, Academic Press, San Diego, Calif, USA, 1994.
  4. M. F. Barnsley, “Fractal functions and interpolation,” Constructive Approximation, vol. 2, pp. 303–329, 1986. View at Google Scholar
  5. A. K. B. Chand and G. P. Kapoor, “Generalized cubic spline fractal interpolation functions,” SIAM Journal on Numerical Analysis, vol. 44, no. 2, pp. 655–676, 2006. View at Google Scholar
  6. M. A. Navascues and M. V. Sebastian, “Generalization of Hermite functions by fractal interpolation,” The Journal of Approximation Theory, vol. 131, pp. 19–29, 2004. View at Google Scholar
  7. J. S. Geronimo and D. Hardin, “Fractal interpolation surfaces and a related 2D multiresolutional analysis,” Journal of Mathematical Analysis and Applications, vol. 176, pp. 561–586, 1993. View at Google Scholar
  8. N. Zhao, “Construction and application of fractal interpolation surfaces,” The Visual Computer, vol. 12, pp. 132–146, 1996. View at Google Scholar
  9. R. Malysz, “The Minkowski dimension of the bivariate fractal interpolation surfaces,” Chaos, Solitons and Fractals, vol. 27, no. 5, pp. 1147–1156, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  10. P. Bouboulis, L. Dalla, and V. Drakopoulos, “Construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension,” The Journal of Approximation Theory, vol. 141, pp. 99–117, 2006. View at Google Scholar
  11. P. Bouboulis, “Construction of Orthogonal Multi-Wavelets using Generalized-Affine Fractal Interpolation Functions,” IMA Journal of Applied Mathematics, vol. 74, no. 6, pp. 904–933, 2009. View at Google Scholar
  12. P. Bouboulis and L. Dalla, “Closed fractal interpolation surfaces,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 116–126, 2007. View at Google Scholar
  13. P. Bouboulis and L. Dalla, “Fractal interpolation surfaces derived from fractal interpolation functions,” Journal of Mathematical Analysis and Applications, vol. 336, no. 2, pp. 919–936, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  14. P. Bouboulis and L. Dalla, “A general construction of fractal interpolation functions on grids of n,” European Journal of Applied Mathematics, vol. 18, no. 4, pp. 449–476, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. F. Barnsley, Fractals Everywhere, Academic Press Professional, Boston, Mass, USA, 2nd edition, 1993.
  16. K. Falconer, Fractal Geometry, John Wiley & Sons, New York, NY, USA, 2003.