References
- M.F. Barnsley, Fractals Everywhere, Academic Press, Boston, MA, 2014.
- G.M. Chaikin, An algorithm for high-speed curve generation, Comput. Graph. Image Process. 3(4) (1974), pp. 346–349. doi: 10.1016/0146-664X(74)90028-8
- C. Conti and K. Hormann, Polynomial reproduction for univariate subdivision schemes of any arity, J. Approx. Theory 163(4) (2011), pp. 413–437. doi: 10.1016/j.jat.2010.11.002
- N. Dyn, D. Levin, and J.A. Gregory, A 4-point interpolatory subdivision scheme for curve design, Comput. Aided Geom. Des. 4(4) (1987), pp. 257–268. doi: 10.1016/0167-8396(87)90001-X
- R. Goldman, The fractal nature of Bezier curves, Proceedings Geometric Modeling and Processing, Beijing, China, 2004, pp. 3–11.
- M.F Hassan, I.P. Ivrissimitzis, N.A. Dodgson, and M.A. Sabin, An interpolating-4 point C2 ternary stationary subdivision scheme, Comput. Aided Geom. Des. 19(1) (2002), pp. 1–18. doi: 10.1016/S0167-8396(01)00084-X
- P. Lenka, Fractals and Splines, University of West Bohemia, Pilsen, Czech Republic, 2012.
- J.-A. Lian, On a-ary subdivision for curve design: I. 4-point and 6-point interpolatory schemes, Appl. Appl. Math. 3 (1) (2008), pp. 18–29.
- B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, CA, 1982.
- S. Schaefer, D. Levin, and R. Goldman, Subdivision schemes and attractors, Proceedings of the Eurographics Symposium on Geometry Processing, Vienna, Austria, 2005, pp. 171–180.
- S.S. Siddiqi, S. Siddiqui, and N. Ahmad, Fractal generation using ternary 5-point interpolatory subdivision scheme, Appl. Math. Comput. 234 (2014), pp. 402–411.
- S.S. Siddiqi, U. Idrees, and K. Rehan, Generation of fractal curves and surfaces using ternary 4-point interpolatory subdivision scheme, Appl. Math. Comput. 246 (2014), pp. 210–220.
- Z. Wang and Y. Pang, A recursive algorithm based four-point interpolation scheme for curve design and its application to rendering of fractals, J. CAD & CG 9(3) (1997), pp. 223–227. [in Chinese].
- J. Wang and X. Qian, Dimensionality estimation of the fractal interpolatory curve generated by 4-point interpolatory subdivision scheme, J. Gansu Univ. Technol. 29(3) (2003), pp. 120–122. [in Chinese].
- J. Wang, H. Zheng, F. Xu, and D. Liu, Fractal properties of the generalized Chaikin corner-cutting subdivision scheme, Comput. Math. Appl. 61 (2011), pp. 2197–2200. doi: 10.1016/j.camwa.2010.09.014
- K. Zhang and Z. Xu, Theorem of Matrices, Science Press, Beijing, 2014. [in Chinese].
- H. Zheng, Z. Ye, Y. Lei, and X. Liu, Fractal properties of interpolatory subdivision schemes and their application in fractal generation, Chaos Solitons Fractals 32 (2007), pp. 113–123. doi: 10.1016/j.chaos.2005.10.075
- H.C. Zheng, Y Li, G.H. Peng, and Y.N. Tang, A multicontrol p-ary subdivision scheme to generate fractal curves, Appl. Mech. Mater. 263–266 (2012), pp. 1830–1833. doi: 10.4028/www.scientific.net/AMM.263-266.1830