The Box Fractal Sets Based on Bilinear Transformation Iterated Function System

Abstract: For solving the problem which typical Iterated Function System(IFS for short) attractor is very "regular",we attempt to use bilinear transformation IFS through geometric approach, and use it to generate a kinds of fractal set: box fractal set. The result shows that bilinear transformation IFS can generate attractors with a higher degree of flexibility、reality, and a higher modeling capability. It's important to research nonlinear interactive fractal modeling algorithm REFERENCES [1] Mandelbrot BB. Fractal geometry of nature. New York: W.H. Freeman, 1983 [2] Barnsley MF. Fractals everywhere, 2nd ed. Boston Academic Press;,1993 [3] Ping Wang,Lei Li,et al.,Effects of fractal surface on C6 glioma cell morphogenesis and differentiation in vitro. Biomaterials 31(2010)6201-6206 [4] James G McNally, Davide Mazza, Fractal geometry in the nucleus.The EMBO Journal (2010) 29, 2–3 [5] Daniele Mancardi, Gianfranco Varetto, et al., Fractal parameters and vascular networks: facts & artifacts. Theoretical Biology and Medical Modelling 2008, 5:12 [6] Bai-lin Hao, H.C. Lee, et al., Fractals related to long DNA sequences and complete genomes.Chaos, Solitons and Fractals 11 (2000) 825-836 [7] Jianbo Gao,Yan Qi,et al.,Protein coding sequence identification by simultaneously characterizing the periodic and random features of DNA sequences.Journal of Biomedicine and Biotechnology 2 (2005) 139–146 [8] Nazneen Akhter, Yusuf Talib, et al.,Fractal application for characterisation of structure of macromolecules like carbohydrate. J. Microbiol. Biotech. Res., 2012, 2 (1):108-114 [9] Michel L. Lapidus, et al.,Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators. Advances in Mathematics 227 (2011) 1349–1398 [10] Tomasz Martyn,Realistic rendering 3D IFS fractals in real-time with graphics accelerators.Computers & Graphics 34 (2010) 167–175 [11] M.R. Browna,R.,Errington P. Rees,et al.,A highly efficient algorithm for the generation of random fractal aggregates. Physica D 239 (2010) 1061-1066 [12] Enrique de Amo, Manuel Díaz Carrillo,et al.,PCF self-similar sets and fractal interpolation. Mathematics and Computers in Simulation 92 (2013) 28–39 [13] Zhigang Fenga,Yizhuo Feng,et al.,Fractal interpolation surfaces with function vertical scaling factors.Applied Mathematics Letters 25 (2012) 1896–1900 [14] Song-Gyong Ri,Huo-Jun Ruan,Some properties of fractal interpolation functions on Sierpinski gasket..J. Math. Anal. Appl. 380 (2011) 313– 322 [15] Eduard Groller,Modeling and rendering of nonlinear iterated function systems. Comput. & graphics, 1994, 18(6):739- 748 [16] Eduard Groller, Rainer Wegenkittl,Interactive design of nonlinear functions for iterated function systems. 93-102. http://wscg.zcu.cz/WSCG1996/papers96/Groll er_96.