A New Approach to Pattern Recognition in Fractal Ferns

Barnsley (2006) used chaos game in function systems and it gave rise to interesting fractals by combining it with function iterations. A fractal fern is generated by taking different probabilities in the chaos game. In this paper, we introduce two advanced iterations from nonlinear analysis into the study of IFS for generation and pattern recognition of new fractal ferns. Gottfried (1991), and Martyn (2002a, 2002b). Jones (1990) has extended Barnsley’s method of chaos game from triangles to regular polygons (Barnsley, 2006). A fractal fern may be generated by taking different probabilities in chaos game. Duis et al. (1987) studied the origin of superficial lightning burns with the help of fern-shaped mathematical models. Michelitsch (1990) generated fern like structures using trigonometric functions. In 1999, Chang, Chang, and Wen (1999) proposed a fixed-point-searching algorithm which automatically determines the original size and the coordinates of a fractal fern. Recently, Ahammer and Devaney (2003, 2005) computed the correlation dimension of fractal ferns and influence of noise on the same, while Zodrow (2007) reconstructed interesting tree ferns. Fractal ferns have enjoyed its applications in many areas of mathematical sciences such as biology, chemistry, physics and coding DOI: 10.4018/jalr.2010040102 22 International Journal of Artificial Life Research, 1(2), 21-28, April-June 2010 Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. theory. For details, one may refer to Barnsley (1989), Korn (1993), Xu, Leung, Liang, and Leung (2003) and Zhu, Hsu, Zhou, Terrones, Kroto, and Walton (2001). Method of function iterations have found staggering applications in several areas of mathematical sciences. In particular, theory of discrete dynamics is the study of such iterative processes. In general, an IFS is based on function iterations (also called Picard iterations). Recently, Chandra and Rani (2009) and Rani and Kumar (2004a, 2004b, 2005) introduced superior iterations in the study of fractals and offered impressive comparison in favor of this new host in discrete dynamics. The purpose of this paper is to introduce superior iterations and I-superior iterations as generalized approaches for generation and pattern recognition in fractal ferns. In Section 2, we give preliminaries of chaos game and iterative procedures. In Section 3, we generate and study the pattern of fractal ferns followed by conclusions in Section 4.