Abstract—In this paper, fractal properties of 7-point binary approximating subdivision scheme are presented. It is shown by the graphical presentation that the 7-point binary approximating scheme is helpful for fitting 2-dimensional data and has elegant well designed properties. Ranges of parameter are also defined to obtain fractals which lie inside and outside of the convex hull. Due to the parametric range, we can easily handle the limit curve according to our own choice. Since the given scheme is approximating, so we can get better smoothness as compare to interpolating scheme. Some numerical examples have been presented to fit the data points. It has been observed that 7-point scheme is quite suitable for fitting data points and a good selection for construction of fractals for the modeling purpose of decoration pieces and fabric designing etc. Nowadays one major approach of fractal is the generation of fractal antennas which are very helpful in the cell phone companies.

Index Terms—Approximation, data fitting, fractal, subdivision.

Mehwish Bari and Abid Hussain are with National College of Business Administration and Economics, Sub-Campus, Bahawalpur, Punjab, Pakistan (email: mehwishbari@yahoo.com).
Ghulam Mustafa is with The Islamia University of Bahawalpur, Pakistan.

Cite: Mehwish Bari, Ghulam Mustafa, Abid Hussain, "Fractal Generation by 7-Point Binary Approximating Subdivision Scheme," International Journal of Applied Physics and Mathematics vol. 8, no. 4, pp. 105-111, 2018.