Biomedical Engineering and Bioengineering Commons^™

Generalized Fractals For Computer Generated Art: Preliminary Results, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

This paper explores new types of fractals created by iteration of the functions xn+1 = f1(xn, yn) and yn+1 = f2(xn, yn) in a general plane, rather than in the complex plane. Iteration of such functions generates orbits with novel fractal patterns. Especially interesting are N-th order polynomials, raised to a positive or negative integer power, p.

Such functions create novel fractal patterns, including budding, spiked, striped, dragon head, and bat-like forms. The present faculty working paper shows how to create a rich variety of complex and fascinating fractals using this generalized approach, which is accessible to students with high …

New Fractals For Computer Generated Art Created By Iteration Of Polynomial Functions Of A Complex Variable, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

Novel fractal forms can be created by iteration of higher order polynomials of the complex variable, z, with both positive and negative exponents, followed by optional integer power transformation, k zz . Such functions lead to an expanded universe of fascinating fractal patterns that can be incorporated into computer generated art.