Fractals for functions with rational exponent
This paper investigates the fractals generated by the iteration of functions of the form f (z) = z(alpha) + c, where alpha is a rational non-integer number larger than 2, and z and c are complex numbers. We will examine both the dynamic and parameter spaces and discuss the consequences of the discontinuity of the function f(z). The images of these fractals allow for remarkable insight into the difficulty encountered in trying to extend results from polynomial cases to more generalized functions. (C) 2004 Elsevier Ltd. All rights reserved.
fractals iteration complex variables