Research on Parameters of Construction of IFSs from Non-Analytical Complex Mappings

To construct fractals or strange attractors from the non-analytical complex mappings, we investigate how the parameters from the 1-period region of the generalized Mandelbrot sets（M sets） of the complex mapping family f（z）=e^iπ/2zⁿ+c have the impacts on the construction of the iterating function system（IFS）. We randomly choose a parameter in the 1-period region of a generalized M set. According to the symmetries of the M set, we construct the IFS with the parameters located in the symmetrical positions in the M set about the choosed parameter. We construct all of the filled-in Julia sets and their common attracting basin from the functions of the IFS in the dynamic plane. We choose the attracting fixed point of the function, constructed from the parameter randomly choosed in the M set, as the initial iterating point and compute the orbit of the point by randomly choosing a function of the IFS in the common attracting basin. According to a great number of experiments, we find a way of choosing the parameters to construct the nonlinear IFS for generating fractals. The result shows that the parameters of the 1-period region of the generalized M sets of the complex mapping family f（z）=e^iπ/2zⁿ+c can be used to construct the nonlinear IFS, which can be used to generate the fractal mountains and the new types of fractals with symmetries Z_n+1 and D_n+1.