Parameter space of one-parameter complex mappings

We find that the effective mappings of the one-parameter complex mappings of parameters in the neighborhood of the centers such that a critical point is also a periodic point have the forms of simplest polynomial mappings. The appearance of an infinite number of small copies of the Mandelbrot-like sets in the parameter space is a consequence of these effective mappings. Thus we are able to calculate the positions, the sizes, and the orientations of these small copies of the Mandelbrot-like set for any one-parameter complex mapping.