Nonlinear IFS from Quintic Complex Polynomial Mappings with Single Complex Parameter and Multiperiodic Orbits

To construct the new fractals or new strange attractors,we present a method which can be used to construct a nonlinear IFS composed of the quintic complex polynomial mappings with the single complex parameter and the multiperiodic orbit.In the M set of the parameter plane,an ellipse is constructed,which connects the 4 vertexes of the periodic bud with the 4 transmutative petal-structure in every high-periodic parameter region;( k≥2 ) parameters are chosen in or near the ellipse; 5 topological conjugate mappings are defined in the filled-in Julia set for every parameter; an IFS is composed of the 5k mappings; a fractal is constructed by randomly iterating the IFS in the common attracting basin of the 5k mappings.The results show that the parameters,chosen in or near the ellipse of the high-periodic parameter region from the mapping of f (z)=z^5+c ,can be used to construct the valid IFSs.The fractals or strange attractors with 5 rotational symmetry and the different structures can be generated by the method presented in this paper.