Construction of planar dynamic systems with function of non-linear angle variables

This paper constructs the planar dynamic systems with non-equidistant cyclic windows. To generate planar tiling images with different visual effects by the same iterative mapping, we propose a method that allows the planar tessellations to be constructed by a planar dynamic system with non-equidistant cyclic windows. A family of iterative mappings are constructed which generate cyclic windows of variant size in the dynamic plane by incorporating cosine functions and non-linear angle variables with the same parameters. Filled-in Julia sets in different cyclic windows are created by generating the coordinates of any cyclic windows. The images in different windows are continuous but with individual structures. We can choose any cyclic windows as the basic computing region and stretch or compress it into a square, which is transferred to the plane to compose the planar tilling. Experimental results show the effectiveness of the proposed approach. © (2012) Trans Tech Publications, Switzerland.