Construction and Visualization of Planar Dynamic Systems with Non-equidistant Cyclic Windows

To generate planar tiling images with different visual effect by the same iterating mapping,we present a method that allows the P1 planar tessellations to be constructed by a planar dynamic systems with non-equidistant cyclic windows.We construct a family of iterative mappings,which yield cyclic windows of variant size in the dynamical plane by incorporating cosine functions and non-linear angle variables with parameters.Chaotic attractors and filled-in Julia sets in the different cyclic windows are created by establishing the coordinates of any cyclic windows and the maximal window,then clarifying the relationship of corresponding points between these cyclic windows.The respective images in different windows are continuous but with individual structures.We can choose any cyclic window 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.