Rotational and Contracting Tilings of Ordinary Images in Hyperbolic Limit Disk
To construct the limit disk patterns with hyperbolic symmetries from ordinary images,we set the computing regions,which are corresponding to images,and the hyperbolic limit disks in the same Euclidian plane.We regard the ordinary images as strange attractors of some IFS iterated function systems.We investigate the relative positional relations between a vertex or the midpoint of one border about central lattice of the hyperbolic limit disk and the farmost point from the original in the strange attractors so that the compression ratios and rotational angles can be automatically obtained to compress images into the central lattice of a hyperbolic plane with p-rotational symmetry.We compress the point selected randomly from the image into the hyperbolic plane by choosing hyperbolic symmetric matrixes according to cumulative probabilities,which were calculated about the area compression ratios for every matrixes in the Euclidian plane.The research shows that our method to generate the hyperbolic limit disks with symmetry + or presented in this paper is simple and effective.