Iteration dynamical systems of discrete Laplacians on the plane lattice (I) (Basic properties and computer simulations of the dynamical systems)

In this study we introduce a concept of discrete Laplacian on the plane lattice and consider its iteration dynamical system. At first we discuss some basic properties on the dynamical system to be proved. Next making their computer simulations, we show that we can realize the following phenomena quite well:(1) The crystal of waters (2) The designs of carpets, embroideries (3) The time change of the numbers of families of extinct animals, and (4) The echo systems of life things. Hence we may expect that we can understand the evolutions and self organizations by use of the dynamical systems. Here we want to make a stress on the following fact: Although several well known chaotic dynamical systems can describe chaotic phenomena, they have difficulties in the descriptions of the evolutions and self organizations.