ITERATION LOGISTIC MAP DYNAMICS IN THE POLAR COORDINATES

The complicated dynamics of logistic maps with four fundamental operat ions in the polar coordinates are analyzed in this paper. Iterations o f single logistic map in polar coordinates exhibit similar characteris tics as in the Cartesian coordinates. Iterations of double logistic ma ps, however, are more interesting in polar coordinates than those in C artesian coordinates. Under different iterative rules, the dynamics of double logistic maps show some funny artistic patterns. Some of them look like the formation of an embryo, and some even look Like Taiji di agram, which is the representative symbol of Taoism in ancient China. It is interesting to see that Taiji, which is believed in Taoism to be the mysterious origination of the world, is an interim phenomenon wit hin the evolution of the systems governed by the law of the logistic e quations.