A study on initial values of the logistic map over integers

We are investigating the logistic may over intergers with finite precision and sequences outputted by the interative mapping. One of our goals is to provide a guide-line for design of pseudorandom number generators with the map. In this paper, we set a basic model in which internal initial values are updated after a certain iteration, and show that an updating way of the internal initial value does not have a critical influence on radomness of output by the basic model with minor exceptions.