Advances in Machine Learning & Artificial Intelligence(AMLAI)

Findeisen-Str, 5/7, 71665 Vaihingen an der Enz, Germany

Publications

• Research Article   
  About Structure of a connected Quaternion-JUllA-Set and Symmetries of u related JULIA-Network
  Author(s): Udo E. Steinemann*
  
  If a variable is replace by its square and subsequently enlarged by a constant during a number of iteration-steps in quaternion-space, a network of (3) sets will be built gradually. As long as for the iteration-constant certain conditions are fulfilled, the network will consist of: an rrnbounded set (escape-set) with trajectories escaping to infinity during course of the iteration, a bounded set (prisoner-set) with trajectories tending to a sink-point and a further bounded one (JULIA-set) with a fixed-point as repeller having a repulsive effect on all points of both the other sets. The iteration will continue until the attracting sink-point of prisoner-set and the repeliing fixedpoint on JULIA-set have been found. This situation is reached if predecessor- and successor-state of the iteration became equal. The fixed-point-condition provisionally formulated in general terms of quaternio.. Read More»
  

  Abstract HTML PDF