Julia sets of the complex Carotid-Kundalini function

The properties of the iterated complex Carotid-Kundalini function, given by z(j+1) = cos(Nz(j)cos(-1)(z(j))) + c, where z, c, and N are complex constants, are studied. Depending on the valu es of N, c, and z, used, trajectories either tended to a fixed point, displ ayed periodic behaviour, or increased in value in an unbounded manner at ea ch iteration. Trajectories that tended to fixed points were observed to do so in an are-like manner for some parameter values. Trifurcations were seen as convergence to a single fixed point which was replaced by period-3 and period-9 motion, as the imaginary part of c was varied. (C) 2001 Published by Elsevier Science Ltd.