Chimeras confined by fractal boundaries in the complex plane

Complex-valued quadratic maps either converge to fixed points, enter into periodic cycles, show aperiodic behavior, or diverge infinity. Which of these scenarios takes place depends on the map’s complex-valued parameter c and initial conditions. The Mandelbrot set is defined by values for which map remains bounded when initiated at origin complex plane. In this study, we analyze dynamics a coupled network two pairs in dependence c. Across four maps, kept same whereby are identical. analogy behavior individual iterates infinity remain bounded. solutions settle different stable states, including full synchronization desynchronization all maps. Furthermore, symmetric partially synchronized states within-pair across-pair as well symmetry broken chimera state found. boundaries between divergent domain fractals showing rich variety intriguingly esthetic patterns. Moreover, divided countless subsets throughout length scales Each subset contains only one enclosed within fractal leading divergence.