  The evolution of networks of coupled chaotic maps with delayed interactions
can be studied in the usual way by analyzing the evolution of the state of
elements at each iteration time (the "Simulator" point of view), or it can be
analyzed from the point of view of a single element (the "Observer"
perspective) that is receiving delayed information from the other elements in
the system. In the usual"Simulator" timeframe, an absolute time (i.e. the
number of iterations $t$) is adopted to define the system state at each time
$t$. In the"Observer" framework, the state of an element in the system is given
by its state at the "Simulator" time $t-\tau$, where $\tau$ is the information
travel time between that element and the Observer. We emphasize the convenience
of the analysis of the system dynamics in the "Observer" timeframe by showing
that the "Observer" dynamics differs substantially from the one in the
"Simulator" timeframe, and that the system dynamics in the "Observer" timeframe
reflects the proper causality of the interactions among the elements.

Pattern Formation and Solitons;Chaotic Dynamics