The set of initial states which are drawn to an attractor of the system.
                                                            
                                                     
                        
                                                
                        
                        
                            Most important attribute of an attractor of a DS * Set of initial points tending to the same attractor
                                                            
                                                     
                        
                                                
                        
                        
                            The set of states (initial conditions in the phase space) that approach a particular attractor as time goes to infinity.
                                                            
                                                     
                        
                                                
                        
                        
                            The subset of states of a dynamical system's state space that converge into an attractor.