In Ray Bradbury's classic short story "A Sound of Thunder", a character named Lesperance explains why he wouldn't bump in to a time-traveling himself:
Time doesn't permit that sort of mess—a man meeting himself. When such occasions threaten, Time steps aside. Like an airplane hitting an air pocket. You felt the Machine jump just before we stopped? That was us passing ourselves on the way back to the Future. We saw nothing.
What does this mean? Did the machine/Time somehow hide the previous Lesperance? Does the machine/Time duplicate realities where Lesperance somehow didn't visit while keeping the paint he made onto the dinosaur?