States of elementary cellular automata with periodic boundary conditions and periodic binary numbers in general can be visualized by picking either ones or zeros from n overlapping disks on the unit circle. Those areas covered by an odd number of selected disks are marked.
This Demonstration shows the evolutions of initial conditions with 12 bits. Enable color encoding to identify the 4096 possible 12-bit states with 4-bit intensities of red, green, and blue channels. The overlapping disks cover range-1 neighborhoods to group each value with its two neighbors. Periodic repetitions of images and similar colors indicate that the evolution has entered a map orbit.