Cycle diagram

A cycle diagram is a graph used in the study of cellular automata, wherein the nodes represent the possible configurations of a region and the links describe their interconnection by evolution. To combat the shrinkage of the region with time, cyclic boundary conditions are usually imposed. The result depicts the evolution of a unit cell for all time, in constast to a de Bruijn diagram which portrays cells of all lengths at a fixed stage of evolution. The cycle diagram will consist of trees rooted on cycles, leaves revealing configurations belonging to the Garden of Eden. Roots contain oscillators or still lifes.

References

• Wuensche, Andrew; Lesser, Mike (1992), The Global Dynamics of Cellular Automata: An Atlas of Basin of Attraction Fields of One Dimensional Cellular Automata, Santa Fe Institute Studies in the Sciences of Complexity Reference Volumes, Perseus Books