Since their inception at Macy conferences in later 1940s, complex systems have remained the most controversial topic of interdisciplinary sciences. The term "complex system" is the most vague and liberally used scientific term. Using elementary cellular automata (ECA), and exploiting the CA classification, we demonstrate elusiveness of "complexity" by shifting space-time dynamics of the automata from simple to complex by enriching cells with memory. This way, we can transform any ECA class to another ECA class — without changing skeleton of cell-state transition function — and vice versa by just selecting a right kind of memory. A systematic analysis displays that memory helps "discover" hidden information and behavior on trivial — uniform, periodic, and nontrivial — chaotic, complex — dynamical systems.
Martinez, G. J., Adamatzky, A. and Alonso-Sanz, R. (2013) Designing complex dynamics in cellular automata with memory. International Journal of Bifurcation and Chaos, 23 (10). p. 1330035. ISSN 0218-1274