Designing Complex Dynamics in Cellular Automata with Memory

Since their inception at {\it Macy conferences} in later 1940s complex systems remain the most controversial topic of inter-disciplinary 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 ofcomplexity' by shifting space-time dynamics of the automata from simple to complex by enriching cells with {\it 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 display that memory helps `discover' hidden information and behaviour on trivial uniform, periodic, and non-trivial chaotic, complex dynamical systems.