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In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and show that using the memory function we can transform quasi-chaotic dynamics of classical Rule 30 into domains of travelling structures with predictable behaviour. We analyse morphological complexity of the automata and classify dynamics of gliders (particle, self-localizations) in memory-enriched Rule 30. We provide formal ways of encoding and classifying glider dynamics using de Bruijn diagrams, soliton reactions and quasi-chemical representations.

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Since their inception at 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 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 display that memory helps 'discover' hidden information and behaviour on trivialuniform, periodic, and non-trivial -chaotic, complex -dynamical systems.

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