Designing Complex Dynamics in Cellular Automata with Memory

TL;DR

This paper explores how adding memory to elementary cellular automata can transform their dynamics, revealing hidden behaviors and enabling the systematic study of complexity in simple computational models.

Contribution

It introduces a method to shift cellular automata classes by enriching cells with memory, without altering the core transition rules, thus uncovering hidden dynamics.

Findings

Memory enriches automata dynamics, revealing hidden information.

Any ECA class can be transformed into another via memory.

Memory helps discover behaviors in trivial and complex systems.

Abstract

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 of `complexity' 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.