Introduction: Leibniz,Turing Zuse, and Beyond -- Simplicity in the Unviverse of Cellular Automata -- Complexity in the Universe of Cellular Automata -- Symmetry in the Universe of Cellular Automata -- Attractors in the Universe of Cellular Automata -- Time in the Universe of Cellular Automata -- Matter in the Universe of Cellular Automata -- Life and Brain in the Universe of Cellular Automata -- Outlook: Is the Universe a Computer?.

This booklet is an essay at the interface of philosophy and complexity research, trying to inspire the reader with new ideas and new conceptual developments of cellular automata.  Going beyond the numerical experiments of Steven Wolfram, it is argued that cellular automata must be considered complex dynamical systems in their own right, requiring appropriate analytical models in order to find precise answers and predictions in the universe of cellular automata.  Indeed, eventually we have to ask whether cellular automata can be considered models of the real world and, conversely, whether there are limits to our modern approach of attributing the world, and the universe for that matter, essentially a digital reality.