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?.