  We consider Clifford Quantum Cellular Automata (CQCAs) and their time
evolution. CQCAs are an especially simple type of Quantum Cellular Automata,
yet they show complex asymptotics and can even be a basic ingredient for
universal quantum computation. In this work we study the time evolution of
different classes of CQCAs. We distinguish between periodic CQCAs, fractal
CQCAs and CQCAs with gliders. We then identify invariant states and study
convergence properties of classes of states, like quasifree and stabilizer
states. Finally we consider the generation of entanglement analytically and
numerically for stabilizer and quasifree states.
