Prove that there is no oscillator of period \(4\) (i.e: the whole pattern repeats every \(4\) generations) which has exactly one cell that also has period \(4\).
A pattern \(P\) is called a garden of Eden if there exists no pattern \(P'\) distinct to \(P\) such that \(P'\) evolves into \(P\) after one generation. Show that a garden of Eden exists. You do not need to provide an example of such a pattern.