You might be a little pessimistic about needing 3 operators. Turing's original machines have only decision making and substitution. With that you can emulate a

You might be a little pessimistic about needing 3 operators. Turing's original machines have only decision making and substitution. With that you can emulate anything you want, and go on to higher levels and more and more complexity. Apparently even Conway's Game of Life is Turing complete ... it's horribly obtuse but can be used to build something, which is used to build something, and so on, until eventually you have an automata that could compute anything computable (though rather slowly!)