A Turing machine is a minimal idealization of a computer. It consists of a line of cells known as the "tape," with an active element called the "head" that can move back and forth and can change the colors of the tape according to a set of rules. Its evolution can be represented by causal networks that show how the events update. A small subset of selected rules is used in order to avoid trivial or repeated behaviors for 2-, 3-, and 4-state, 2-color cases, and for 2-state, 3-color cases. Gray scales reflect the value of the states (circles) and the colors of the tape (arrows).