A Turing machine is a theoretical computing machine made-up by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine having of a line of cells called as a "tape" that can be moved back and forth, an active element called as the "head" that possesses a property called as "state" and that can change the property called as "color" of the active cell underneath it, and a set of instructions for how the head should modify the active cell and move the tape. At every step, the machine may changes the color of the active cell, modify the state of the head, and then move the tape one unit to the left or right.