What is Turing machine and Turing completeness (1)

The composition of Turing machine

There is a classic picture on the Internet to express the composition of the Turing machine, the picture is as follows:

What does this picture mean? How can such a simple machine/device be the theoretical model of all electronic computers?

Turing’s basic idea is to use a machine to simulate the process of people using paper and pen to perform mathematical operations. The operation process is regarded as the following two simple actions:

• Write or erase a symbol on paper;
• Move the attention from one position of the paper to another; the
  Turing machine abstracts the complex process into the above two actions: reading and writing and moving

The Turing machine is composed of four parts in logical structure:

1. An infinite storage tape, the tape is composed of a continuous storage grid, each grid can store a number or symbol
2. A read-write head, the read-write head can move left and right on the storage tape, and can read and modify the numbers or symbols on the storage grid
3. Internal state memory, the memory can record the current state of the Turing machine, and there is a special state for shutdown
4. Control program instructions. The instructions can determine the next action (left or right) of the read/write head according to the current state and the symbol on the grid pointed to by the current read/write head, and change the value of the state memory to make the machine enter a new The state or keep the state unchanged.

You can understand why the Turing machine is composed of the above four parts.

Of course these are just ideal Turing machines, because there is no infinite storage tape in reality.