AVirtualMachineForExploringSpaceTimeAndBeyond : The execution of a very simple program on a Turing Machine (L'execution d'un programme tres simple sur une machine de Turing).

The execution of a very simple program on a Turing Machine [L'exécution d'un programme très simple sur une machine de Turing].

The Turing Machine is a mathematical model of computation.

It is made on one hand of an infinite discrete cell tape and on the other hand of a head that can read and write one tape cell at each time step.

The head contents an "internal state" S (S ∈ {A,B,...}).

Each cell C has a number N (an address...).

For these visualizations, only 2 symbols {0,1} (that recall our binary computers...) are used in order to define the content of each cell.

Let's assume that at time T the head is in state S(T) and is located over the cell C(N). Then S(T) and the symbol B=C(N) are defining:

S(T+1),
the new content of C(N) (that can be unchanged)
and the elementary translation of the head on the Right (N --> N+1) or on the Left (N --> N-1).

At last there exists a special state "Halt" that means the end of the computation.

On this picture the horizontal plane displays the contain of the tape at time T as horizontal lines (from T=0 -background- to T=47176870 -foreground-) as grey spheres (dark grey: C(N)=0, light grey: C(N)=1). The colored spheres display the current state S of the head: on the top left corner, the 5+1 color spheres exhibit horizontally the code used for each possible state (S ∈ {A,B,...} from left to right), the right one -white- being for the "Halt" state (bold below).

At T=0, the "Current State" is 'A' and the "Bit Read" is 0 (bold below).

cwCurrent State	A	A	B	B	C	C	D	D	E	E
Bit Read	0	1	0	1	0	1	0	1	0	1
Bit Read	1	1	1	1	1	0	1	1	0	0
Elementary Translation	Right	Left	Right	Right	Right	Left	Left	Left	Right	Left
Next State	B	C	C	B	D	E	A	D	Halt	A

Here are the first steps of the computation (47176870 time steps):

See some related pictures (including this one):