What type of automaton is Google's Turing Doodle? In celebration of Alan Turing's birthday, Google published a doodle showing a machine. What kind of machine is the doodle? Can it express a Turing Complete
language?  

There are obvious differences to the classical turing machine: a finite tape, constraints in how state can be connected,...

The doodle is still be available here


(The display on the top right shows the expected output.)

The  tape in the middle is divided into squares that can hold a blank, a zero or a one. The head is positioned above one of the squares and is used for reading and writing.

Below the tape you can see a green arrow which you can click on to start the machine. There are two lines of circles next to it, some of which are connected. I will call them "states".

After the machine starts, the first state to the right of the green button lights up, then the next one to the right, and so on... Each state contains one of the following commands:


blank = do nothing (just move to the next state)
1 = write a one to the tape at the current position of the head
0 = write a zero to the tape at the current position of the head
arrow to the left = move the head one step to the left
arrow to the right = move the head one step to the right
condition: if the value under the head is equal to the value shown in the square go down to the second line of states. if not, move to the next state to the right
left jump: return to a (fixed) previous state but only on the upper row [I originally forgot that one, thanks  @Marzio!]


There is no way to "overlap" two jumps (one over another). 
The machine stops when there it leaves a state and there is no next state to the right of it.

(After the machine stops the contents of the tape are compared to the contents of the display, but I don't consider that to be part of the intended functionality of the machine.)
Assuming that:


we can add an arbitrarily large number of rows ("status lines")
the rows can be arbitrarily long
the tape is infinite


I tried to build an Alan Turing's Doodle machine configuration that emulates the machine $M_4$ described in "Small Turing Machines and generalized busy beaver competition" that has a halting problem that depends on an open (up to my knowledge) Collatz-like problem. The full picture is available here.



... so even if the A.T.'s Doodle is perhaps not Turing complete (due to the non-overlapping left-only jump operator available only in the first row), it is powerful enough to walk the fine line of (un)decidability :-D

EDIT: TURING DOODLE IS TURING COMPLETE

(I leave the previous answer above, because I'm not sure that this part is correct :-)

I think that even with a single left non-overlapping jump the Turing Doodle is Turing complete!. The (simple) idea is to use the tape itself to store the current state and use multiple cells to represent a larger alphabet.

For example a 2 states 8 symbols TM can be simulated using the following tape representation:

    HEAD POSITION
    v
...[s][b2 b1 b0] [_][b2 b1 b0] [_][b2 b1 b0] ....
   ^^^^^^^^^^^^^
    "macro cell"


The Turing doodle can:


read $s$ and branch to one of the two different horizontal areas representing STATE A and STATE B;
read $b2, b1, b0$ and branch to a row representing one of the eight symbols;
write the next symbol, move the head to the "macro cell" on the left or right, and store on it the next state; in the figure below these operations (that can be done on a sequence of cells using the actions move left/right and write) are called "MW";
finally transfer the control to the upper row that with a single left jump will bring the control back to step 1.


The full picture is available here.



In the same manner, given a $TM$ with an arbitrary number of states and alphabet symbols we can build an equivalent Turing Doodle machine $DM$.