Atomtrap puzzle game

[apg]

A while ago (several years), I made a Windows-compatible puzzle game called Atomtrap. At the moment, only Dave Greene has played it, but I've decided to release it to the public:

https://docs.google.com/leaf?id=0B7zc3W ... ist&num=50

There are 40 built-in puzzle levels, of increasing difficulty. The aim in each level is to direct the atom(s) into the exit(s).

You can create and upload your own levels, either with the built-in level editor or Golly. (I use Extended RLE for the file format!)


I look forward to seeing your customised levels. (And, after uploading them, I have to authorise them before they become publicly accessible. This measure is to prevent phallic levels and suchlike.)


I wonder how long before someone (probably Axaj!) implements a Minecraft-style computer in Atomtrap. I've proven it possible, by showing that a universal set of logic components can be built.



Also, don't even consider cheating. The checksum systems are very, very complex; even I can't remember exactly how I designed it.



Enjoy!

[apg]

Oh, yes, please give yourselves unique names. Someone has entered their name as 'Dave', over-writing Dave Greene's score (>100000) with a measly 2008.

[Axaj]

Unfortunately, I was not able to make it run under wine; I'll try it next time I go on Windows. I do recommend a cross-platform version if at all possible, though.

[Batmanifestdestiny]

Is it possible to make it windowed instead of fullscreen?

[Axaj]

Arrg, it just shows an error message saying "MSVCR71.dll was not found".

[apg]

Arrg, it just shows an error message saying "MSVCR71.dll was not found".

You need the absolute latest version of DirectX 9.0c, or higher.

[iconmaster]

It's a cool game, but it needs a Pause button. I find that there are levels that are overly difficult because you can't stop to reflect on your next moves.

Also, it's cool that you save and load levels via Golly patterns. Just a fun 'extra'.

Also a suggestion: There should be a tile with some mechanism of creating new atoms during the game.

[apg]

It's a cool game, but it needs a Pause button. I find that there are levels that are overly difficult because you can't stop to reflect on your next moves.

Right-clicking should freeze the game.

Also, what is the speed like? On my machine (which is 1.3GHz), atoms propagate at 3 squares per second. If the speed of your computer differs sufficiently from this (by a factor of two or more), then this would be detrimental to the general enjoyment of the game. I may have to incorporate some kind of delay, which attempts to maintain the speed as close to ideal as possible.

[iconmaster]

Btw, I can't get Atomtrap to work on my Vista computer. It says:

Runtime Error 1507 - Display using 32 bit is not supported by available hardware
at line 1487

Any way to fix this? 64 bit mode please?

About the speed, I checked the speed of the atoms and it was around 3-4 sq/sec. So I guess I'M the one that's slow, lol.

[apg]

Runtime Error 1507 - Display using 32 bit is not supported by available hardware

Oh, that would be your graphics card and/or visual output device.

Any way to fix this? 64 bit mode please?

As far as I know, there is no 64-bit display mode (32-bit display, with 2^24 colours, is comparable to the colour-resolution of the human retina).

[apg]

The game is provably PSPACE-complete, using the following theorems:

(1) Every tile in Atomtrap can be emulated by a decision-augmented linear-bounded automaton.
(2) Every decision-augmented linear-bounded automaton can be emulated in Atomtrap.
(3) Every tile in Sokoban can be emulated by a decision-augmented linear-bounded automaton.
(4) Every decision-augmented linear-bounded automaton can be emulated in Sokoban.
(5) Sokoban is PSPACE-complete.

(4) and (5) are proven here:

http://web.cs.ualberta.ca/~joe/Preprint ... index.html

(1) and (3) are obvious from the fact that there are computer implementations, which require memory polynomial in the size of the grid. A personal computer is a decision-augmented linear-bounded automaton.

(2) relies on the construction of three components in Atomtrap:

(a) The decision junction:

Code: Select all

x = 11, y = 7, rule = Atomtrap
11A$4.RpDR$5A.5A$4.ATA$4.A.A$4.A.A$4.A.A!

(b) The universal latch:

Code: Select all

x = 23, y = 21, rule = Atomtrap
8.APA2.ATA$8.APA2.ATA$8.APA2.ATA$8.ApWA2.ApWA$8.APA2.ATA$8.APA2.ATA$
9AP4ATA$8V.P4.T8A$7ApTpUpS4.U4VpX3V$6.A6.U2.7A$6.A.pV2.TU3.A$6.A4RpLV
3.A$6.A3.QP4.7A$6.A2.Q.P2.pS4RpX3R$7A.pV2.PpV.pT.7A$7RQ3.P2.pUTA$15AT
A$14.ATA$14.ATA$14.ATA$14.ATA!

(c) The merge junction:

Code: Select all

x = 11, y = 7, rule = Atomtrap
11A$4.RTV$5AT5A$4.ATA$4.A.A$4.A.A$4.A.A!

With these basic, primitive components, more complex devices can be constructed. A particularly interesting one is the subroutine:

Code: Select all

x = 95, y = 40, rule = Atomtrap
18.ATA27.ATA27.ATA$18.ATA27.ATA27.ATA$18.ATA27.ATA27.ATA$19AT29AT29AT
15A$AT17V.29V.29V.15V$AT12AP4AT24AP4AT24AP4AT15A$ATA10.APA2.ATA22.APA
2.ATA22.APA2.ATA$ACA10.APA2.ATA22.APA2.ATA22.APA2.ATA$ACA10.APA2.ATA
22.APA2.ATA22.APA2.ATA$ACA2.9AP4AT10A5.9AP4AT10A5.9AP4AT10A$ACA2.A8R.
4R.8RTA5.A8R.4R.8RTA5.A8R.4R.8RTA$ACA2.AP7AP4AT8ATA5.AP7AP4AT8ATA5.AP
7AP4AT8ATA$ACA2.APA5.APA2.ATA6.ATA5.APA5.APA2.ATA6.ATA5.APA5.APA2.ATA
6.ATA$ACA2.APA5.APA2.ATA6.ATA5.APA5.APA2.ATA6.ATA5.APA5.APA2.ATA6.ATA
$ACA2.APA5.ApWA2.ApWA6.ATA5.APA5.ApWA2.ApWA6.ATA5.APA5.ApWA2.ApWA6.AT
A$ACA2.APA5.APA2.ATA6.ATA5.APA5.APA2.ATA6.ATA5.APA5.APA2.ATA6.ATA$ACA
2.APA5.APA2.ATA6.ATA5.APA5.APA2.ATA6.ATA5.APA5.APA2.ATA6.ATA$ACA2.AP
7AP4ATA6.ATA5.AP7AP4ATA6.ATA5.AP7AP4ATA6.ATA$ACA2.AP6V.P4.T8ATA5.AP6V
.P4.T8ATA5.AP6V.P4.T8ATA$ACA2.7ApTpUpS4.U4VpX4VA5.7ApTpUpS4.U4VpX4VA
5.7ApTpUpS4.U4VpX4VA$ACA8.A6.U2.9A11.A6.U2.9A11.A6.U2.9A$ACA8.A.pV2.T
U3.A19.A.pV2.TU3.A19.A.pV2.TU3.A$ACA8.A4RpLV3.A19.A4RpLV3.A19.A4RpLV
3.A$ACA8.A3.QP4.7A13.A3.QP4.7A13.A3.QP4.7A$ACA8.A2.Q.P2.pS4RpXRTA13.A
2.Q.P2.pS4RpXRTA13.A2.Q.P2.pS4RpXRTA$ACA8.A.pV2.PpV.pT.5ATA13.A.pV2.P
pV.pT.5ATA13.A.pV2.PpV.pT.5ATA$ACA8.AQ3.P2.pUTA3.ATA13.AQ3.P2.pUTA3.A
TA13.AQ3.P2.pUTA3.ATA$ACA8.AP7ATA3.ATA13.AP7ATA3.ATA13.AP7ATA3.ATA$AT
A8.APA5.ATA3.ATA13.APA5.ATA3.ATA13.APA5.ATA3.ATA$AT10APA5.AT5AT15APA
5.AT5AT15APA5.AT5AT8A$A11RPA5.A6R.15RPA5.A6R.15RPA5.A6R.8R$14A5.7AT
17A5.7AT17A5.7AT8A$25.ATA27.ATA27.ATA$25.ATA27.ATA27.ATA$18.8ATA20.8A
TA20.8ATA$18.AT7VA20.AT7VA20.AT7VA$18.AT8A20.AT8A20.AT8A$18.ATA27.ATA
27.ATA$18.ATA27.ATA27.ATA$18.ATA27.ATA27.ATA!

Shown above are three 'gosub' devices connected to an arbitrary subroutine.


Universal latches can be chained to allow them to be read from different parts of the program:

Code: Select all

x = 25, y = 90, rule = Atomtrap
2.9A2.ATA6.ATA$2.AT6VA2.ATA6.ATA$2.AT5APA2.ATA6.ATA$2.ATA3.APA2.ATA6.
ATA$2.ATA3.ApWA2.ApWA6.ATA$2.ATA3.APA2.ATA6.ATA$2.ATA3.APA2.ATA6.ATA$
3AT5AP4ATA6.ATA$3V.4V.P4.T8ATA$3AT3ApTpUpS4.U4VpX4VA$2.ATA.A6.U2.9A$
2.ATA.A.pV2.TU3.A$2.ATA.A4RpLV3.A$2.ATA.A3.QP4.9A$2.ATA.A2.Q.P2.pS4RpX
3RTA$3AT3A.pV2.PpV.pT.7ATA$3R.3RQ3.P2.pUTA5.ATA$3AT11ATA5.ATA$2.ATA9.
ATA5.ATA$2.ATA9.ATA5.ATA$2.ATA9.ATA5.ATA$3AT11ATA5.ATA$3V.12VA5.ATA$
3AT13A5.ATA$2.ATA17.ATA$2.ATA17.ATA$2.AT12A6.ATA$2.A11RTA6.ATA$2.12AT
A6.ATA$13.ATA6.ATA$2.9A2.ATA6.ATA$2.AT6VA2.ATA6.ATA$2.AT5APA2.ATA6.AT
A$2.ATA3.APA2.ATA6.ATA$2.ATA3.ApWA2.ApWA6.ATA$2.ATA3.APA2.ATA6.ATA$2.
ATA3.APA2.ATA6.ATA$3AT5AP4ATA6.ATA$3V.4V.P4.T8ATA$3AT3ApTpUpS4.U4VpX
4VA$2.ATA.A6.U2.9A$2.ATA.A.pV2.TU3.A$2.ATA.A4RpLV3.A$2.ATA.A3.QP4.9A$
2.ATA.A2.Q.P2.pS4RpX3RTA$3AT3A.pV2.PpV.pT.7ATA$3R.3RQ3.P2.pUTA5.ATA$
3AT11ATA5.ATA$2.ATA9.ATA5.ATA$2.ATA9.ATA5.ATA$2.ATA9.ATA5.ATA$3AT11AT
A5.ATA$3V.12VA5.ATA$3AT13A5.ATA$2.ATA17.ATA$2.ATA17.ATA$2.AT12A6.ATA$
2.A11RTA6.ATA$2.12ATA6.ATA$13.ATA6.ATA$2.9A2.ATA6.ATA$2.AT6VA2.ATA6.A
TA$2.AT5APA2.ATA6.ATA$2.ATA3.APA2.ATA6.ATA$2.ATA3.ApWA2.ApWA6.ATA$2.A
TA3.APA2.ATA6.ATA$2.ATA3.APA2.ATA6.ATA$3AT5AP4ATA6.ATA$3V.4V.P4.T8ATA
$3AT3ApTpUpS4.U4VpX4VA$2.ATA.A6.U2.9A$2.ATA.A.pV2.TU3.A$2.ATA.A4RpLV
3.A$2.ATA.A3.QP4.9A$2.ATA.A2.Q.P2.pS4RpX3RTA$3AT3A.pV2.PpV.pT.7ATA$3R
.3RQ3.P2.pUTA5.ATA$3AT11ATA5.ATA$2.ATA9.ATA5.ATA$2.ATA9.ATA5.ATA$2.AT
A9.ATA5.ATA$3AT11ATA5.ATA$3V.12VA5.ATA$3AT13A5.ATA$2.ATA17.ATA$2.ATA
17.ATA$2.AT12A6.ATA$2.A11RTA6.ATA$2.12ATA6.ATA$13.ATA6.ATA!

This is all of the flexibility necessary for the construction of a single cell of the tape of a binary Turing machine. Here is the template for the cell of an arbitrary 2-state 2-symbol machine:

Code: Select all

x = 185, y = 99, rule = Atomtrap
11.152A$11.A149RTA$11.AP148ATA$11.APA146.ATA$11.APA.118A$11.APA.A115R
TA$11.APA.AP114ATA$11.APA.APA112.ATA$11.APA.APA.84A$11.APA.APA.A81RTA
$11.APA.APA.AP80ATA$11.APA.APA.APA78.ATA$11.APA.APA.APA.50A$11.APA.AP
A.APA.A47RTA$11.APA.APA.APA.AP46ATA$11.APA.APA.APA.APA44.ATA$11.APA.A
PA.APA.APA$11.APA.APA.APA.APA12.17A$11.APA.APA.APA.APA12.AT14VA$11.AP
A.APA.APA.APA12.AT13APA15.ATA10.ATA14.ATA10.ATA14.ATA10.ATA14.ATA10.A
TA$11.APA.APA.APA.APA12.ATA11.APA15.ATA10.ATA14.ATA10.ATA14.ATA10.ATA
14.ATA10.ATA$11.APA.APA.APA.APA12.ATA11.APA15.ATA10.ATA14.ATA10.ATA
14.ATA10.ATA14.ATA10.ATA$11.APA.APA.APA.APA12.ATA6.6AP17AT12AT16AT12A
T16AT12AT16AT12AT2A$11.APA.APA.APA.APA12.ATA6.AT4V.17V.12V.16V.12V.
16V.12V.16V.12V.2V$11.APA.APA.APA.APA12.ATA6.AT4AP12AP4AT12AT11AP4AT
12AT11AP4AT12AT11AP4AT12AT2A$11.APA.APA.APA.APA12.ATA6.ATA2.APA10.APA
2.ATA10.ATA9.APA2.ATA10.ATA9.APA2.ATA10.ATA9.APA2.ATA10.ATA$11.APA.AP
A.APA.APA.9A2.ATA6.ATA2.APA10.APA2.ATA10.ATA9.APA2.ATA10.ATA9.APA2.AT
A10.ATA9.APA2.ATA10.ATA$11.APA.APA.APA.APA.AT6VA2.ATA6.ATA2.APA10.APA
2.ATA10.ATA9.APA2.ATA10.ATA9.APA2.ATA10.ATA9.APA2.ATA10.ATA$11.APA.AP
A.APA.APA.AT5APA2.ATA6.ATA2.APA2.9AP4AT10A.ATA.9AP4AT10A.ATA.9AP4AT
10A.ATA.9AP4AT10A.ATA$11.APA.APA.APA.APA.ATA3.APA2.ATA6.ATA2.APA2.A8R
.4R.8RTA.ATA.A8R.4R.8RTA.ATA.A8R.4R.8RTA.ATA.A8R.4R.8RTA.ATA$11.APA.A
PA.APA.APA.ATA3.ApWA2.ApWA6.ATA2.APA2.AP7AP4AT8ATA.ATA.AP7AP4AT8ATA.A
TA.AP7AP4AT8ATA.ATA.AP7AP4AT8ATA.ATA$11.APA.APA.APA.APA.ATA3.APA2.ATA
6.ATA2.APA2.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.A
TA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA$11.APA.APA.APA.APA.ATA3.APA2.ATA6.
ATA2.APA2.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA
6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA$11.APA.APA.APA.AP3AT5AP4ATA6.ATA2.AP
A2.APA5.ApWA2.ApWA6.ATA.ATA.APA5.ApWA2.ApWA6.ATA.ATA.APA5.ApWA2.ApWA
6.ATA.ATA.APA5.ApWA2.ApWA6.ATA.ATA$11.APA.APA.APA.AP3V.4V.P4.T8ATA2.A
PA2.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.
ATA.APA5.APA2.ATA6.ATA.ATA$11.APA.APA.APA.5AT3ApTpUpS4.U4VpX4VA2.APA
2.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.AT
A.APA5.APA2.ATA6.ATA.ATA$11.APA.APA.APA5.ATA.A6.U2.9A2.APA2.AP7AP4ATA
6.ATA.ATA.AP7AP4ATA6.ATA.ATA.AP7AP4ATA6.ATA.ATA.AP7AP4ATA6.ATA.ATA$
11.APA.APA.APA5.ATA.A.pV2.TU3.A10.APA2.AP6V.P4.T8ATA.ATA.AP6V.P4.T8AT
A.ATA.AP6V.P4.T8ATA.ATA.AP6V.P4.T8ATA.ATA$11.APA.APA.APA5.ATA.A4RpLV
3.A10.APA2.7ApTpUpS4.U4VpX4VA.ATA.7ApTpUpS4.U4VpX4VA.ATA.7ApTpUpS4.U
4VpX4VA.ATA.7ApTpUpS4.U4VpX4VA.ATA$11.APA.APA.APA5.ATA.A3.QP4.9A2.APA
8.A6.U2.9A.ATA7.A6.U2.9A.ATA7.A6.U2.9A.ATA7.A6.U2.9A.ATA$11.APA.APA.A
PA5.ATA.A2.Q.P2.pS4RpX3RTA2.APA8.A.pV2.TU3.A9.ATA7.A.pV2.TU3.A9.ATA7.
A.pV2.TU3.A9.ATA7.A.pV2.TU3.A9.ATA$12AP3AP3AP7AT3A.pV2.PpV.pT.7ATA2.A
PA8.A4RpLV3.A9.ATA7.A4RpLV3.A9.ATA7.A4RpLV3.A9.ATA7.A4RpLV3.A9.ATA$A
11R.3R.3R.7R.3RQ3.P2.pUTA5.ATA2.APA8.A3.QP4.7A3.ATA7.A3.QP4.7A3.ATA7.
A3.QP4.7A3.ATA7.A3.QP4.7A3.ATA$AP10AP3AP3AP7AT11ATA5.ATA2.APA8.A2.Q.P
2.pS4RpXRTA3.ATA7.A2.Q.P2.pS4RpXRTA3.ATA7.A2.Q.P2.pS4RpXRTA3.ATA7.A2.
Q.P2.pS4RpXRTA3.ATA$APA8.APA.APA.APA5.ATA9.ATA5.ATA2.APA8.A.pV2.PpV.pT
.5ATA3.ATA7.A.pV2.PpV.pT.5ATA3.ATA7.A.pV2.PpV.pT.5ATA3.ATA7.A.pV2.PpV
.pT.5ATA3.ATA$APA8.APA.APA.APA5.ATA9.ATA5.ATA2.APA8.AQ3.P2.pUTA3.ATA
3.ATA7.AQ3.P2.pUTA3.ATA3.ATA7.AQ3.P2.pUTA3.ATA3.ATA7.AQ3.P2.pUTA3.ATA
3.ATA$APA8.APA.APA.APA5.ATA9.ATA5.ATA2.APA8.AP7ATA3.ATA3.ATA7.AP7ATA
3.ATA3.ATA7.AP7ATA3.ATA3.ATA7.AP7ATA3.ATA3.ATA$APA8.APA.APA.AP7AT11AT
A5.ATA2.APA8.APA5.ATA3.ATA3.ATA7.APA5.ATA3.ATA3.ATA7.APA5.ATA3.ATA3.A
TA7.APA5.ATA3.ATA3.ATA$APA8.APA.APA.AP7V.12VA5.ATA2.APA2.7APA5.AT5AT
5AT9APA5.AT5AT5AT9APA5.AT5AT5AT9APA5.AT5AT5AT2A$APA8.APA.APA.9AT13A5.
ATA2.APA2.A6RPA5.A6R.5R.9RPA5.A6R.5R.9RPA5.A6R.5R.9RPA5.A6R.5R.2R$APA
8.APA.APA9.ATA17.ATA2.APA2.AP7A5.7AT5AT11A5.7AT5AT11A5.7AT5AT11A5.7AT
5AT2A$APA8.APA.APA9.ATA17.ATA2.APA2.APA17.ATA3.ATA21.ATA3.ATA21.ATA3.
ATA21.ATA3.ATA$APA8.APA.APA9.AT12A6.ATA2.APA2.APA17.ATA3.ATA21.ATA3.A
TA21.ATA3.ATA21.ATA3.ATA$APA8.APA.APA9.A11RTA6.ATA2.APA2.APA6.12ATA3.
ATA10.12ATA3.ATA10.12ATA3.ATA10.12ATA3.ATA$APA8.APA.APA9.12ATA6.ATA2.
APA2.APA6.AT11VA3.ATA10.AT11VA3.ATA10.AT11VA3.ATA10.AT11VA3.ATA$APA8.
APA.APA20.ATA6.ATA2.APA2.APA6.AT12A3.ATA10.AT12A3.ATA10.AT12A3.ATA10.
AT12A3.ATA$APA8.APA.APA9.9A2.ATA6.ATA2.APA2.APA6.ATA14.ATA10.ATA14.AT
A10.ATA14.ATA10.ATA14.ATA$APA8.APA.APA9.AT6VA2.ATA6.ATA2.APA2.APA6.AT
A14.ATA10.ATA14.ATA10.ATA14.ATA10.ATA14.ATA$APA8.APA.APA9.AT5APA2.ATA
6.ATA2.APA2.APA6.ATA14.ATA10.ATA14.ATA10.ATA14.ATA10.ATA14.ATA$APA8.A
PA.APA9.ATA3.APA2.ATA6.ATA2.APA2.APA6.ATA14.ATA10.ATA14.ATA10.ATA14.A
TA10.ATA14.ATA$APA8.APA.APA9.ATA3.ApWA2.ApWA6.ATA2.APA2.APA6.ATA14.AT
A10.ATA14.ATA10.ATA14.ATA10.ATA14.ATA$APA8.APA.APA9.ATA3.APA2.ATA6.AT
A2.APA2.APA6.ATA14.ATA10.ATA14.ATA10.ATA14.ATA10.ATA14.ATA$APA8.APA.A
PA9.ATA3.APA2.ATA6.ATA2.AP4AP8AT16AT12AT16AT12AT16AT12AT16AT10A$APA8.
APA.AP11AT5AP4ATA6.ATA2.AP4V.8V.16V.12V.16V.12V.16V.12V.16V.10V$APA8.
APA.AP11V.4V.P4.T8ATA2.6AP8AT11AP4AT12AT11AP4AT12AT11AP4AT12AT11AP4AT
10A$APA8.APA.13AT3ApTpUpS4.U4VpX4VA7.APA6.ATA9.APA2.ATA10.ATA9.APA2.A
TA10.ATA9.APA2.ATA10.ATA9.APA2.ATA$APA8.APA13.ATA.A6.U2.9A7.APA6.ATA
9.APA2.ATA10.ATA9.APA2.ATA10.ATA9.APA2.ATA10.ATA9.APA2.ATA$APA8.APA
13.ATA.A.pV2.TU3.A15.APA6.ATA9.APA2.ATA10.ATA9.APA2.ATA10.ATA9.APA2.A
TA10.ATA9.APA2.ATA$APA8.APA13.ATA.A4RpLV3.A15.APA6.ATA.9AP4AT10A.ATA.
9AP4AT10A.ATA.9AP4AT10A.ATA.9AP4AT10A$APA8.APA13.ATA.A3.QP4.17APA6.AT
A.A8R.4R.8RTA.ATA.A8R.4R.8RTA.ATA.A8R.4R.8RTA.ATA.A8R.4R.8RTA$APA8.AP
A13.ATA.A2.Q.P2.pS4RpX13RPA6.ATA.AP7AP4AT8ATA.ATA.AP7AP4AT8ATA.ATA.AP
7AP4AT8ATA.ATA.AP7AP4AT8ATA$APA.8AP15AT3A.pV2.PpV.pT.19A6.ATA.APA5.AP
A2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.AP
A2.ATA6.ATA$APA.A7R.15R.3RQ3.P2.pUTA24.ATA.APA5.APA2.ATA6.ATA.ATA.APA
5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA$APA.AP
6AP15AT11ATA24.ATA.APA5.ApWA2.ApWA6.ATA.ATA.APA5.ApWA2.ApWA6.ATA.ATA.
APA5.ApWA2.ApWA6.ATA.ATA.APA5.ApWA2.ApWA6.ATA$APA.APA4.APA13.ATA9.ATA
24.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.A
TA.ATA.APA5.APA2.ATA6.ATA$APA.APA4.APA13.ATA9.ATA24.ATA.APA5.APA2.ATA
6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA6.ATA.ATA.APA5.APA2.ATA
6.ATA$APA.APA4.APA13.ATA9.ATA24.ATA.AP7AP4ATA6.ATA.ATA.AP7AP4ATA6.ATA
.ATA.AP7AP4ATA6.ATA.ATA.AP7AP4ATA6.ATA$APA.APA4.AP15AT11ATA24.ATA.AP
6V.P4.T8ATA.ATA.AP6V.P4.T8ATA.ATA.AP6V.P4.T8ATA.ATA.AP6V.P4.T8ATA$APA
.APA4.AP15V.12VA24.ATA.7ApTpUpS4.U4VpX4VA.ATA.7ApTpUpS4.U4VpX4VA.ATA.
7ApTpUpS4.U4VpX4VA.ATA.7ApTpUpS4.U4VpX4VA$APA.APA4.17AT13A24.ATA7.A6.
U2.9A.ATA7.A6.U2.9A.ATA7.A6.U2.9A.ATA7.A6.U2.9A$APA.APA20.ATA36.ATA7.
A.pV2.TU3.A9.ATA7.A.pV2.TU3.A9.ATA7.A.pV2.TU3.A9.ATA7.A.pV2.TU3.A$APA
.APA20.ATA36.ATA7.A4RpLV3.A9.ATA7.A4RpLV3.A9.ATA7.A4RpLV3.A9.ATA7.A4R
pLV3.A$APA.APA20.ATA36.ATA7.A3.QP4.7A3.ATA7.A3.QP4.7A3.ATA7.A3.QP4.7A
3.ATA7.A3.QP4.7A$APA.APA20.ATA36.ATA7.A2.Q.P2.pS4RpXRTA3.ATA7.A2.Q.P
2.pS4RpXRTA3.ATA7.A2.Q.P2.pS4RpXRTA3.ATA7.A2.Q.P2.pS4RpXRTA$APA.APA
20.ATA36.ATA7.A.pV2.PpV.pT.5ATA3.ATA7.A.pV2.PpV.pT.5ATA3.ATA7.A.pV2.P
pV.pT.5ATA3.ATA7.A.pV2.PpV.pT.5ATA$APA.APA20.ATA36.ATA7.AQ3.P2.pUTA3.
ATA3.ATA7.AQ3.P2.pUTA3.ATA3.ATA7.AQ3.P2.pUTA3.ATA3.ATA7.AQ3.P2.pUTA3.
ATA$APA.APA20.ATA36.ATA7.AP7ATA3.ATA3.ATA7.AP7ATA3.ATA3.ATA7.AP7ATA3.
ATA3.ATA7.AP7ATA3.ATA$APA.APA20.ATA36.ATA7.APA5.ATA3.ATA3.ATA7.APA5.A
TA3.ATA3.ATA7.APA5.ATA3.ATA3.ATA7.APA5.ATA3.ATA$APA.APA20.AT38AT9APA
5.AT5AT5AT9APA5.AT5AT5AT9APA5.AT5AT5AT9APA5.AT5AT3A$APA.APA20.A39R.9R
PA5.A6R.5R.9RPA5.A6R.5R.9RPA5.A6R.5R.9RPA5.A6R.3R$APA.APA20.40AT11A5.
7AT5AT11A5.7AT5AT11A5.7AT5AT11A5.7AT3A$APA.APA59.ATA21.ATA3.ATA21.ATA
3.ATA21.ATA3.ATA21.ATA$APA.APA59.ATA21.ATA3.ATA21.ATA3.ATA21.ATA3.ATA
21.ATA$APA.APA59.AT23ATA3.AT23ATA3.AT23ATA3.AT23ATA$APA.APA59.AT24VA
3.AT24VA3.AT24VA3.AT24VA$APA.APA59.AT25A3.AT25A3.AT25A3.AT25A$APA.APA
59.ATA27.ATA27.ATA27.ATA$APA.APA59.ATA27.ATA27.ATA27.ATA$APA.APA59.AT
A27.ATA27.ATA27.ATA!

This can clearly be extended to a k-state 2-symbol Turing machine, for arbitrary k, thus completing the proof. The decision junction can be used to provide user input, extending this to a k-state 2-symbol oracle machine.