List of the Turing-complete totalistic life-like CA

For discussion of other cellular automata.
Naszvadi
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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » January 26th, 2018, 3:31 pm

DryLife is Turing-complete, the usual Wolfram rule-110 simulation is in the attachment (pattern 000001 evolved to 001011 on a thoroidal surface). Unit cell size is 2726x2726, should be set diagonally in "host" CA. Period is 13200. Used only Guns, Gliders and Eaters. Except for the guns, all reactions are B3/S23-B378/S23678 compatible, "portable" between that rule interval. A cell is alive if there is an absent glider in the (inverted) stream in the middle towards the upper left corner.

Bad news for the impatient: "Your message contains 80901 characters. The maximum number of allowed characters is 60000." So no embedded playable simulation in the viewer.

With replacing p600 guns (composed of p30, p50 or p60), the following rules are proven to be Turing-complete too:
  • B37/S23
  • B37/S237
  • B37/S238
  • B378/S237
They are ready, p600 guns to be published in the above rules. Credits will be given to the corresponding authors of the small guns.

[EDIT #1]
The following rules are NOT supported without modification:
  • B3/S23
  • B3/S237
  • B3/S238
  • B3/S2378
  • B37/S236
  • B38/S23
  • B38/S237
  • B38/S238
  • B38/S2378
Attachments
Drylife6UnitCells.rle.gz
Naszvadi, Peter, DryLife Unit cells in action
(146.63 KiB) Downloaded 389 times

Naszvadi
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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » January 30th, 2018, 7:44 pm

Updated covered rules list, see attached unit cell. Denotes ON state - for OFF state, simply remove dot before the glider
Connect still lifes in corners within diagonals from South-West to North-East. Cell is 2726x2726, period is still 13200.
Attachments
uc_ON_cell_b_3___7+s__23___7_.mc.gz
gzipped .mc format, Rule-110 Unit cell. Open with golly.
(14.05 KiB) Downloaded 383 times

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gameoflifemaniac
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Re: List of the Turing-complete totalistic life-like CA

Post by gameoflifemaniac » January 31st, 2018, 4:52 am

Naszvadi wrote:DryLife is Turing-complete, the usual Wolfram rule-110 simulation is in the attachment (pattern 000001 evolved to 001011 on a thoroidal surface). Unit cell size is 2726x2726, should be set diagonally in "host" CA. Period is 13200. Used only Guns, Gliders and Eaters. Except for the guns, all reactions are B3/S23-B378/S23678 compatible, "portable" between that rule interval. A cell is alive if there is an absent glider in the (inverted) stream in the middle towards the upper left corner.

Bad news for the impatient: "Your message contains 80901 characters. The maximum number of allowed characters is 60000." So no embedded playable simulation in the viewer.

With replacing p600 guns (composed of p30, p50 or p60), the following rules are proven to be Turing-complete too:
  • B37/S23
  • B37/S237
  • B37/S238
  • B378/S237
They are ready, p600 guns to be published in the above rules. Credits will be given to the corresponding authors of the small guns.

[EDIT #1]
The following rules are NOT supported without modification:
  • B3/S23
  • B3/S237
  • B3/S238
  • B3/S2378
  • B37/S236
  • B38/S23
  • B38/S237
  • B38/S238
  • B38/S2378
Thoroidal? Rather toroidal.
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee...

Naszvadi
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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » January 31st, 2018, 5:56 am

gameoflifemaniac wrote:
Naszvadi wrote:... (... thoroidal surface)....
Thoroidal? Rather toroidal.
Typo? Sorry for that.

Anyway, the following can be fixed via altering the bottom gun's supressing glider stream in the following 4 rules, so Life patterns implemeting logic heavily based on kickback reactions work fine:
  • B3/S23
  • B3/S238
  • B38/S23
  • B38/S238
But in that case, rules containing B7 won't work with the altered glider stream. And the other listed ones are completely ruined both ways. But hey, it is still 8 Turing-complete rules, 4 new!

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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » February 26th, 2018, 3:03 pm

New year, new rule-110 simulator Unit cell. Ready: rule B2e3ainqr4w/S1c2-in3aiq5q7c, which was inspected by AbhpzTa and published neat XOR "gate" block, see here: ../forums/viewtopic.php?f=11&t=376&start=725#p55465.

What is interesting is that the OFF state cell is a still life, so it is gunless. Unit cell's height is 333. ON state cell has at least one glider in most generations (or sparky blocks in the others). Only gliders, blocks and carriers were used. Can be smaller, I know :D

Code: Select all

#C Unit cell simulating rule-110, proof for Turing-completeness, by Naszvadi, Peter
x = 202, y = 1872, rule = B2e3ainqr4w/S1c2-in3aiq5q7c:T0,1998
135b2o$135b2o5$153b2o$151bo2bo$151b2o13$151b2o$151bo2bo$153b2o5$141b2o
$141b2o3$190b2o$190b2o9$94b2o$94b2o3$182b2o$183bo$128b2o51bo$128bo52b
2o$108b2o20bo$108bo2bo17b2o$110b2o7$97b2o$97b2o9$9b2o$9b2o3$73b2o$71bo
2bo$71b2o12b2o$85b2o$23b2o$23bo2bo$25b2o$103b2o$73b2o28b2o$73bo2bo$75b
2o6$61b2o$59bo2bo$59b2o12b2o$73b2o4$91b2o$61b2o28b2o$61bo2bo$63b2o2$
186b2o$186b2o3$63b2o$61bo2bo$61b2o5$79b2o95b2o$79b2o39b2o54b2o$120b2o
4$200b2o$200b2o2$10b2o$10b2o65b2o$78bo$76bo33b2o$76b2o32b2o44b2o$156bo
2bo$158b2o3$144b2o$144b2o5$21b2o$21bo$23bo$22b2o$68b2o$18b2o48b2o$18bo
$20bo$19b2o41$16b2o128b2o$14bo2bo128b2o$14b2o$182b2o$182bo$184bo$183b
2o3$2o$2o8$138b2o$139bo51b2o$137bo53b2o$137b2o127$135b2o$135b2o5$153b
2o$151bo2bo$151b2o13$151b2o$151bo2bo$153b2o5$141b2o$141b2o3$190b2o$
190b2o9$94b2o$94b2o3$182b2o$183bo$128b2o51bo$128bo52b2o$108b2o20bo$
108bo2bo17b2o$110b2o7$97b2o$97b2o9$9b2o$9b2o3$73b2o$71bo2bo$71b2o12b2o
$85b2o$23b2o$23bo2bo$25b2o$103b2o$73b2o28b2o$73bo2bo$75b2o6$61b2o$59bo
2bo$59b2o12b2o$73b2o4$91b2o$61b2o28b2o$61bo2bo$63b2o2$186b2o$186b2o3$
63b2o$61bo2bo$61b2o5$79b2o95b2o$79b2o39b2o54b2o$120b2o4$200b2o$200b2o
2$10b2o$10b2o65b2o$78bo$76bo33b2o$76b2o32b2o44b2o$156bo2bo$158b2o3$
144b2o$144b2o5$21b2o$21bo$23bo$22b2o$68b2o$18b2o48b2o$18bo$20bo$19b2o
41$16b2o128b2o$14bo2bo128b2o$14b2o$182b2o$182bo$184bo$183b2o3$2o$2o8$
138b2o$139bo51b2o$137bo53b2o$137b2o127$135b2o$135b2o5$153b2o$151bo2bo$
151b2o13$151b2o$151bo2bo$153b2o5$141b2o$141b2o3$190b2o$190b2o9$94b2o$
94b2o3$182b2o$183bo$128b2o51bo$128bo52b2o$108b2o20bo$108bo2bo17b2o$
110b2o7$97b2o$97b2o9$9b2o$9b2o3$73b2o$71bo2bo$71b2o12b2o$85b2o$23b2o$
23bo2bo$25b2o$103b2o$73b2o28b2o$73bo2bo$75b2o6$61b2o$59bo2bo$59b2o12b
2o$73b2o4$91b2o$61b2o28b2o$61bo2bo$63b2o2$186b2o$186b2o3$63b2o$61bo2bo
$61b2o5$79b2o95b2o$79b2o39b2o54b2o$120b2o4$200b2o$200b2o2$10b2o$10b2o
65b2o$78bo$76bo33b2o$76b2o32b2o44b2o$156bo2bo$158b2o3$97b2o45b2o$98bo
45b2o$97b2o4$21b2o$21bo$23bo$22b2o$68b2o$18b2o48b2o$18bo$20bo$19b2o41$
16b2o128b2o$14bo2bo128b2o$14b2o$182b2o$182bo$184bo$183b2o3$2o$2o8$138b
2o$139bo51b2o$137bo53b2o$137b2o127$135b2o$135b2o5$153b2o$151bo2bo$151b
2o13$151b2o$151bo2bo$153b2o5$141b2o$141b2o3$190b2o$190b2o9$94b2o$94b2o
3$182b2o$183bo$128b2o51bo$128bo52b2o$108b2o20bo$108bo2bo17b2o$110b2o7$
97b2o$97b2o9$9b2o$9b2o3$73b2o$71bo2bo$71b2o12b2o$85b2o$23b2o$23bo2bo$
25b2o$103b2o$73b2o28b2o$73bo2bo$75b2o6$61b2o$59bo2bo$59b2o12b2o$73b2o
4$91b2o$61b2o28b2o$61bo2bo$63b2o2$186b2o$186b2o3$63b2o$61bo2bo$61b2o5$
79b2o95b2o$79b2o39b2o54b2o$120b2o4$200b2o$200b2o2$10b2o$10b2o65b2o$78b
o$76bo33b2o$76b2o32b2o44b2o$156bo2bo$158b2o3$144b2o$144b2o5$21b2o$21bo
$23bo$22b2o$68b2o$18b2o48b2o$18bo$20bo$19b2o41$16b2o128b2o$14bo2bo128b
2o$14b2o$182b2o$182bo$184bo$183b2o3$2o$2o8$138b2o$139bo51b2o$137bo53b
2o$137b2o127$135b2o$135b2o5$153b2o$151bo2bo$151b2o13$151b2o$151bo2bo$
153b2o5$141b2o$141b2o3$190b2o$190b2o9$94b2o$94b2o3$182b2o$183bo$128b2o
51bo$128bo52b2o$108b2o20bo$108bo2bo17b2o$110b2o7$97b2o$97b2o9$9b2o$9b
2o3$73b2o$71bo2bo$71b2o12b2o$85b2o$23b2o$23bo2bo$25b2o$103b2o$73b2o28b
2o$73bo2bo$75b2o6$61b2o$59bo2bo$59b2o12b2o$73b2o4$91b2o$61b2o28b2o$61b
o2bo$63b2o2$186b2o$186b2o3$63b2o$61bo2bo$61b2o5$79b2o95b2o$79b2o39b2o
54b2o$120b2o4$200b2o$200b2o2$10b2o$10b2o65b2o$78bo$76bo33b2o$76b2o32b
2o44b2o$156bo2bo$158b2o3$144b2o$144b2o5$21b2o$21bo$23bo$22b2o$68b2o$
18b2o48b2o$18bo$20bo$19b2o41$16b2o128b2o$14bo2bo128b2o$14b2o$182b2o$
182bo$184bo$183b2o3$2o$2o8$138b2o$139bo51b2o$137bo53b2o$137b2o127$135b
2o$135b2o5$153b2o$151bo2bo$151b2o13$151b2o$151bo2bo$153b2o5$141b2o$
141b2o3$190b2o$190b2o9$94b2o$94b2o3$182b2o$183bo$128b2o51bo$128bo52b2o
$108b2o20bo$108bo2bo17b2o$110b2o7$97b2o$97b2o9$9b2o$9b2o3$73b2o$71bo2b
o$71b2o12b2o$85b2o$23b2o$23bo2bo$25b2o$103b2o$73b2o28b2o$73bo2bo$75b2o
6$61b2o$59bo2bo$59b2o12b2o$73b2o4$91b2o$61b2o28b2o$61bo2bo$63b2o2$186b
2o$186b2o3$63b2o$61bo2bo$61b2o5$79b2o95b2o$79b2o39b2o54b2o$120b2o4$
200b2o$200b2o2$10b2o$10b2o65b2o$78bo$76bo33b2o$76b2o32b2o44b2o$156bo2b
o$158b2o3$144b2o$144b2o5$21b2o$21bo$23bo$22b2o$68b2o$18b2o48b2o$18bo$
20bo$19b2o41$16b2o128b2o$14bo2bo128b2o$14b2o$182b2o$182bo$184bo$183b2o
3$2o$2o8$138b2o$139bo51b2o$137bo53b2o$137b2o!
[APPEND 2018.02.28]

Notice: This is a nontotalistic rule!

Naszvadi
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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » March 29th, 2018, 5:10 am

Naszvadi wrote:DryLife is Turing-complete...
Now, One Unit Cell can be played in pattern viewer!

Code: Select all

#C Naszvadi Peter, 2015-2018, DryLife Rule-110 emulator Unit Cell
#C Proves Turing-Completeness of the rules - this is a polyglot, so
#C the following 3 rules are Turing-Complete. too:
#C B37/S237, B37/S238 and B378/S237 - guns must be replaced, of course
#C Period is 13200, size is 2726x2726, P600 guns are used
#C place unit cells from SW to NE on a common diagonal
#C This represents the "ON" state: Glider is killed at (1833,1628)
#C [[ STOP 13200 ]]
x = 2726, y = 2726, rule = B37/S23
2o2722b2o$obo2720bobo$bo2722bo56$1160bo$969b2o189b3o$969b2o192bo$1162b
2o10$1182bo5bo$1182b2o3b2o$1182b2o3b2o$1183bo3bo2$1178b2o$974bo5bo197b
obo16bo$974b2o3b2o197bo16bo2bo$969b2o3b2o3b2o214bo2bo$968bo2bo3bo3bo
205bo5bo4bo$966bo2bobo212b2o5b2o$970bo100bo5bo85b2o3b2o15bo5bo4bo$966b
ob2o101b2o3b2o84bo7bo24bo2bo$967bo103b2o3b2o87bobo27bo2bo$973b3o88b2o
6bo3bo86b2o3b2o27bo$972bo3bo9bo78bo$972bo3bo7bo2bo77bobo126b2o$961b2o
9bo3bo7bo2bo78b2o18bo92bo13bo2bo$962bo10b3o9bo98bo2bo65b3o25bo12bobo$
962bobo119bo2bo66b3o22b3o10b2obo$963b2o8b3o9bo88bo5bo4bo106b3o$972bo3b
o7bo2bo85b2o5b2o110b2o$972bo3bo7bo2bo64b2o3b2o15bo5bo4bo77bo5bo37bo$
972bo3bo9bo64bo7bo24bo2bo66b3o5bobo3bobo34b3o$973b3o78bobo27bo2bo52bo
12b3o5bo3bobo3bo32bo$1052b2o3b2o27bo53b2o20bobo3bobo4b3o26b2o$946b2o3b
2o186bobo21bo5bo5bo$945bo7bo129b2o71b2o18bo35bo$948bobo5b2o14b3o20bo
72bo13bo2bo69bo2bo52bob2o$946b2o3b2o2bo2bo15bo18b3o46b3o25bo12bobo69bo
bo2bo54bo$955bobo15bo18bo50b3o22b3o10b2obo71bo54bo2bobo18b2o$949bo6bob
2o32b2o87b3o73b2obo52bo2bo18b2o$948bobo6b3o19bo101b2o76bo35bo18b2o$
958b2o18bo73bo5bo37bo99bo5bo5bo$948b3o27b3o62b3o5bobo3bobo34b3o69b2o
26b3o4bobo3bobo$996b3o43b3o5bo3bobo3bo32bo73bo32bo3bobo3bo5b3o$939b3o
46bo6b3o53bobo3bobo4b3o26b2o69b3o34bobo3bobo5b3o$940b3o44bobo62bo5bo5b
o99bo37bo5bo$948b3o94b2o18bo35bo76b2o$987b3o54bo2bo52bob2o73b3o$948bob
o44b3o46bobo2bo54bo29bo5bo35bob2o10b3o22b3o$940b3o6bo46b3o27b2o17bo54b
o2bobo28b2o3b2o34bobo12bo25b3o$939b3o84bobo17b2obo52bo2bo28b2o3b2o34bo
2bo13bo$957b3o27b3o39bo18bo35bo18b2o30bo3bo6b2o28b2o$959bo18b2o50bo54b
o5bo5bo48bo$944bo13bo19b3o6bobo41bo23b2o26b3o4bobo3bobo45bobo27bo27b2o
3b2o$944bobo31b2obo6bo43bo23bo32bo3bobo3bo5b3o17bo18b2o27bo2bo27bobo$
944b2o18bo15bobo50bo19b3o34bobo3bobo5b3o17bo2bo2bo5b3o34bo2bo24bo7bo$
963bo15bo2bo2b2o3b2o42bo18bo37bo5bo26bo2bo47bo4bo5bo15b2o3b2o$963b3o
14b2o5bobo45bo31b2o57bo10bo41b2o5b2o$984bo7bo43bo29b3o70b3o33bo4bo5bo$
985b2o3b2o45bo27bob2o10b3o22b3o19bo10bo15b2o3b2o13bo2bo$1038bo25bobo
12bo25b3o16bo2bo24bo7bo12bo2bo$962b3o74bo24bo2bo13bo42bo2bo2bo5b3o16bo
bo16bo18b2o$951bo9bo3bo74bo24b2o58bo27b2o3b2o33bobo$950bo2bo7bo3bo31bo
5bo37bo153bo$950bo2bo7bo3bo31b2o3b2o38bo20bo27b2o3b2o29b2o55bo3bo6b2o$
952bo9b3o8b2o22b2o3b2o3b2o34bo18bo2bo27bobo30bo2bo53b2o3b2o$973bobo22b
o3bo3bo2bo34bo17bo2bo24bo7bo27bobo38b3o13b2o3b2o$952bo9b3o10bo30bobo2b
o33bo18bo4bo5bo15b2o3b2o29bob2o22bo5bo6b3o14bo5bo$950bo2bo7bo3bo9b2o
30bo38bo21b2o5b2o51b3o8bo12b2o4bobo$928b2o20bo2bo7bo3bo42b2obo35bo16bo
4bo5bo53b2o7bo13bobo$927bobo21bo9bo3bo44bo37bo13bo2bo49bo22b3o17b3o$
927bo34b3o84bo12bo2bo16bo32b3o32bo15b3o$926b2o42bo20bo7b3o3b3o42bo12bo
16bobo35bo32bo15b3o$968b2obo18bo2bo5bobo3bobo43bo29b2o34b2o31bo2bo$
967bo22bo2bo5b3o3b3o7b2o35bo99bo5b3o$966bobo2bo20bo22bo37bo19bo3bo32bo
41bobo10b2o$958bo3bo3bo2bo43bobo38bo17b2o3b2o29b2obo41bo4bobo3bo2bo$
957b2o3b2o3b2o23bo20b2o40bo16b2o3b2o28bo45bo5bo2bo2bobo$957b2o3b2o26bo
2bo62bo15bo5bo27bobo2bo2bo5bo45bo$957bo5bo26bo2bo4bobo4bob2o48bo48bo2b
o3bobo4bo41bob2o$991bo6b2o3bo3bo50bo48b2o10bobo41bo$999bo3bo55bo53b3o
5bo$1003bo56bo59bo2bo31b2o$1025b2o3b2o29bo42b3o15bo32bo$1024bo7bo29bo
42b3o15bo32b3o$982bo37b2o5bobo33bo49b3o17b3o22bo$982b3o34bo2bo2b2o3b2o
32bo32bo21bobo13bo7b2o$985bo34bobo42bo29bobo15bobo4b2o12bo8b3o$984b2o
32b2obo44bo29b2o7b3o6bo5bo22b2obo$1018b3o46bo36b3o38bobo$964bo53b2o48b
o75bo2bo$963b2o24bo79bo75b2o$963bobo13b3o7bo11bo68bo$980b3o19bo33b3o
32bo42b2o3b2o27bo$986bo5bo7b3o32b3o34bo43bobo16b3o5bo2bo2bo$986b3ob3o
32bo5bo41bo39bo7bo24bo2bo$986bo5bo32b3ob3o42bo39b2o3b2o15bo10bo$980b3o
32b3o7bo5bo43bo56b3o$979b3o33bo19b3o38bo59bo10bo$1016bo11bo7b3o38bo68b
o2bo$1028bo49bo56b3o5bo2bo2bo$998b2o79bo32bo35bo$997b3o80bo29bobo$996b
ob2o81bo29b2o13bo$995bobo79b2o3bo43bobo5bo3bo$986b2o3b2o2bo2bo37bo40b
2o4bo42b2o5b2o3b2o$988bobo5b2o36bobo47bo48b2o3b2o$985bo7bo41b2o48bo47b
o5bo$986b2o3b2o84b2o7bo$1014bo61bobo8bo$1014bo3bo56bo12bo$1010bo3bo3b
2o6bo47bo14bo$1009b2obo4bobo4bo2bo45bo16bo$1024bo2bo44bo18bo$1003b2o
20bo45bo20bo$1002bobo65bo22bo$1002bo22bo43bo24bo$1001b2o7b3o3b3o5bo2bo
40bo26bo$1010bobo3bobo5bo2bo39bo28bo$1010b3o3b3o7bo6b2o31bo30bo$1032bo
bo30bo32bo$1007bo26bo29bo34bo$1006bob2o53bo36bo$1010bo51bo36b2o$1006bo
2bobo49bo$985bo5bo16bo2bo3bo3bo41b2o$985b2o3b2o17b2o3b2o3b2o$980b2o3b
2o3b2o22b2o3b2o$979bo2bo3bo3bo23bo5bo$977bo2bobo$981bo125b2o$977bob2o
126bobo$978bo74b2o55bo$984b3o65bobo41bo14bo$983bo3bo9bo20b2o31bo44bobo
13bo$983bo3bo7bo2bo18bobo30bo15bo29b2o15bo$972b2o9bo3bo7bo2bo20bo29bo
14bobo47bo$973bo10b3o9bo51bo16b2o48bo$973bobo71bo68bo$974b2o8b3o9bo49b
o70bo$983bo3bo7bo2bo46bo72bo$983bo3bo7bo2bo45bo74bo$983bo3bo9bo45bo76b
o$984b3o55bo78bo$1041bo80bo$957b2o3b2o76bo82bo$956bo7bo74bo84bo2b2o$
959bobo5b2o14b3o52bo84b2o2b2o$957b2o3b2o2bo2bo15bo51bo$966bobo15bo18b
2o31bo$960bo6bob2o31bobo30bo$959bobo6b3o19bo13bo29bo$969b2o18bo43bo$
959b3o27b3o40bo$1007b3o21bo$950b3o46bo6b3o21bo$951b3o44bobo28bo$959b3o
66bo$998b3o26bo$959bobo44b3o17bo$951b3o6bo46b3o15bo$950b3o71bo$968b3o
27b3o22bo$970bo18b2o31bo$969bo19b3o6bobo20bo$955b2o32b2obo6bo20bo$956b
o18bo15bobo25bo$953b3o18bo15bo2bo2b2o3b2o15bo$953bo20b3o14b2o5bobo16bo
$995bo7bo12bo$996b2o3b2o12bo$1014bo$973b3o37bo$962bo9bo3bo35bo$961bo2b
o7bo3bo34bo$961bo2bo7bo3bo33bo$963bo9b3o8b2o23bo$984bobo21bo$963bo9b3o
10bo20bo$961bo2bo7bo3bo9b2o18bo$961bo2bo7bo3bo28bo$962bo9bo3bo27bo$
973b3o27bo$981bo20bo$979b2obo18bo$978bo21bo$977bobo2bo16bo$969bo3bo3bo
2bo17bo$968b2o3b2o3b2o17bo$968b2o3b2o21bo$968bo5bo20bo$994bo$993bo$
992bo$991bo$990bo$989bo$988bo$987bo$986bo$985bo$984bo$983bo$982bo$981b
o$980bo$980b2o116$784bo$784b3o$787bo$786b2o10$806b2o3b2o$805bo7bo$808b
obo$736b2o68b2o3b2o$736b2o$802b2o$801b2o$803bo16b3o$819b3o$808b2o5b2o$
808b3o3b3o$695b2o3b2o85bo5bo14b2o5b2o$694bo7bo84b2o3b2o25b3o$697bobo
87b2o3b2o26b3o$688b2o5b2o3b2o71bo14bo3bo$689bo83bobo$689bobo81b2o43b2o
$690b2o86bo38bo2bo$709b3o65bo2bo22bobo10bobobo$708b3o66bo2bo23b2o10bo
2bo$623bo73b2o5b2o73bo24bo10bo$623b3o71b3o3b3o110bobo$626bo49bo5bo14b
2o5b2o73bo7bo5bo37bo$625b2o49b2o3b2o25b3o66bo2bo5b3o3b3o34b3o$676b2o3b
2o26b3o65bo2bo4b2ob2ob2ob2o4bo27bo$677bo3bo96bo7b3o3b3o4b2o27b2o$787bo
5bo5bobo$707b2o71b2o54b2o$667bo38bo2bo69bo2bo53b3o$666bo2bo22bobo10bob
obo69bobo54b2obo$666bo2bo23b2o10bo2bo71bob2o54bobo18b2o$668bo24bo10bo
76b3o53bo2bo18b2o$705bobo74b2o54b2o$668bo7bo5bo37bo97bobo5bo5bo$666bo
2bo5b3o3b3o34b3o69b2o27b2o4b3o3b3o7bo$666bo2bo4b2ob2ob2ob2o4bo27bo73bo
27bo4b2ob2ob2ob2o4bo2bo$667bo7b3o3b3o4b2o27b2o69b3o34b3o3b3o5bo2bo$
676bo5bo5bobo97bo37bo5bo7bo$669b2o54b2o74bobo$668bo2bo53b3o76bo10bo24b
o$668bobo54b2obo29b2o3b2o35bo2bo10b2o23bo2bo$650b2o17bob2o54bobo27bo7b
o33bobobo10bobo22bo2bo$650bobo17b3o53bo2bo30bobo36bo2bo38bo$653bo17b2o
54b2o29b2o3b2o5b2o28b2o$654bo52bobo5bo5bo48bo$655bo23b2o27b2o4b3o3b3o
7bo37bobo56bo3bo$656bo23bo27bo4b2ob2ob2ob2o4bo2bo29bo6b2o27b3o26b2o3b
2o$657bo19b3o34b3o3b3o5bo2bo16b3o10bo36b3o25b2o3b2o$658bo18bo37bo5bo7b
o19b3o8bobo40b2o5b2o14bo5bo$659bo30bobo71bo38b3o3b3o$660bo32bo10bo24bo
32bobo38b2o5b2o$661bo27bo2bo10b2o23bo2bo32bo12bo5bo14b3o$662bo25bobobo
10bobo22bo2bo17b3o8bobo14b2o3b2o13b3o$663bo24bo2bo38bo17b3o10bo15b2o3b
2o33b2o$664bo24b2o70bo16bo3bo34bobo$665bo153bo$666bo49bo3bo30b2o54b2o
3b2o5b2o$667bo18b3o26b2o3b2o28bo2bo38bo16bobo$668bo18b3o25b2o3b2o28bob
obo35bo2bo12bo7bo$669bo22b2o5b2o14bo5bo29bo2bo21b2o5bo6bo2bo13b2o3b2o$
670bo21b3o3b3o54bo20bobo4bo7bo$671bo20b2o5b2o51bobo7bobo11bo5bobo$672b
o14b3o49bo22b2o19bo7bo$673bo12b3o16bo33b3o21bo19bo6bo2bo$674bo31b2o34b
o31b2o14bo2bo$675bo29b2o34b2o32b2o6bo8bo$676bo98b2o6bo$677bo18b2o3b2o
30b2o41bo5bobo4b2o$678bo19bobo31b3o41b3o4bo4bo2bo$679bo15bo7bo27bob2o
48bo5bobo$680bo15b2o3b2o27bobo5bo48b2obo$681bo48bo2bo4bo4b3o41b3o$682b
o48b2o4bobo5bo41b2o$683bo54bo6b2o$684bo44bo8bo6b2o32b2o$685bo42bo2bo
14b2o31bo$686bo41bo2bo6bo19bo21b3o$687bo42bo7bo19b2o22bo$688bo31bo16bo
bo5bo11bobo7bobo$689bo31b2o7bo7bo4bobo20bo$690bo29b2o6bo2bo6bo5b2o21bo
2bo$691bo36bo2bo35bobobo$692bo36bo38bo2bo$693bo75b2o$694bo$695bo43bo3b
o16bo$696bo41b2o3b2o15bo10b3o$697bo40b2o3b2o14bobo8b3o$698bo39bo5bo12b
o$699bo57bobo$700bo56bo$701bo57bobo8b3o$702bo57bo10b3o$703bo31bo24bo$
704bo31b2o$705bo29b2o14bo$706bo42b2o6b2o3b2o$707bo42b2o7bobo$708bo47bo
7bo$709bo47b2o3b2o$710bo$711bo$712bo$713bo$714bo$715bo$716bo$717bo$
718bo$719bo$720bo$721bo$722bo$723bo$724bo$723b2o7$725b2o4b2o$725bobo3b
obo$725bo8bo$735bo$736bo$737bo$738bo$739bo$740bo$722b2o2b2o13bo$722b2o
2bo15bo$727bo15bo$728bo15bo$729bo15bo$730bo15bo$731bo15bo$732bo15bo2b
2o$733bo13b2o2b2o$734bo$735bo$736bo$737bo$738bo$739bo$740bo$741bobo$
742b2o7$750b2o$750bo$751bo$752bo$753bo$754bo$755bo$756bo$757bo$758bo$
759bo$760bo$761bo$762bo$730b2o31bo$764bo$711b2o3b2o47bo$710bo7bo47bo$
713bobo51bo$711b2o3b2o50bo$769bo$770bo$771bo$701b3o68bo$702b3o68bo$
774bo$710b2o5b2o56bo$711b2o3b2o12bo5bo39bo$702b3o3bo2bobobobo2b2obo6b
2o3b2o9b2o29bo$701b3o4bo11bo3bo5b2o3b2o8b2o31bo$708bo2bobobobo3b2o8bo
3bo11bo31bo$711b2o3b2o62bo$704b2o4b2o5b2o62bo$703bo2bo25b3o10bo36bo$
703bobobo24b3o8bo2bo36bo$704bo2bo25bo9bo2bo37bo$708bo35bo40bo$705bobo
78bo$692bo51bo42bo$692b3o38bo9bo2bo41bo$695bo36b3o8bo2bo42bo$694b2o36b
3o10bo44bo$791bo$686b2o54b2o17b2o29bo$685b3o20bobo30bo2bo15b2o31bo$
684bob2o20b2o8bo23bobo17bo9b2o3b2o15bo$683bobo23bo8b2o20b2obo27bo7bo
15bo$683bo2bo30bobo20b3o31bobo19bo$684b2o54b2o30b2o3b2o18bo$798bo$682b
o10b3o36b2o65bo$681bo2bo8b3o36bo67bo$681bo2bo9bo38b3o50b3o12bo$683bo
51bo49b3o14bo$720bobo80bo$683bo35bo84bo$661b2o3b2o13bo2bo9bo25bo2bo29b
o5bo45bo$660bo7bo12bo2bo8b3o24bobobo28b2o3b2o12bo5bo6b3o18bo$663bobo
16bo10b3o25bo2bo28b2o3b2o12b3ob3o7b3o18bo$654b2o5b2o3b2o41b2o5b2o4b2o
30bo3bo13bo5bo29bo$655bo54b2o3b2o46b2o44bo$655bobo34bo3bo8b2o3bobobobo
2bo42bobo10bo8b2o24bo$656b2o33b2o3b2o5bo3bo11bo4b3o17bo19bo10bo7bo2bo
24bo$675b3o13b2o3b2o6bob2o2bobobobo2bo3b3o17bo2bo35bobobo25bo$674b3o
14bo5bo12b2o3b2o26bo2bo35bo2bo27bo$709b2o5b2o27bo3b3o3b3o23bo32bo$749b
obo3bobo24bobo30bo$642bo5bo74b3o19bo3b3o3b3o39bo18bo$642b2o3b2o12bo5bo
6b3o47b3o16bo2bo48b3o19bo$642b2o3b2o12b3ob3o7b3o27b2o36bo2bo47bo23bo$
643bo3bo13bo5bo36bobo37bo31bobo15b2o23bo$652b2o50bo72b2o41bo8b2o$651bo
bo10bo8b2o28b2o5b2o3b2o29b2o29bo24b2o17bo7bobo$633bo19bo10bo7bo2bo36bo
bo30bo2bo41b3o9b3o17bobo4bo$632bo2bo35bobobo33bo7bo27bobo12bo31bo9b2ob
o17b2o$632bo2bo35bo2bo35b2o3b2o29bob2o9bo31bo12bobo$634bo3b3o3b3o23bo
76b3o9b3o41bo2bo$638bobo3bobo24bobo74b2o24bo29b2o$634bo3b3o3b3o39bo86b
2o$632bo2bo48b3o69b2o15bobo31bo$632bo2bo47bo73bo47bo2bo$633bo31bobo15b
2o69b3o48bo2bo$666b2o86bo39b3o3b3o3bo$635b2o29bo24b2o74bobo24bobo3bobo
$614b2o18bo2bo41b3o9b3o76bo23b3o3b3o3bo$614b2o18bobo12bo31bo9b2obo71bo
2bo35bo2bo$635bob2o9bo31bo12bobo69bobobo35bo2bo$636b3o9b3o41bo2bo69bo
2bo7bo10bo19bo$637b2o24bo29b2o71b2o8bo10bobo$662b2o123b2o$645b2o15bobo
31bo76bo5bo13bo3bo$646bo47bo2bo65b3o7b3ob3o12b2o3b2o$643b3o48bo2bo66b
3o6bo5bo12b2o3b2o$643bo39b3o3b3o3bo96bo5bo$656bobo24bobo3bobo$659bo23b
3o3b3o3bo$655bo2bo35bo2bo66b3o$654bobobo35bo2bo65b3o$654bo2bo7bo10bo
19bo86b2o$655b2o8bo10bobo104bobo$676b2o107bo$662bo5bo13bo3bo86b2o3b2o
5b2o$652b3o7b3ob3o12b2o3b2o87bobo$653b3o6bo5bo12b2o3b2o84bo7bo$681bo5b
o85b2o3b2o3$653b3o$652b3o3$687bo$662b2o3b2o18bobo$664bobo20b2o$661bo7b
o$662b2o3b2o9bo$679b2o$678b2o8$687b2o$687bo$688b3o$690bo93$979b2o$979b
obo$979bo79$101b2o$101b2o17$106bo5bo$106b2o3b2o$101b2o3b2o3b2o$100bo2b
o3bo3bo$98bo2bobo$102bo$98bob2o$99bo2$118bo$116bo2bo$93b2o11bo5bo3bo2b
o$94bo10b3o3b3o3bo$94bobo7b2ob2ob2ob2o$95b2o8b3o3b3o3bo$106bo5bo3bo2bo
$116bo2bo$118bo3$78b2o3b2o$77bo7bo$80bobo5b2o37bo$78b2o3b2o2bo2bo34b3o
$87bobo34bo$88bob2o25bobo4b2o$89b3o8b3o13bo$90b2o10bo13b2o2bo$101bo11b
ob2o4bo$80b2o5b2o24bo2bo4bo6b3o$71b3o6b3o3b3o24bobo3bobo5b3o$72b3o5b2o
5b2o3$113b2o5b2o5b3o$72b3o5bobo3bobo24b3o3b3o6b3o$71b3o6bo4bo2bo24b2o
5b2o$80bo4b2obo11bo$81bo2b2o13bo10b2o$85bo13b3o8b3o$82bobo25b2obo$112b
obo$111bo2bo2b2o3b2o$112b2o5bobo$116bo7bo$117b2o3b2o3$83bo$82bo2bo43bo
5bo$65bo16bo2bo3bo5bo33b2o3b2o$65bobo16bo3b3o3b3o8b2o22b2o3b2o3b2o988b
2o$65b2o20b2ob2ob2ob2o7bobo22bo3bo3bo2bo987bobo$84bo3b3o3b3o10bo30bobo
2bo985bo$82bo2bo3bo5bo11b2o30bo$60b2o20bo2bo54b2obo$59bobo21bo58bo$59b
o75bo$58b2o42bo20bo11bo$100b2obo18bo2bo8bobo$99bo22bo2bo9bo11b2o$98bob
o2bo20bo10bo11bo$90bo3bo3bo2bo43bobo$89b2o3b2o3b2o23bo10bo9b2o$89b2o3b
2o26bo2bo9bo$85bo3bo5bo26bo2bo8bobo$84b2o37bo11bo$84bobo48bo2$157b2o3b
2o$156bo7bo$114bo37b2o5bobo$114b3o19b3o12bo2bo2b2o3b2o$117bo18bo15bobo
$116b2o9b2o8bo12b2obo$127b3o20b3o7bo$126b2ob2o19b2o8bo$126b3obo28bobo$
111b3o13b5o31bo$112b3o12b3o31bobo4b3o$121bo6bo34bo3b3o$121bo4bobo30bob
o$120bobo30bobo4bo$112b3o3bo34bo6bo$111b3o4bobo31b3o12b3o$118bo31b5o
13b3o$120bobo28bob3o$121bo8b2o19b2ob2o8bo$121bo7b3o20b3o7bobo$128bob2o
12bo8b2o8b2o$127bobo15bo63b2o$118b2o3b2o2bo2bo12b3o63b2o$120bobo5b2o$
117bo7bo$118b2o3b2o84b2o$208bobo$146bo60bo$146bo11bo47bo$145bobo8bo2bo
45bo$146bo9bo2bo44bo$135b2o9bo10bo45bo$134bobo65bo$134bo11bo10bo43bo$
133b2o11bo9bo2bo40bo$145bobo8bo2bo39bo$146bo11bo39bo$146bo50bo$139bo
56bo$138bob2o53bo$142bo18b2o31bo$138bo2bobo16bobo30bo$117bo5bo16bo2bo
3bo3bo10bo30b2o$117b2o3b2o17b2o3b2o3b2o$112b2o3b2o3b2o22b2o3b2o$111bo
2bo3bo3bo23bo5bo$109bo2bobo$113bo$109bob2o$110bo74b2o$184bobo$129bo53b
o$127bo2bo51bo$104b2o11bo5bo3bo2bo50bo$105bo10b3o3b3o3bo51bo$105bobo7b
2ob2ob2ob2o20b2o31bo$106b2o8b3o3b3o3bo16bobo30bo$117bo5bo3bo2bo16bo29b
o$127bo2bo45bo$129bo45bo$174bo$173bo$89b2o3b2o76bo$88bo7bo74bo23b2o2b
2o8bo$91bobo5b2o69bo24b2o2bo7bobo$89b2o3b2o2bo2bo67bo30bo7b2o$98bobo
67bo32bo$99bob2o25bobo36bo34bo$100b3o8b3o13bo38bo36bo$101b2o10bo13b2o
2bo33bo38bo$112bo11bob2o4bo31bo40bo$91b2o5b2o24bo2bo4bo6b3o21bo42bo$
82b3o6b3o3b3o24bobo3bobo5b3o21bo44bo$83b3o5b2o5b2o61bo46bo$160bo48bo$
159bo50bo$124b2o5b2o5b3o17bo52bo$83b3o5bobo3bobo24b3o3b3o6b3o15bo54bo$
82b3o6bo4bo2bo24b2o5b2o23bo56bo$91bo4b2obo11bo43bo58bobo$92bo2b2o13bo
10b2o31bo60b2o$96bo13b3o8b3o29bo$87b2o4bobo25b2obo27bo$88bo34bobo25bo$
85b3o34bo2bo2b2o3b2o15bo$85bo37b2o5bobo16bo$127bo7bo12bo$128b2o3b2o12b
o75b2o$146bo76bo$145bo78bo$94bo49bo80bo$93bo2bo46bo66b2o14bo$93bo2bo3b
o5bo35bo66bobo15bo$95bo3b3o3b3o8b2o23bo69bo16bo$98b2ob2ob2ob2o7bobo21b
o88bo$95bo3b3o3b3o10bo20bo90bo$93bo2bo3bo5bo11b2o18bo92bo$93bo2bo40bo
94bo$94bo41bo96bo$135bo98bo$113bo20bo100bo$111b2obo18bo102bo$110bo21bo
104bo$109bobo2bo16bo52bo5bo47bo$101bo3bo3bo2bo17bo53b2o3b2o48bo$100b2o
3b2o3b2o17bo54b2o3b2o49bo$100b2o3b2o21bo56bo3bo5b2o44bo$100bo5bo20bo
66bobo45bo$126bo69bo15b2o29bo$125bo49bo36bobo29bo$124bo49bo2bo3bo5bo
24bo32bo$123bo50bo2bo2b3o3b3o57bo$122bo53bob2obobobobobo57bo$121bo56b
3ob2ob2ob3o57bo$120bo55bob2obobobobobo13b2o3b2o39bo$119bo54bo2bo2b3o3b
3o13bo7bo39bo$118bo55bo2bo3bo5bo17bobo43bo$117bo57bo27b2o3b2o42bo$116b
o136bo$115bo61b2o75bo$114bo61bo2bo75bo$113bo62bobo38b3o36bo$112bo64bob
2o9bo25b3o38bo$112b2o64b3o8bo13bo5bo17b2o29bo$179b2o8b3o11bo5bo17bobo
29bo$165bo36bobo3bobo16bo32bo$165b3o31b2o11bo3b3o42bo$168bo29bobo9bobo
4b3o42bo$167b2o43bo50bo$202bobo3bobo53bo$160bo42bo5bo5b2o48bo$158b2obo
41bo5bo4bo2bo48bo$157bo54bo2bobo27bo5bo15bo1011b2o$156bobo2bo54bo28b2o
3b2o16bo1010bobo$156bo2bo4bo5bo41bob2o29b2o3b2o17bo1009bo$157b2o5bo5bo
42bo32bo3bo19bo$163bobo3bobo99bo$161bo43b2o65bo$154b3o4bobo9bobo29bo
36b2o16bo12bo$155b3o3bo11b2o31b3o33bobo5b3o5bo2bo12bo$163bobo3bobo36bo
33bo15bo2bo13bo$164bo5bo11b3o8b2o53bo5bo4bo16bo$164bo5bo13bo8b3o52b3ob
3o22bo$134bo5bo14b3o25bo9b2obo29b2o3b2o16bo3bo5bo18bo$134b2o3b2o13b3o
38bobo27bo7bo16bobo5bo2bo17bo$134b2o3b2o53bo2bo30bobo15bo11bo2bo18bo$
127b2o6bo3bo55b2o29b2o3b2o11bo5bo9bo20bo$128bo115bo4bo32bo$128bobo33b
2o3b2o27bo42b4obob3o6b2o24bo$129b2o18bo16bobo17bo5bo3bo2bo42b2o12bo2bo
24bo$139b3o5bo2bo12bo7bo13b3o3b3o2bo2bo16b3o24b2o3bo8bobo25bo$147bo2bo
13b2o3b2o13bobobobobob2obo19b3o24b3o8b2obo27bo$137bo5bo4bo34b3ob2ob2ob
3o59b3o29bo$137b3ob3o40bobobobobob2obo57b2o31bo$115b2o3b2o16bo3bo5bo
36b3o3b3o2bo2bo70bo18bo$114bo7bo16bobo5bo2bo35bo5bo3bo2bo17b3o5b2o5b2o
34b3o19bo$117bobo15bo11bo2bo27b2o18bo17b3o6b3o3b3o33bo23bo$115b2o3b2o
11bo5bo9bo27bobo45b2o5b2o33b2o23bo$133bo4bo38bo61b3o51bo$130b4obob3o6b
2o28b2o6bo3bo30b2o18bo35bo18bo$131b2o12bo2bo34b2o3b2o8bobo17bo2bo18bo
33bob2o17bobo$105b3o24b2o3bo8bobo34b2o3b2o8b2o18bobo2bo54bo17b2o$106b
3o24b3o8b2obo35bo5bo9bo19bo54bo2bobo$144b3o73b2obo33bo18bo2bo$144b2o
76bo35bo18b2o$159bo96b3o$106b3o5b2o5b2o34b3o69b2o33b2o5b2o$105b3o6b3o
3b3o33bo73bo33b3o3b3o6b3o$114b2o5b2o33b2o69b3o34b2o5b2o5b3o$128b3o96bo
$108b2o18bo35bo76b2o$87b2o18bo2bo18bo33bob2o73b3o$87b2o18bobo2bo54bo
71bob2o8b3o24b3o$108bo54bo2bobo69bobo8bo3b2o24b3o$109b2obo33bo18bo2bo
69bo2bo12b2o$111bo35bo18b2o71b2o6b3obob4o$145b3o100bo4bo$118b2o33b2o5b
2o75bo9bo5bo11b2o3b2o$119bo33b3o3b3o6b3o65bo2bo11bo15bobo$116b3o34b2o
5b2o5b3o66bo2bo5bobo16bo7bo$116bo121bo5bo3bo16b2o3b2o$130b2o111b3ob3o$
129b3o106bo4bo5bo$128bob2o8b3o24b3o66bo2bo$127bobo8bo3b2o24b3o65bo2bo
5b3o$127bo2bo12b2o92bo18b2o$128b2o6b3obob4o110bobo$137bo4bo115bo$126bo
9bo5bo11b2o3b2o86bo3bo6b2o$125bo2bo11bo15bobo87b2o3b2o$125bo2bo5bobo
16bo7bo84b2o3b2o$127bo5bo3bo16b2o3b2o85bo5bo$132b3ob3o$127bo4bo5bo$
125bo2bo15bo$125bo2bo5b3o5bobo$126bo16b2o3$136bo3bo$135b2o3b2o$135b2o
3b2o$135bo5bo7$159bo$157bo$158bo2bo$161bo$160bo$161b3o$163bo23$2566bo$
2566b3o$2569bo$2568b2o8$2577b2o$2577bobo$2577bo10bo5bo$2588b2o3b2o$
2588b2o3b2o$2589bo3bo3$2603bo$2601bo2bo$2601bo2bo$2602bo2$2477bo5bo85b
2o3b2o26bo$2477b2o3b2o84bo7bo12bo3bo7bo2bo$2477b2o3b2o87bobo13b2o5b2o
5bo2bo$2470b2o6bo3bo86b2o3b2o13bobobo9bo$2471bo107bo$2471bobo105b2o9b
3o7b2o$2472b2o18bo85bobo18bo2bo$2490bo2bo65b3o38bobo$2490bo2bo66b3o35b
2obo$2491bo74bo5bo25b3o$2564b2ob2ob2ob2o23b2o$2458b2o3b2o26bo74bo5bo
40bo$2457bo7bo12bo3bo7bo2bo66b3o48b3o$2460bobo13b2o5b2o5bo2bo65b3o31bo
16bo$2458b2o3b2o13bobobo9bo101bo15b2o$2468bo123b3o$2468b2o9b3o7b2o71b
2o54bo$2467bobo18bo2bo69bo2bo41b2o9bob2o$2448b3o38bobo69bobo2bo10bo29b
2o12bo$2449b3o35b2obo71bo12b2o29bo10bo2bobo18b2o$1429b2o1024bo5bo25b3o
73b2obo9b2o41bo2bo18b2o$1429bobo1021b2ob2ob2ob2o23b2o76bo54b2o$1429bo
1025bo5bo40bo86b3o$2449b3o48b3o69b2o15bo$2448b3o31bo16bo73bo16bo31b3o$
2483bo15b2o69b3o48b3o$2481b3o86bo40bo5bo$2451b2o54bo76b2o23b2ob2ob2ob
2o$2450bo2bo41b2o9bob2o73b3o25bo5bo$2450bobo2bo10bo29b2o12bo29bo5bo35b
ob2o35b3o$2432b2o17bo12b2o29bo10bo2bobo28b2o3b2o34bobo38b3o$2432bobo
17b2obo9b2o41bo2bo28b2o3b2o34bo2bo18bobo$2435bo18bo54b2o30bo3bo6b2o28b
2o7b3o9b2o$2436bo41b3o71bo51bo$2437bo23b2o15bo71bobo27bo9bobobo13b2o3b
2o$2438bo23bo16bo31b3o17bo18b2o27bo2bo5b2o5b2o13bobo$2439bo19b3o48b3o
17bo2bo45bo2bo7bo3bo12bo7bo$2440bo18bo40bo5bo23bo2bo47bo26b2o3b2o$
2441bo31b2o23b2ob2ob2ob2o23bo7bo5bo$2442bo29b3o25bo5bo33bo5bo34bo$
2443bo27bob2o35b3o5bobo11bo7b2o3b2o12b2o3b2o13bo2bo$2444bo25bobo38b3o
4b2o10bo2bo16bobo5bo7bo12bo2bo$2445bo24bo2bo18bobo24bo10bo2bo2b3o2b2ob
2o2b2ob2o8bobo16bo18b2o$2446bo24b2o7b3o9b2o37bo19bobo5b2o3b2o33bobo$
2447bo45bo46b2o3b2o54bo$2448bo20bo9bobobo13b2o3b2o29b2o5bo5bo43bo3bo6b
2o$2449bo18bo2bo5b2o5b2o13bobo30bo2bo4bo5bo15bo26b2o3b2o$2450bo17bo2bo
7bo3bo12bo7bo27bobo26b3o9b3o13b2o3b2o$2451bo18bo26b2o3b2o29bob2o35b3o
14bo5bo$2452bo81b3o$2453bo16bo64b2o$2454bo13bo2bo49bo$2455bo12bo2bo49b
3o48b3o$2456bo12bo54bo36b3o9b3o$2457bo65b2o37bo$2458bo$2459bo19bo3bo
32bo21bo32b2o$2460bo17b2o3b2o29b2obo19bo32bo2bo$2461bo16b2o3b2o28bo23b
3o28bo2bobo$2462bo15bo5bo10bo16bobo2bo28b3o23bo$2463bo29bobo16bo2bo32b
o19bob2o$2464bo29b2o17b2o32bo21bo$2465bo$2466bo56bo37b2o$2467bo42b3o9b
3o36bo$2468bo42b3o48b3o$2469bo94bo$2470bo78b2o$2471bo77b3o$2472bo38b3o
35b2obo$2473bo36b3o9b3o26bobo$2474bo48bo15bo5bo4bo2bo$2475bo63bo5bo5b
2o$2476bo62b2o3b2o$2477bo32bo9b2o3b2o5bobo19bo$2478bo29bobo11bobo8b2ob
2o2b2ob2o2b3o2bo2bo$2479bo29b2o8bo7bo5bobo16bo2bo$2480bo39b2o3b2o12b2o
3b2o7bo$2481bo57bo5bo$2482bo56bo5bo7bo$2483bo68bo2bo$2484bo67bo2bo$
2485bo68bo$2486bo$2487bo$2488bo51bo3bo$2489bo49b2o3b2o$2490bo48b2o3b2o
$2491bo47bo5bo$2492bo31b2o$2493bo$2494bo31b2o$2495bo$2496bo$2497bo$
2498bo$2499bo$2500bo$2501bo$2502bo$2066b2o435bo$2066b2o436bo$2505bo$
2506bo$2505b2o7$2513b2o$2513bobo$2516bo$2517bo$2518bo$2519bo$2520bo$
2071b2o3b2o443bo$2070bo7bo443bo$2066b2o5bobo447bo$2065bo2bo2b2o3b2o
446bo$2066bobo456bo$2064b2obo458bo$2064b3o460bo$2064b2o462bo$2529bo$
2070b3o457bo2b2o$2070bobo9b3o444b2o2b2o$2058b2o10b3o8b3o$2059bo$2059bo
bo$2060b2o$2070b3o8b3o$2070bobo9b3o$2070b3o3$2043bo5bo$2043b2o3b2o$
2043b2o3b2o3b2o14bo22bo$2044bo3bo3bo2bo13b2o19b3o$2052bobobo11bobo18bo
$2053bo2bo20bobo9b2o$2057bo18bo$2045b3o6bobo19bobo$2046bo30bo16bo$
2037bo8bo28bo16bo2bo$2036bo2bo2b2o48bo2bo$2036bo2bo6bo46bo$2038bo7bo
32bo4b3o$2045b3o4bo32bo7bo$2038bo46bo6bo2bo$2036bo2bo48b2o2bo2bo$2036b
o2bo16bo28bo8bo$2037bo16bo30bo$2043bo9bobo19bobo6b3o$2041b2o12bo18bo$
2042b2o8bobo20bo2bo$2061bobo11bobobo$2061b2o13bo2bo3bo3bo$2062bo14b2o
3b2o3b2o$2082b2o3b2o$2082bo5bo3$2059b3o$2047b3o9bobo32b2o3b2o$2048b3o
8b3o31bo7bo$2070b2o24bobo5b2o$1579b2o489bobo21b2o3b2o2bo2bo$1579bobo
490bo30bobo$1579bo468b3o8b3o10b2o30bob2o$2025b2o20b3o9bobo43b3o$2024bo
bo32b3o44b2o$2024bo$2023b2o41b2o28b2o5b2o$2065b3o19b3o6b3o3b3o$2064bob
2o20b3o5b2o5b2o7b2o$2063bobo46bo$2054b2o3b2o2bo2bo43bobo$2056bobo5b2o
44b2o$2053bo7bo26b3o5bobo3bobo$2054b2o3b2o26b3o6bo4bo2bo$2096bo4b2obo$
1788bo308bo2b2o$1788b3o310bo$1791bo306bobo21bo5bo$1790b2o330b2o3b2o$
2079bo37b2o3b2o3b2o$2079b3o34bo2bo3bo3bo$2082bo32bobobo$2081b2o32bo2bo
$2114bo6bobo3bobo$2115bobo3bo7bo$2077bo45bo3bo$2076bo2bo5b3o8bobo25bob
o7bo285bo$2076bo2bo17b2o33bo2bo284bobo$1810b2o3b2o261bo4bo5bo7bo26bobo
5bo2bo284b2o$1809bo7bo265b3ob3o33bo3bo5bo$1812bobo263bo5bo3bo33b3ob3o$
1810b2o3b2o259bo2bo5bobo26bo7bo5bo4bo$2076bo2bo33b2o17bo2bo$1806b2o
269bo7bobo25bobo8b3o5bo2bo$1805b2o277bo3bo45bo$1807bo16b3o255bo7bo3bob
o$1823b3o256bobo3bobo6bo$1812b2o5b2o272bo2bo$1812b3o3b3o271bobobo34bo
42b2o$1699b2o3b2o85bo5bo14b2o5b2o263bo3bo3bo2bo36b2o40b2o$1698bo7bo84b
2o3b2o25b3o257b2o3b2o3b2o36b2o$1701bobo87b2o3b2o26b3o256b2o3b2o$1692b
2o5b2o3b2o71bo14bo3bo286bo5bo21bobo60b2o$1693bo83bobo330bo62bobo$1693b
obo81b2o43b2o286b2o2bo57bo$1694b2o86bo38bo2bo256bo25bob2o4bo55bo$1713b
3o65bo2bo22bobo10bobobo254bobo25bo2bo4bo6b3o45bo$1712b3o66bo2bo23b2o
10bo2bo256b2o25bobo3bobo5b3o45bo$1701b2o5b2o73bo24bo10bo280b2o66bo$
1701b3o3b3o110bobo276bobo65bo$1680bo5bo14b2o5b2o73bo7bo5bo37bo263bo66b
o$1680b2o3b2o25b3o66bo2bo5b3o3b3o34b3o262b2o7b2o5b2o5b3o41bo$1680b2o3b
2o26b3o65bo2bo4b2ob2ob2ob2o4bo27bo274b3o3b3o6b3o39bo$1681bo3bo96bo7b3o
3b3o4b2o27b2o273b2o5b2o47bo$1791bo5bo5bobo323b2o31bo$1711b2o71b2o54b2o
262b2o24b2o29bo$1671bo38bo2bo69bo2bo53b3o261b3o22bo30bo$1670bo2bo22bob
o10bobobo69bobo54b2obo260b2obo51bo$1670bo2bo23b2o10bo2bo71bob2o54bobo
18b2o241bobo49bo$1672bo24bo10bo76b3o53bo2bo18b2o217b2o3b2o16bo2bo2b2o
3b2o40b2o$1709bobo74b2o54b2o237bo7bo16b2o5bobo$1672bo7bo5bo37bo97bobo
5bo5bo240b2o5bobo23bo7bo$1670bo2bo5b3o3b3o34b3o69b2o27b2o4b3o3b3o7bo
230bo2bo2b2o3b2o22b2o3b2o$1670bo2bo4b2ob2ob2ob2o4bo27bo73bo27bo4b2ob2o
b2ob2o4bo2bo230bobo$1671bo7b3o3b3o4b2o27b2o69b3o34b3o3b3o5bo2bo228b2ob
o$1680bo5bo5bobo97bo37bo5bo7bo230b3o$1673b2o54b2o74bobo267b2o73b2o$
1672bo2bo53b3o76bo10bo24bo304bobo$1672bobo54b2obo29b2o3b2o35bo2bo10b2o
23bo2bo234b3o64bo$1654b2o17bob2o54bobo27bo7bo33bobobo10bobo22bo2bo234b
obo9b3o18b2o31bo$1654bobo17b3o53bo2bo30bobo36bo2bo38bo223b2o10b3o8b3o
20b2o29bo$1657bo17b2o54b2o29b2o3b2o5b2o28b2o264bo43bo30bo$1658bo52bobo
5bo5bo48bo295bobo71bo$1659bo23b2o27b2o4b3o3b3o7bo37bobo56bo3bo235b2o
70bo$1660bo23bo27bo4b2ob2ob2ob2o4bo2bo29bo6b2o27b3o26b2o3b2o244b3o8b3o
47bo$1661bo19b3o34b3o3b3o5bo2bo16b3o10bo36b3o25b2o3b2o244bobo9b3o45bo$
1662bo18bo37bo5bo7bo19b3o8bobo40b2o5b2o14bo5bo244b3o56bo$1663bo30bobo
71bo38b3o3b3o323bo$1664bo32bo10bo24bo32bobo38b2o5b2o322bo$1665bo27bo2b
o10b2o23bo2bo32bo12bo5bo14b3o249bo5bo76bo$1666bo25bobobo10bobo22bo2bo
17b3o8bobo14b2o3b2o13b3o250b2o3b2o75bo$1667bo24bo2bo38bo17b3o10bo15b2o
3b2o33b2o231b2o3b2o3b2o14bo54bo$1668bo24b2o70bo16bo3bo34bobo231bo3bo3b
o2bo13b2o52bo$1669bo153bo239bobobo11bobo51bo$1670bo49bo3bo30b2o54b2o3b
2o5b2o239bo2bo20bobo8b2o31bo$1671bo18b3o26b2o3b2o28bo2bo38bo16bobo252b
o18bo12b2o29bo$1672bo18b3o25b2o3b2o28bobobo35bo2bo12bo7bo237b3o6bobo
19bobo9bo30bo$1673bo22b2o5b2o14bo5bo29bo2bo21b2o5bo6bo2bo13b2o3b2o239b
o30bo16bo23bo$1674bo21b3o3b3o54bo20bobo4bo7bo252bo8bo28bo16bo2bo21bo$
1675bo20b2o5b2o51bobo7bobo11bo5bobo258bo2bo2b2o48bo2bo20bo$1676bo14b3o
49bo22b2o19bo7bo251bo2bo6bo46bo21bo$1677bo12b3o16bo33b3o21bo19bo6bo2bo
251bo7bo32bo4b3o27bo$1678bo31b2o34bo31b2o14bo2bo258b3o4bo32bo7bo19bo$
1679bo29b2o34b2o32b2o6bo8bo252bo46bo6bo2bo16bo$1680bo98b2o6bo259bo2bo
48b2o2bo2bo15bo$1681bo18b2o3b2o30b2o41bo5bobo4b2o252bo2bo16bo28bo8bo
15bo$1682bo19bobo31b3o41b3o4bo4bo2bo252bo16bo30bo23bo$1683bo15bo7bo27b
ob2o48bo5bobo268bobo19bobo6b3o21bo$1684bo15b2o3b2o27bobo5bo48b2obo271b
o18bo32bo71b2o$1685bo48bo2bo4bo4b3o41b3o258b2o9bobo20bo2bo27bo72bo$
1686bo48b2o4bobo5bo41b2o260bo18bobo11bobobo25bo74b3o$1687bo54bo6b2o
299b3o19b2o13bo2bo3bo3bo16bo77bo$1688bo44bo8bo6b2o32b2o265bo22bo14b2o
3b2o3b2o14bo$1689bo42bo2bo14b2o31bo309b2o3b2o13bo$1690bo41bo2bo6bo19bo
21b3o306bo5bo12bo$1691bo42bo7bo19b2o22bo324bo$1692bo31bo16bobo5bo11bob
o7bobo336bo$1693bo31b2o7bo7bo4bobo20bo299b3o36bo$1694bo29b2o6bo2bo6bo
5b2o21bo2bo283b3o9bobo35bo$1695bo36bo2bo35bobobo283b3o8b3o34bo$1696bo
36bo38bo2bo305b2o23bo$1697bo75b2o306bobo21bo$1698bo384bo20bo$1699bo43b
o3bo16bo294b3o8b3o10b2o18bo$1700bo41b2o3b2o15bo10b3o280b3o9bobo29bo$
1701bo40b2o3b2o14bobo8b3o293b3o28bo$1702bo39bo5bo12bo338bo$1703bo57bob
o313b2o20bo$1704bo56bo314b3o19bo$1705bo57bobo8b3o298bob2o18bo$1706bo
57bo10b3o296bobo19bo$1707bo31bo24bo300b2o3b2o2bo2bo17bo$1708bo31b2o
325bobo5b2o17bo$1709bo29b2o14bo308bo7bo20bo$1710bo42b2o6b2o3b2o297b2o
3b2o20bo$1711bo42b2o7bobo325bo$1712bo47bo7bo321bo$1713bo47b2o3b2o321bo
$1714bo373bo$1715bo371bo$1716bo369bo$1717bo367bo$1718bo365bo$1719bo
363bo$1720bo361bo$1721bo359bo$1722bo357bo$1723bo355bo$1724bo353bo$
1725bo351bo$1726bo350b2o$1727bo$1728bo$1727b2o7$1729b2o4b2o$1729bobo3b
obo$1729bo8bo$1739bo$1740bo$1741bo$1742bo$1743bo$1744bo$1726b2o2b2o13b
o$1726b2o2bo15bo$1731bo15bo$1732bo15bo$1733bo15bo$1734bo15bo$1735bo15b
o$1736bo15bo2b2o$1737bo13b2o2b2o$1738bo$1739bo$1740bo$1741bo$1742bo$
1743bo$1744bo$1745bobo$1746b2o522bo$2081bo188bobo$2081b3o186b2o$2084bo
$2083b2o3$1754b2o$1754bo$1755bo$1756bo$1757bo$1758bo$1759bo$1760bo333b
2o$1761bo331b2o$1762bo332bo$1763bo$1764bo$1765bo$1766bo$1734b2o31bo$
1768bo$1715b2o3b2o47bo$1714bo7bo47bo$1717bobo51bo$1715b2o3b2o50bo$
1773bo$1774bo$1775bo$1705b3o68bo$1706b3o68bo$1778bo$1714b2o5b2o56bo$
1715b2o3b2o12bo5bo39bo$1706b3o3bo2bobobobo2b2obo6b2o3b2o9b2o29bo$1705b
3o4bo11bo3bo5b2o3b2o8b2o31bo487b2o$1712bo2bobobobo3b2o8bo3bo11bo31bo
487bo$1715b2o3b2o62bo485bo$1708b2o4b2o5b2o62bo483bo$1707bo2bo25b3o10bo
36bo481bo$1707bobobo24b3o8bo2bo36bo479bo$1708bo2bo25bo9bo2bo37bo477bo$
1712bo35bo40bo475bo$1709bobo78bo473bo$1696bo51bo42bo471bo$1696b3o38bo
9bo2bo41bo469bo$1699bo36b3o8bo2bo42bo467bo$1698b2o36b3o10bo44bo465bo$
1795bo463bo$1690b2o54b2o17b2o29bo461bo$1689b3o20bobo30bo2bo15b2o31bo
459bo$1688bob2o20b2o8bo23bobo17bo9b2o3b2o15bo457bo20b2o3b2o$1687bobo
23bo8b2o20b2obo27bo7bo15bo455bo20bo7bo$1687bo2bo30bobo20b3o31bobo19bo
453bo17b2o5bobo$1688b2o54b2o30b2o3b2o18bo451bo17bo2bo2b2o3b2o$1802bo
449bo19bobo$1686bo10b3o36b2o65bo447bo18b2obo$1685bo2bo8b3o36bo67bo445b
o19b3o4bo$1685bo2bo9bo38b3o50b3o12bo443bo20b2o5bo$1687bo51bo49b3o14bo
441bo28bo$1724bobo80bo439bo26bo5bo$1687bo35bo84bo437bo27bobobobo7b3o$
1665b2o3b2o13bo2bo9bo25bo2bo29bo5bo45bo435bo18b2o8bo5bo6b3o$1664bo7bo
12bo2bo8b3o24bobobo28b2o3b2o12bo5bo6b3o18bo433bo20bo$1667bobo16bo10b3o
25bo2bo28b2o3b2o12b3ob3o7b3o18bo431bo21bobo$1658b2o5b2o3b2o41b2o5b2o4b
2o30bo3bo13bo5bo29bo429bo23b2o$1659bo54b2o3b2o46b2o44bo427bo32bo5bo6b
3o$1659bobo34bo3bo8b2o3bobobobo2bo42bobo10bo8b2o24bo425bo33bobobobo7b
3o$1660b2o33b2o3b2o5bo3bo11bo4b3o17bo19bo10bo7bo2bo24bo33b2o388bo34bo
5bo$1679b3o13b2o3b2o6bob2o2bobobobo2bo3b3o17bo2bo35bobobo25bo32bo388bo
$1678b3o14bo5bo12b2o3b2o26bo2bo35bo2bo27bo29bobo387bo39b2o$1713b2o5b2o
27bo3b3o3b3o23bo32bo28b2o387bo12bo5bo20bobo$1753bobo3bobo24bobo30bo
415bo13b2o3b2o$1646bo5bo74b3o19bo3b3o3b3o39bo18bo413bo14b2o3b2o3b2o16b
o20bo$1646b2o3b2o12bo5bo6b3o47b3o16bo2bo48b3o19bo411bo16bo3bo3bo2bo34b
3o$1646b2o3b2o12b3ob3o7b3o27b2o36bo2bo47bo23bo409bo25bobobo32bo$1647bo
3bo13bo5bo36bobo37bo31bobo15b2o23bo407bo19b3o5bo2bo32b2o$1656b2o50bo
72b2o41bo9bo395bo19bo3bo8bo$1655bobo10bo8b2o28b2o5b2o3b2o29b2o29bo24b
2o17bo7bobo393bo20bo3bo5bobo$1637bo19bo10bo7bo2bo36bobo30bo2bo41b3o9b
3o17bobo4bo394bo21bo3bo25bobo17bo$1636bo2bo35bobobo33bo7bo27bobo12bo
31bo9b2obo17b2o398bo15bo7b3o26b2o16bo2bo$1636bo2bo35bo2bo35b2o3b2o29bo
b2o9bo31bo12bobo415bo15bo2bo35bo8b3o5bo2bo$1638bo3b3o3b3o23bo76b3o9b3o
41bo2bo414bo16bo2bo5b3o35bo3bo5bo$1642bobo3bobo24bobo74b2o24bo29b2o
414bo19bo5bo3bo34bo3bo$1638bo3b3o3b3o39bo86b2o444bo26bo3bo34bo3bo5bo$
1636bo2bo48b3o69b2o15bobo31bo410bo21bo5bo3bo35b3o5bo2bo$1636bo2bo47bo
73bo47bo2bo408bo20bo2bo5b3o8bo35bo2bo$1637bo31bobo15b2o69b3o48bo2bo
407bo21bo2bo16b2o26b3o7bo$1670b2o86bo39b3o3b3o3bo408bo23bo17bobo25bo3b
o$1639b2o29bo24b2o74bobo24bobo3bobo411bo62bobo5bo3bo$1618b2o18bo2bo41b
3o9b3o76bo23b3o3b3o3bo406bo62bo8bo3bo$1618b2o18bobo12bo31bo9b2obo71bo
2bo35bo2bo403bo30bo33bo2bo5b3o$1639bob2o9bo31bo12bobo69bobobo35bo2bo
402bo29b2o34bobobo$1640b3o9b3o41bo2bo69bo2bo7bo10bo19bo402bo31b2o34bo
2bo3bo3bo$1641b2o24bo29b2o71b2o8bo10bobo419bo52bo16b2o3b2o3b2o$1666b2o
123b2o419bo75b2o3b2o$1649b2o15bobo31bo76bo5bo13bo3bo409bo53bobo20bo5bo
$1650bo47bo2bo65b3o7b3ob3o12b2o3b2o407bo54b2o$1647b3o48bo2bo66b3o6bo5b
o12b2o3b2o406bo$1647bo39b3o3b3o3bo96bo5bo405bo54bo5bo$1660bobo24bobo3b
obo511bo45b3o7bobobobo$1663bo23b3o3b3o3bo506bo47b3o6bo5bo$1659bo2bo35b
o2bo66b3o434bo70b2o$1658bobobo35bo2bo65b3o434bo71bobo$1658bo2bo7bo10bo
19bo86b2o414bo74bo$1659b2o8bo10bobo104bobo412bo51b3o6bo5bo8b2o$1680b2o
107bo411bo30bo20b3o7bobobobo$1666bo5bo13bo3bo86b2o3b2o5b2o409bo29b2o
31bo5bo$1656b3o7b3ob3o12b2o3b2o87bobo415bobo31b2o33bo$1657b3o6bo5bo12b
2o3b2o84bo7bo412b2o67bo5b2o$1685bo5bo85b2o3b2o482bo4b3o$2250b2o18bob2o
$2250bobo16bobo$1657b3o571b2o3b2o12bo9b2o3b2o2bo2bo$1656b3o571bo7bo23b
obo5b2o$2233bobo5b2o16bo7bo$2189b2o40b2o3b2o2bo2bo16b2o3b2o$1691bo498b
o49bobo$1666b2o3b2o18bobo495bo51bob2o$1668bobo20b2o495bo53b3o$1665bo7b
o513bo45b3o7b2o$1666b2o3b2o9bo503bo30bo$1683b2o500bo29b2o14bo4bobo2bo$
1682b2o500bo31b2o6b3o4bo4bobo4bo$2183bo41b3o3bo4bobo4bo5b2o$2182bo66bo
$2181bo51b3o3b3o5bobo$2180bo58bobo5b2o$2179bo45b3o11bobo$2178bo45b3o
12bo2bo$2177bo53bo7bo2bo$1691b2o483bo54bobo3bob3o$1691bo481bobo55b2o4b
ob3o$1692b3o478b2o39b2o43bo5bo$1694bo518b2o44b2o3b2o$2215bo38b2o3b2o3b
2o$2173b2o78bo2bo3bo3bo$2173b2o77bobobo$2252bo2bo$2251bo$2252bobo$
2214bo$2213bo2bo54bo$2213bo2bo52bo2bo$1292b2o921bo3b3o3b3o7bobo31bo2bo
$1292b2o925bobo3bobo8b2o11bo8b3o3b3o3bo$2215bo3b3o3b3o8bo11b2o8bobo3bo
bo$2213bo2bo31bobo7b3o3b3o3bo$2213bo2bo52bo2bo$2120bo93bo54bo2bo$2120b
obo148bo$2120b2o109bobo$2234bo$2230bo2bo32b2o$2229bobobo32bo$2221bo3bo
3bo2bo34b3o$2220b2o3b2o3b2o37bo$2220b2o3b2o$2220bo5bo$2244b3obo4b2o$
2244b3obo3bobo$2243bo2bo7bo$1297bo5bo939bo2bo12b3o26b2o3b2o$1297b2o3b
2o940bobo11b3o26bo7bo$1292b2o3b2o3b2o933b2o5bobo36b2o5bobo$1291bo2bo3b
o3bo933bobo5b3o3b3o29bo2bo2b2o3b2o$1290bobobo941bo46bobo$1290bo2bo941b
2o5bo4bobo4bo3b3o20b2obo$1289bo952bo4bobo4bo4b3o19b3o4bo$1290bobo951bo
2bobo4bo26b2o5bo35b2o$2288bo35bo$1309bo931b2o7b3o32bo5bo30bobo$1307bo
2bo930b3o41bobobobo7b3o20b2o$1284b2o21bo2bo930b2obo30b2o8bo5bo6b3o$
1285bo11bo5bo4bo934bobo30bo$1285bobo8b2o5b2o937bo2bo2b2o3b2o21bobo$
1286b2o9bo5bo4bo934b2o5bobo24b2o$1307bo2bo936bo7bo29bo5bo6b3o$1307bo2b
o937b2o3b2o30bobobobo7b3o$1309bo975bo5bo2$2288b2o$1269b2o3b2o984bo5bo
20bobo$1268bo7bo983b2o3b2o$1271bobo5b2o26bo10bo941b2o3b2o3b2o16bo$
1269b2o3b2o2bo2bo26b2o6b3o942bo3bo3bo2bo34b2o$1278bobobo24b2o6bo953bob
obo34b2o$1279bob3o25bo5b2o945b3o5bo2bo33bo$1275bo5b3o24bo952bo3bo8bo$
1275bo14b2o16bo952bo3bo5bobo$1275bo13bobo969bo3bo25bobo17bo$1291bo12b
3o3b3o6b3o932bo7b3o26b2o16bo2bo$1262b3o6b3o3b3o26bobobo7b3o932bo2bo35b
o8b3o5bo2bo$1263b3o7bobobo30bo944bo2bo5b3o35bo3bo5bo$1275bo979bo5bo3bo
34bo3bo$1308bo952bo3bo34bo3bo5bo$1275bo30bobobo7b3o934bo5bo3bo35b3o5bo
2bo$1263b3o7bobobo26b3o3b3o6b3o931bo2bo5b3o8bo35bo2bo$1262b3o6b3o3b3o
12bo960bo2bo16b2o26b3o7bo$1292bobo13bo945bo17bobo25bo3bo$1275bo16b2o
14bo983bobo5bo3bo$1275bo24b3o5bo982bo8bo3bo$1274bo25b3obo953b2o32bo2bo
5b3o$1275b2o24bobobo807b2o144bo32bobobo$1274b2o26bo2bo2b2o3b2o799bo
141b3o34bo2bo3bo3bo$1276bo26b2o5bobo800bo142bo20bo16b2o3b2o3b2o$1307bo
7bo796bo186b2o3b2o$1308b2o3b2o796bo164bobo20bo5bo$2110bo165b2o$2109bo$
1258bo15bo833bo165bo5bo$1257bo15bo2bo43bo5bo780bo156b3o7bobobobo$1257b
3o13bo2bo43b2o3b2o779bo158b3o6bo5bo$1275bo4bo5bo9b2o22b2o3b2o3b2o773bo
181b2o$1279b2o5b2o8bobo22bo3bo3bo2bo771bo182bobo$1275bo4bo5bo11bo30bob
obo769bo185bo$1273bo2bo21b2o30bo2bo768bo162b3o6bo5bo8b2o$1251b2o20bo2b
o57bo766bo162b3o7bobobobo$1250bobo21bo56bobo766bo173bo5bo$1250bo848bo
20bo5bo150bo$1249b2o40bobo20bo783bo21b2o3b2o150bo5b2o$1294bo18bo2bo2bo
5b3o769bo17b2o3b2o3b2o150bo4b3o$1290bo2bo19bo2bo21b2o756bo17bo2bo3bo3b
o155bob2o$1289bobobo21bo10bo11bo756bo16bo2bobo162bobo$1281bo3bo3bo2bo
35b3o5bobo755bo21bo154b2o3b2o2bo2bo$1280b2o3b2o3b2o23bo10bo9b2o755bo
18bob2o157bobo5b2o$1280b2o3b2o26bo2bo775bo20bo156bo7bo$1280bo5bo26bo2b
o2bo5b3o655b2o106bo27b3o149b2o3b2o$1314bo668bobo104bo27bo3bo9bo$1983bo
105bo28bo3bo7bo2bo$2088bo18b2o9bo3bo7bo2bo$1348b2o3b2o732bo20bo10b3o9b
o$1347bo7bo730bo21bobo$1305bo37b2o5bobo732bo23b2o8b3o9bo$1305b3o34bo2b
o2b2o3b2o729bo33bo3bo7bo2bo$1308bo20b2o10bobobo737bo34bo3bo7bo2bo$
1307b2o20bobo8b3obo737bo35bo3bo9bo$1315bo13bo10b3o738bo37b3o$1309b3o3b
ob3o760bo$1309bo5bo4bo24b2o3b3o726bo12b2o3b2o$1302b3o5bo6b2obo22bo3bob
o3bo724bo12bo7bo$1303b3o12b2o23bo3bobo3bo5b3o715bo16bobo5b2o14b3o20bo$
1343bo3bobo3bo4b3o715bo15b2o3b2o2bo2bo15bo18b3o$1344b3o3b3o722bo25bobo
15bo18bo$1311b3o3b3o754bo20bo6bob2o32b2o141b2o$1303b3o4bo3bobo3bo752bo
20bobo6b3o19bo155b2o$1302b3o5bo3bobo3bo23b2o12b3o711bo31b2o18bo$1310bo
3bobo3bo22bob2o6bo5b3o709bo22b3o27b3o$1311b3o3b2o24bo4bo5bo715bo71b3o$
1344b3obo3b3o714bo15b3o46bo6b3o$1321b3o10bo13bo719bo17b3o44bobo$1319bo
b3o8bobo732bo26b3o$1318bobobo10b2o65b2o664bo66b3o$1309b2o3b2o2bo2bo78b
2o663bo28bobo44b3o$1301bo9bobo5b2o743bo21b3o6bo46b3o$1302b2o4bo7bo746b
o21b3o$1301b2o6b2o3b2o84b2o660bo40b3o27b3o$1399bobo659bo43bo18b2o$
1398bo661bo29bo13bo19b3o6bobo$1349bo47bo661bo30bobo31b2obo6bo$1336b3o
5bo2bo2bo45bo661bo31b2o18bo15bobo$1347bo2bo44bo661bo51bo15bo2bo2b2o3b
2o$1326b2o9bo10bo45bo571b2o2b2o84bo52b3o14b2o5bobo$1325bobo5b3o57bo
572b2o2bo84bo74bo7bo$1325bo11bo10bo43bo578bo82bo76b2o3b2o$1324b2o21bo
2bo40bo580bo80bo$1336b3o5bo2bo2bo39bo582bo78bo55b3o$1349bo39bo584bo76b
o45bo9bo3bo$1388bo586bo74bo45bo2bo7bo3bo$1330bobo54bo588bo72bo46bo2bo
7bo3bo$1329bo56bo590bo70bo49bo9b3o8b2o$1330bo2bo51bo592bo68bo71bobo$
1330bobobo49bo594bo66bo51bo9b3o10bo$1308bo5bo16bo2bo3bo3bo7b3o31b2o
594bo64bo29bo20bo2bo7bo3bo9b2o$1308b2o3b2o17b2o3b2o3b2o8bo628bo62bo30b
obo18bo2bo7bo3bo$1303b2o3b2o3b2o22b2o3b2o7bo630bo60bo31b2o20bo9bo3bo$
1302bo2bo3bo3bo23bo5bo639bo56bobo65b3o$1301bobobo678bo55b2o74bo$1301bo
2bo680bobo126b2obo$1300bo685b2o125bo$1301bobo72b2o734bobo2bo$1375bobo
696bo5bo23bo3bo3bo2bo$1320bo53bo699b2o3b2o22b2o3b2o3b2o$1318bo2bo51bo
700b2o3b2o3b2o17b2o3b2o$1295b2o21bo2bo50bo659b2o41bo3bo3bo2bo16bo5bo$
1296bo11bo5bo4bo51bo661bo49bobo2bo$1296bobo8b2o5b2o54bo623b2o36bo51bo$
1297b2o9bo5bo4bo49bo624bo36bo53b2obo$1318bo2bo13b3o30bo626bo34bo29bo
26bo$1318bo2bo15bo29bo628bo32bo30bobo$1320bo15bo29bo630bo30bo31b2o6bo
7b3o3b3o$1365bo632bo28bo39bo2bo5bobo3bobo$1364bo634bo26bo40bo2bo5b3o3b
3o7b2o$1280b2o3b2o76bo636bo24bo43bo22bo$1279bo7bo74bo638bo22bo65bobo$
1282bobo5b2o26bo42bo640bo20bo45bo20b2o$1280b2o3b2o2bo2bo26b2o39bo642bo
18bo44bo2bo$1289bobobo24b2o39bo644bo16bo45bo2bo4bobo4bob2o$1290bob3o
25bo37bo646bo14bo47bo6b2o3bo3bo$1286bo5b3o24bo37bo648bo12bo56bo3bo$
1286bo14b2o16bo36bo650bo8bobo61bo$1286bo13bobo52bo652bo7b2o84b2o3b2o$
1302bo12b3o3b3o6b3o21bo600bo5bo47bo48b2o41bo7bo$1273b3o6b3o3b3o26bobob
o7b3o21bo601b2o3b2o48bo47bobo36b2o5bobo$1274b3o7bobobo30bo32bo602b2o3b
2o5b2o42bo4b2o40bo37bo2bo2b2o3b2o$1286bo64bo604bo3bo5bobo43bo3b2o79bob
o$1319bo30bo617bo13b2o29bo81b2obo$1286bo30bobobo7b3o17bo632bobo29bo80b
3o$1274b3o7bobobo26b3o3b3o6b3o15bo597bo35bo32bo79b2o$1273b3o6b3o3b3o
12bo43bo597bo2bo2bo5b3o56bo49bo$1303bobo13bo26bo598bo2bo68bo38b3o7bo
11bo$1286bo16b2o14bo25bo601bo10bo59bo38b3o19bo33b3o$1286bo24b3o5bo24bo
615b3o56bo43bo5bo7b3o32b3o$1278b2o5bo25b3obo27bo603bo10bo15b2o3b2o39bo
42b3ob3o32bo5bo$1279bo6b2o24bobobo25bo602bo2bo24bo7bo39bo41bo5bo32b3ob
3o$1276b3o6b2o26bo2bo2b2o3b2o15bo603bo2bo2bo5b3o16bobo43bo34b3o32b3o7b
o5bo$1276bo10bo26b2o5bobo16bo605bo27b2o3b2o42bo32b3o33bo19b3o$1318bo7b
o12bo684bo68bo11bo7b3o$1319b2o3b2o12bo609b2o75bo79bo$1337bo609bo2bo75b
o48b2o$1336bo610bobo38b3o36bo46b3o$1285bo49bo612bob2o22bo5bo6b3o7b2o
29bo44bob2o32b2o$1284bo2bo46bo614b3o8bo12b2o4bobo15bobo29bo42bobo34bo$
1284bo2bo45bo616b2o7bo13bobo21bo32bo32b2o3b2o2bo2bo34b3o$1286bo4bo5bo
9b2o23bo603bo22b3o17b3o49bo33bobo5b2o37bo$1290b2o5b2o8bobo21bo604b3o
32bo15b3o42bo29bo7bo69bo$1286bo4bo5bo11bo20bo608bo32bo15b3o42bo29b2o3b
2o69b2o$1284bo2bo21b2o18bo608b2o31bo2bo59bo56bo47bobo$1284bo2bo40bo
644bo5b3o53bo55bo3bo$1285bo41bo603bo41bobo10b2o48bo50bo3bo3b2o6bo$
1326bo602b2obo41bo4bobo3bo2bo48bo48b2obo4bobo4bo2bo26bo5bo$1302bobo20b
o602bo45bo5bo2bo2bobo27bo5bo15bo62bo2bo26b2o3b2o$1305bo18bo112b2o488bo
bo2bo2bo5bo45bo28b2o3b2o16bo40b2o20bo23b2o3b2o3b2o$1301bo2bo18bo113bob
o487bo2bo3bobo4bo41bob2o29b2o3b2o17bo38bobo43bo2bo3bo3bo$1300bobobo17b
o116bo488b2o10bobo41bo32bo3bo19bo37bo22bo20bo2bobo$1292bo3bo3bo2bo17bo
117b2o493b3o5bo99bo35b2o7b3o3b3o5bo2bo22bo$1291b2o3b2o3b2o17bo620bo2bo
31b2o34b2o29bo43bobo3bobo5bo2bo18bob2o$1291b2o3b2o21bo605b3o15bo32bo
35bobo16bo12bo42b3o3b3o7bo20bo42b2o$1291bo5bo20bo607b3o15bo32b3o32bo
16bo2bo12bo84b3o34bo$1317bo616b3o17b3o22bo49bo2bo13bo37bo44bo3bo9bo21b
obo$1316bo623bobo13bo7b2o53bo5bo4bo16bo35bob2o42bo3bo7bo2bo20b2o$1315b
o618bobo4b2o12bo8b3o51b2o5b2o21bo38bo30b2o9bo3bo7bo2bo$1314bo590bo5bo
14b3o6bo5bo22b2obo29b2o3b2o15bo5bo4bo18bo33bo2bobo30bo10b3o9bo$1313bo
591b2o3b2o13b3o38bobo27bo7bo24bo2bo17bo34bo2bo3bo3bo22bobo$1312bo592b
2o3b2o53bo2bo30bobo27bo2bo18bo34b2o3b2o3b2o22b2o8b3o9bo$1311bo586b2o6b
o3bo55b2o29b2o3b2o27bo20bo38b2o3b2o31bo3bo7bo2bo$1310bo588bo153bo37bo
5bo31bo3bo7bo2bo$1309bo589bobo33b2o3b2o27bo58b2o24bo74bo3bo9bo$1308bo
591b2o18bo16bobo16b3o5bo2bo2bo42bo13bo2bo24bo74b3o$1307bo610bo2bo12bo
7bo24bo2bo16b3o25bo12bobo25bo$1306bo611bo2bo13b2o3b2o15bo10bo19b3o22b
3o10b2obo27bo45b2o3b2o$1305bo602bo5bo4bo33b3o70b3o29bo43bo7bo$1304bo
602b2o5b2o41bo10bo57b2o31bo45bobo5b2o14b3o$1303bo582b2o3b2o15bo5bo4bo
47bo2bo26bo5bo37bo18bo42b2o3b2o2bo2bo15bo$1303b2o580bo7bo24bo2bo34b3o
5bo2bo2bo17b3o5bobo3bobo34b3o19bo50bobo15bo18b2o$1888bobo27bo2bo27b2o
18bo17b3o5bo3bobo3bo32bo23bo43bo6bob2o31bobo$1886b2o3b2o27bo27bobo45bo
bo3bobo4b3o26b2o23bo41bobo6b3o19bo13bo$1948bo48bo5bo5bo54bo50b2o18bo$
1917b2o28b2o6bo3bo30b2o18bo35bo18bo39b3o27b3o$1081b2o819bo13bo2bo34b2o
3b2o28bo2bo52bob2o17bobo84b3o$1081b2o793b3o25bo12bobo34b2o3b2o28bobo2b
o54bo17b2o27b3o46bo6b3o$1877b3o22b3o10b2obo35bo5bo29bo54bo2bobo46b3o
44bobo$1915b3o73b2obo52bo2bo54b3o$1915b2o76bo35bo18b2o94b3o$1886bo5bo
37bo99bo5bo5bo62bobo44b3o$1877b3o5bobo3bobo34b3o69b2o26b3o4bobo3bobo
53b3o6bo46b3o$1876b3o5bo3bobo3bo32bo73bo32bo3bobo3bo5b3o43b3o$1885bobo
3bobo4b3o26b2o69b3o34bobo3bobo5b3o62b3o27b3o$1886bo5bo5bo99bo37bo5bo
73bo18b2o$1879b2o18bo35bo76b2o101bo19b3o6bobo$1858b2o18bo2bo52bob2o73b
3o87b2o32b2obo6bo$1858b2o18bobo2bo54bo71bob2o10b3o22b3o50bo18bo15bobo$
1879bo54bo2bobo69bobo12bo25b3o46b3o18bo15bo2bo2b2o3b2o$1880b2obo52bo2b
o69bo2bo13bo72bo20b3o14b2o5bobo$1882bo35bo18b2o71b2o129bo7bo$1919bo5bo
5bo210b2o3b2o$1889b2o26b3o4bobo3bobo75bo27b2o3b2o$1086b2o3b2o797bo32bo
3bobo3bo5b3o65bo2bo27bobo78b3o$1085bo7bo793b3o34bobo3bobo5b3o66bo2bo
24bo7bo64bo9bo3bo$1081b2o5bobo796bo37bo5bo77bo4bo5bo15b2o3b2o64bo2bo7b
o3bo$1080bo2bo2b2o3b2o808b2o110b2o5b2o85bo2bo7bo3bo$1081bobo816b3o106b
o4bo5bo88bo9b3o8b2o$1079b2obo816bob2o10b3o22b3o66bo2bo119bobo$1079b3o
4bo811bobo12bo25b3o65bo2bo98bo9b3o10bo$1079b2o5bo811bo2bo13bo92bo18b2o
78bo2bo7bo3bo9b2o$1086bo812b2o43bo82bobo77bo2bo7bo3bo$1083bo5bo854b2o
83bo78bo9bo3bo$1083bobobobo7b3o797bo27b2o3b2o11bobo72bo3bo6b2o88b3o$
1073b2o8bo5bo6b3o797bo2bo27bobo87b2o3b2o103bo$1074bo821bo2bo24bo7bo84b
2o3b2o101b2obo$1074bobo821bo4bo5bo15b2o3b2o85bo5bo100bo$1075b2o825b2o
5b2o212bobo2bo$1083bo5bo6b3o799bo4bo5bo205bo3bo3bo2bo$1083bobobobo7b3o
796bo2bo214b2o3b2o3b2o$1083bo5bo806bo2bo16bo197b2o3b2o$1897bo16bobo
197bo5bo$1086b2o827b2o$1058bo5bo20bobo$1058b2o3b2o842bo3bo$1058b2o3b2o
3b2o16bo20bo798b2o3b2o$1059bo3bo3bo2bo34b3o798b2o3b2o$1067bobobo32bo
801bo5bo$1060b3o5bo2bo32b2o$1059bo3bo8bo$1059bo3bo5bobo$1059bo3bo25bob
o17bo$1052bo7b3o26b2o16bo2bo$1051bo2bo35bo8b3o5bo2bo$1051bo2bo5b3o35bo
3bo5bo$1053bo5bo3bo34bo3bo$1059bo3bo34bo3bo5bo$1053bo5bo3bo35b3o5bo2bo
820b2o$1051bo2bo5b3o8bo35bo2bo820bo192b2o$1051bo2bo16b2o26b3o7bo822b3o
189b2o$1052bo17bobo25bo3bo831bo$1090bobo5bo3bo$1089bo8bo3bo$1056bo33bo
2bo5b3o$1054b2o34bobobo$1055b2o34bo2bo3bo3bo$1075bo16b2o3b2o3b2o$1097b
2o3b2o$1074bobo20bo5bo$1074b2o2$1072bo5bo$1062b3o7bobobobo30b2o3b2o$
1063b3o6bo5bo29bo7bo$1085b2o24bobo5b2o$1085bobo21b2o3b2o2bo2bo$1087bo
30bobo$1063b3o6bo5bo8b2o30bob2o$1040b2o20b3o7bobobobo41b3o$1039bobo30b
o5bo32b3o7b2o$1039bo35bo$1038b2o35bo5b2o26bo4bobo2bo$1075bo4b3o19b3o4b
o4bobo4bo$1079bob2o20b3o3bo4bobo4bo5b2o$1078bobo46bo$1069b2o3b2o2bo2bo
29b3o3b3o5bobo$1071bobo5b2o36bobo5b2o$1068bo7bo26b3o11bobo$1069b2o3b2o
26b3o12bo2bo$1109bo7bo2bo$1109bobo3bob3o$1109b2o4bob3o$1137bo5bo$1137b
2o3b2o$1094bo37b2o3b2o3b2o$1094b3o34bo2bo3bo3bo$1097bo32bobobo$1096b2o
32bo2bo$1074b2o53bo$1074bobo53bobo$1074bo17bo$1091bo2bo54bo$1091bo2bo
52bo2bo$1093bo3b3o3b3o7bobo31bo2bo$1097bobo3bobo8b2o11bo8b3o3b3o3bo$
1093bo3b3o3b3o8bo11b2o8bobo3bobo$1091bo2bo31bobo7b3o3b3o3bo$1091bo2bo
52bo2bo$1092bo54bo2bo$1149bo$1109bobo$1112bo$1108bo2bo$1107bobobo77b2o
$1099bo3bo3bo2bo78b2o$1098b2o3b2o3b2o38bo$1098b2o3b2o44b2o$1098bo5bo
43b2o39b2o$1122b3obo4b2o55bobo$1122b3obo3bobo54bo$1121bo2bo7bo53bo$
1121bo2bo12b3o45bo$1122bobo11b3o45bo$1115b2o5bobo58bo$1114bobo5b3o3b3o
51bo$1114bo66bo$1113b2o5bo4bobo4bo3b3o41bo$1120bo4bobo4bo4b3o6b2o31bo$
1122bo2bobo4bo14b2o29bo$1146bo30bo$1119b2o7b3o45bo$1119b3o53bo$1119b2o
bo51bo$1121bobo49bo$1097b2o3b2o16bo2bo2b2o3b2o40b2o$1096bo7bo16b2o5bob
o$1092b2o5bobo23bo7bo$1091bo2bo2b2o3b2o22b2o3b2o$1092bobo$1090b2obo$
1090b3o4bo$1090b2o5bo67b2o$1097bo33b2o31bobo$1094bo5bo31b2o29bo$1094bo
bobobo7b3o20bo30bo$1084b2o8bo5bo6b3o51bo16bo$1085bo74bo18b2o$1085bobo
71bo18b2o$1086b2o70bo$1094bo5bo6b3o47bo$1094bobobobo7b3o45bo$1094bo5bo
54bo$1154bo$1097b2o54bo$1069bo5bo20bobo53bo264b2o$1069b2o3b2o75bo266bo
$1069b2o3b2o3b2o16bo52bo266bo$1070bo3bo3bo2bo34b2o31bo266bo$1078bobobo
34b2o29bo266bo$1071b3o5bo2bo33bo30bo266bo$1070bo3bo8bo62bo266bo$1070bo
3bo5bobo62bo266bo$1070bo3bo25bobo17bo23bo266bo$1063bo7b3o26b2o16bo2bo
21bo266bo$1062bo2bo35bo8b3o5bo2bo20bo266bo$1062bo2bo5b3o35bo3bo5bo21bo
266bo$1064bo5bo3bo34bo3bo26bo266bo$1070bo3bo34bo3bo5bo19bo266bo$1064bo
5bo3bo35b3o5bo2bo16bo266bo$1062bo2bo5b3o8bo35bo2bo15bo266bo$1062bo2bo
16b2o26b3o7bo15bo266bo20b2o3b2o$1063bo17bobo25bo3bo21bo266bo20bo7bo$
1101bobo5bo3bo20bo266bo17b2o5bobo$1100bo8bo3bo19bo266bo17bo2bo2b2o3b2o
$1067b2o32bo2bo5b3o19bo266bo17bobobo$1068bo32bobobo25bo266bo17b3obo$
1065b3o34bo2bo3bo3bo16bo266bo18b3o$1065bo20bo16b2o3b2o3b2o14bo266bo$
1108b2o3b2o13bo266bo$1085bobo20bo5bo12bo266bo$1085b2o39bo266bo41b3o$
1125bo266bo18b2o21b3o$1083bo5bo34bo266bo20bo10b2o5b2o$1073b3o7bobobobo
33bo266bo21bobo8b3o3b3o$1074b3o6bo5bo32bo266bo23b2o8b2o5b2o$1096b2o23b
o266bo45b3o$1096bobo21bo266bo47b3o$1098bo20bo266bo$1074b3o6bo5bo8b2o
18bo266bo$1073b3o7bobobobo27bo266bo$1083bo5bo26bo266bo12bo5bo$1086bo
28bo266bo13b2o3b2o$1086bo5b2o20bo266bo14b2o3b2o3b2o27bo9bo$1086bo4b3o
19bo112b2o152bo16bo3bo3bo2bo27bo6b3o$1090bob2o18bo113bobo150bo25bobo2b
o23bo7bo$1089bobo19bo116bo149bo27bo27bobo5b2o$1080b2o3b2o2bo2bo17bo
117b2o147bo29b2obo24b2o$1082bobo5b2o17bo266bo24b3o5bo7b2o$1079bo7bo20b
o266bo42b2o12bo5bo8bo$1080b2o3b2o20bo266bo15bo8bo5bo11bo14b3ob3o6bo2bo
$1106bo266bo15bo2bo6b3ob3o27bo3bo7bo2bo$1105bo266bo16bo2bo7bo3bo29bobo
9bo$1104bo266bo19bo9bobo$1103bo266bo63bobo9bo$1102bo266bo21bo9bobo29bo
3bo7bo2bo$1101bo266bo20bo2bo7bo3bo27b3ob3o6bo2bo$1100bo266bo21bo2bo6b
3ob3o14bo11bo5bo8bo$1099bo266bo23bo8bo5bo12b2o$1098bo266bo53b2o7bo5b3o
$1097bo266bo36b2o24bob2o$1096bo266bo37bobo27bo$1095bo266bo40bo23bo2bob
o$1094bo266bo39bo27bo2bo3bo3bo$1093bo266bo41bo27b2o3b2o3b2o$1092bo266b
o75b2o3b2o$1092b2o264bo76bo5bo$1357bo$1356bo$1355bo$1354bo29bobo13b3o$
1353bo30b2o15b3o$1352bo32bo20b2o5b2o8b2o$1351bo54b3o3b3o8bobo$1350bo
55b2o5b2o10bo$1349bo51b3o21b2o$1348bo51b3o$1347bo$1344bobo$1344b2o$
1419b3o$1417bob3o$1416bobobo$1378b2o3b2o22b2o3b2o2bo2bo$1377bo7bo23bob
o5b2o$1369bobo8bobo5b2o16bo7bo$1336b2o31b2o7b2o3b2o2bo2bo16b2o3b2o$
1337bo32bo16bobobo$1336bo51bob3o$1335bo54b3o$1334bo$1333bo$1278b2o2b2o
48bo51bo$1278b2o2bo48bo39b3o10bo$1283bo46bo41b3o8bobo10b2o$1284bo44bo
57bo8bo$1285bo42bo56bobo6bobo$1286bo40bo59bo6b2o$1287bo38bo45b3o8bobo$
1288bo36bo45b3o10bo$1289bo34bo59bo$1290bo32bo$1291bo28bobo$1292bo27b2o
84bo5bo$1293bo112b2o3b2o$1294bo106b2o3b2o3b2o$1295bo24b2o78bo2bo3bo3bo
$1296bo23b2o65b2o9bo2bobo$1297bobo86b2o14bo$1298b2o68bo5bobo11bo9bob2o
$1367b2o3b2o2b2o21bo9bo$1361bo5bobo8bo25bo3b3o$1360bo2bo11b2obo23bo2bo
bobobo6bo$1360bo2bo11b3o22b3ob2ob2ob3o3bo2bo$1362bo38bobobobobobo4bo2b
o$1370bo5bo25b3o3b3o6bo$1306b2o54bo6b3o3b3o25bo5bo$1306bo53bo2bo4bobob
obobobo38bo$1307bo52bo2bo3b3ob2ob2ob3o22b3o11bo2bo13b3o$1308bo52bo6bob
obobo2bo23bob2o11bo2bo13bo$1309bo59b3o3bo25bo8bobo5bo15bo$1310bo59bo9b
o21b2o2b2o3b2o$1311bo66b2obo9bo11bobo5b3o$1312bo64bo14b2o19b2o$1313bo
62bobo2bo9b2o20bo$1314bo53bo3bo3bo2bo34b3o$1315bo51b2o3b2o3b2o37bo$
1316bo50b2o3b2o$1317bo49bo5bo$1318bo$1319bo$1320bo74bo$1267b2o3b2o47bo
73bo10b3o26b2o3b2o$1266bo7bo47bo71bobo8b3o26bo7bo$1269bobo51bo60b2o6bo
37b2o5bobo$1267b2o3b2o50bo58bobo6bobo34bo2bo2b2o3b2o$1325bo57bo8bo35bo
bobo$1326bo55b2o10bobo8b3o19b3obo$1327bo67bo10b3o18b3o$1257b3o68bo66bo
75b2o$1258b3o68bo141bo$1267bo5bo56bo138bobo$1267bo5bo57bo55b3o56b3o20b
2o$1266bobo3bobo11bo5bo9bo29bo54b3obo30b2o21b3o$1258b3o3bo11b2o8b2o3b
2o8b2o30bo54bobobo30bo10b2o5b2o$1257b3o4bobo9bobo7b2o3b2o8bobo30bo54bo
2bo2b2o3b2o21bobo8b3o3b3o$1264bo22bo3bo43bo54b2o5bobo24b2o8b2o5b2o20bo
$816b2o448bobo3bobo61bo57bo7bo42b3o15b2o$816b2o442b2o5bo5bo15bo47bo57b
2o3b2o44b3o13bobo$1259bo2bo4bo5bo15bo11bo36bo$1259bobo2bo23bobo8bo2bo
36bo$1260bo28bo9bo2bo37bo$1261b2obo24bo10bo40bo65bo5bo$1263bo78bo64b2o
3b2o$1248bo40bo10bo42bo63b2o3b2o3b2o27bo$1248b3o38bo9bo2bo41bo63bo3bo
3bo2bo27bo$1251bo36bobo8bo2bo42bo70bobo2bo23bo$1250b2o37bo11bo44bo70bo
27bobo$1289bo27bo29bo70b2obo24b2o$1298b2o16b2o30bo63b3o5bo7b2o$1242b3o
20bo31bo2bo15bobo30bo79b2o12bo5bo8bo$1240bob3o18b2o9b2o20bobobo27b2o3b
2o15bo50bo8bo5bo11bo14b3ob3o6bo2bo$1239bobobo20b2o9b2o18b3obo27bo7bo
15bo48bo2bo6b3ob3o27bo3bo7bo2bo$1239bo2bo31bo20b3o32bobo19bo47bo2bo7bo
3bo29bobo9bo$1240b2o86b2o3b2o18bo48bo9bobo$821b2o3b2o422bo103bo90bobo
9bo$820bo7bo409bo11bo37b2o65bo46bo9bobo29bo3bo7bo2bo$816b2o5bobo411bo
2bo8bobo36bo67bo43bo2bo7bo3bo27b3ob3o6bo2bo$815bo2bo2b2o3b2o409bo2bo9b
o38b3o50b3o12bo42bo2bo6b3ob3o14bo11bo5bo8bo$816bobo420bo10bo40bo49b3o
14bo42bo8bo5bo12b2o$814b2obo458bo82bo70b2o7bo5b3o$814b3o422bo10bo24bob
2o81bo51b2o24bob2o$814b2o401b2o3b2o13bo2bo9bo28bo29bo5bo45bo43b2o5bobo
27bo$1216bo7bo12bo2bo8bobo23bo2bobo28b2o3b2o11b2o5b2o5b3o18bo43bo7bo
23bo2bobo$820b3o396bobo16bo11bo15bo5bo4bo2bo28b2o3b2o11b3o3b3o6b3o18bo
39b3o6bo27bo2bo3bo3bo$820bobo9b3o375b2o5b2o3b2o26bo15bo5bo5b2o30bo3bo
12b2o5b2o28bo38bo9bo27b2o3b2o3b2o$808b2o10b3o8b3o377bo53bobo3bobo45b3o
43bo80b2o3b2o$809bo401bobo34bo3bo22bo45bo18b2o24bo79bo5bo$809bobo400b
2o33b2o3b2o7bobo9bobo4b3o10b3o4bo19bo18bo2bo24bo$810b2o419b3o13b2o3b2o
8b2o11bo3b3o13bo3bo2bo34bo2bobo25bo$820b3o8b3o396b3o14bo5bo11bobo3bobo
20bo4bo2bo3bo5bo28bo27bo$820bobo9b3o431bo5bo28bo3b3o3b3o23bob2o29bo40b
3o$820b3o443bo5bo31b2ob2ob2ob2o23bo32bo40b3o$1198bo5bo74b3o19bo3b3o3b
3o39bo18bo44b2o5b2o8b2o$1198b2o3b2o11b2o5b2o5b3o47b3o16bo2bo3bo5bo38b
3o19bo43b3o3b3o8bobo$793bo5bo398b2o3b2o11b3o3b3o6b3o27b2o36bo2bo47bo
23bo42b2o5b2o10bo$793b2o3b2o399bo3bo12b2o5b2o35bobo37bo32bo16b2o23bo
36b3o21b2o$793b2o3b2o3b2o14bo22bo365b3o49bo73b2o40bo34b3o$794bo3bo3bo
2bo13b2o19b3o367bo18b2o28b2o5b2o3b2o29b2o29b2o12b2o28bo$802bobobo11bob
o18bo349bo19bo18bo2bo36bobo30bo2bo41bobo8b3o18bobo$803bo2bo20bobo9b2o
347bo2bo34bo2bobo33bo7bo27bobobo42bo8b3obo17b2o$807bo18bo361bo2bo3bo5b
o28bo35b2o3b2o29bob3o8bo42bobobo67b3o$795b3o6bobo19bobo361bo3b3o3b3o
23bob2o74b3o8bobo41bo2bo65bob3o$796bo30bo16bo348b2ob2ob2ob2o23bo87b2o
12b2o29b2o65bobobo$787bo8bo28bo16bo2bo344bo3b3o3b3o39bo85b2o88b2o3b2o
2bo2bo$786bo2bo2b2o48bo2bo342bo2bo3bo5bo38b3o69b2o16bo32bo56bobo5b2o$
786bo2bo6bo46bo344bo2bo47bo73bo47bo2bo52bo7bo$788bo7bo32bo4b3o352bo32b
o16b2o69b3o38bo5bo3bo2bo53b2o3b2o$795b3o4bo32bo7bo379b2o85bo39b3o3b3o
3bo$788bo46bo6bo2bo345b2o29b2o12b2o87bo23b2ob2ob2ob2o$786bo2bo48b2o2bo
2bo324b2o18bo2bo41bobo8b3o74b2obo23b3o3b3o3bo$786bo2bo16bo28bo8bo325b
2o18bobobo42bo8b3obo71bo28bo5bo3bo2bo$787bo16bo30bo355bob3o8bo42bobobo
69bobo2bo34bo2bo$793bo9bobo19bobo6b3o356b3o8bobo41bo2bo69bo2bo18bo19bo
$791b2o12bo18bo379b2o12b2o29b2o71b2o18bo$792b2o8bobo20bo2bo388b2o123b
3o$811bobo11bobobo371b2o16bo32bo75b2o5b2o12bo3bo$811b2o13bo2bo3bo3bo
364bo47bo2bo65b3o6b3o3b3o11b2o3b2o$812bo14b2o3b2o3b2o360b3o38bo5bo3bo
2bo66b3o5b2o5b2o11b2o3b2o$832b2o3b2o360bo39b3o3b3o3bo96bo5bo$832bo5bo
375bo23b2ob2ob2ob2o$1212b2obo23b3o3b3o3bo$1211bo28bo5bo3bo2bo66b3o$
809b3o398bobo2bo34bo2bo65b3o$797b3o9bobo32b2o3b2o359bo2bo18bo19bo86b2o
87b2o$798b3o8b3o31bo7bo359b2o18bo107bobo86b2o$820b2o24bobo5b2o375b3o
107bo$820bobo21b2o3b2o2bo2bo360b2o5b2o12bo3bo86b2o3b2o5b2o$822bo30bobo
352b3o6b3o3b3o11b2o3b2o87bobo$798b3o8b3o10b2o30bob2o351b3o5b2o5b2o11b
2o3b2o84bo7bo$775b2o20b3o9bobo43b3o379bo5bo85b2o3b2o$774bobo32b3o44b2o
$774bo$773b2o41b2o28b2o5b2o354b3o$815b3o19b3o6b3o3b3o353b3o$814bob2o
20b3o5b2o5b2o7b2o$813bobo46bo$804b2o3b2o2bo2bo43bobo$806bobo5b2o44b2o
356b2o3b2o$803bo7bo26b3o5bobo3bobo365bobo$804b2o3b2o26b3o6bo4bo2bo362b
o7bo$846bo4b2obo363b2o3b2o$847bo2b2o382bobo$851bo383b2o$848bobo21bo5bo
356bo$872b2o3b2o$829bo37b2o3b2o3b2o$829b3o34bo2bo3bo3bo$832bo32bobobo$
831b2o32bo2bo$864bo6bobo3bobo$865bobo3bo7bo363b2o$827bo45bo3bo365bo$
826bo2bo5b3o8bobo25bobo7bo359b3o$826bo2bo17b2o33bo2bo360bo$828bo4bo5bo
7bo26bobo5bo2bo$833b3ob3o33bo3bo5bo$828bo5bo3bo33b3ob3o$826bo2bo5bobo
26bo7bo5bo4bo$826bo2bo33b2o17bo2bo$827bo7bobo25bobo8b3o5bo2bo$834bo3bo
45bo$832bo7bo3bobo$832bobo3bobo6bo$843bo2bo$842bobobo34bo42b2o$834bo3b
o3bo2bo36b2o40b2o$826b2o5b2o3b2o3b2o36b2o$826bobo4b2o3b2o$826bo6bo5bo
21bobo60b2o$860bo62bobo$860b2o2bo57bo$857bob2o4bo55bo$857bo2bo4bo6b3o
45bo$857bobo3bobo5b3o45bo$850b2o66bo$849bobo65bo$849bo66bo$848b2o7b2o
5b2o5b3o41bo$857b3o3b3o6b3o39bo$857b2o5b2o30bo16bo$879b2o16b2o13bo$
854b2o24b2o14b2o13bo$854b3o22bo30bo$854b2obo51bo$856bobo49bo$832b2o3b
2o16bo2bo2b2o3b2o40b2o$831bo7bo16b2o5bobo$827b2o5bobo23bo7bo$826bo2bo
2b2o3b2o22b2o3b2o$827bobo$825b2obo$825b3o$825b2o73b2o$899bobo$831b3o
64bo$831bobo9b3o18b2o31bo$819b2o10b3o8b3o20b2o29bo$820bo43bo30bo$820bo
bo71bo$821b2o70bo$831b3o8b3o47bo$831bobo9b3o45bo$831b3o56bo$889bo$888b
o$804bo5bo76bo$804b2o3b2o75bo$804b2o3b2o3b2o14bo54bo$805bo3bo3bo2bo13b
2o52bo$813bobobo11bobo51bo$814bo2bo20bobo8b2o31bo$818bo18bo12b2o29bo$
806b3o6bobo19bobo9bo30bo$807bo30bo16bo23bo$798bo8bo28bo16bo2bo21bo$
797bo2bo2b2o48bo2bo20bo$797bo2bo6bo46bo21bo$799bo7bo32bo4b3o27bo$806b
3o4bo32bo7bo19bo$799bo46bo6bo2bo16bo$797bo2bo48b2o2bo2bo15bo$797bo2bo
16bo28bo8bo15bo$798bo16bo30bo23bo$814bobo19bobo6b3o21bo$816bo18bo32bo$
802b2o9bobo20bo2bo27bo$803bo18bobo11bobobo25bo$800b3o19b2o13bo2bo3bo3b
o16bo$800bo22bo14b2o3b2o3b2o14bo$843b2o3b2o13bo$843bo5bo12bo$861bo$
860bo$820b3o36bo$808b3o9bobo35bo$809b3o8b3o34bo$831b2o23bo$831bobo21bo
$833bo20bo$809b3o8b3o10b2o18bo$808b3o9bobo29bo$820b3o28bo$850bo$827b2o
20bo$826b3o19bo$825bob2o18bo$824bobo19bo$815b2o3b2o2bo2bo17bo$817bobo
5b2o17bo$814bo7bo20bo$815b2o3b2o20bo$841bo$840bo$839bo$838bo$837bo$
836bo$835bo$834bo336bo$833bo337b3o$832bo341bo$831bo341b2o$830bo$829bo$
828bo$827bo$827b2o350b2o$1179bobo$1179bo3$1193bo5bo$1193b2o3b2o$1193b
2o3b2o$1194bo3bo3$1208bo$1206bo2bo$1206bo2bo$1193bo5bo7bo$1193bo5bo$
1082bo5bo85b2o3b2o12b2o3b2o7bo$1082b2o3b2o84bo7bo5bobo16bo2bo$1082b2o
3b2o87bobo8b2ob2o2b2ob2o2b3o2bo2bo$1075b2o6bo3bo86b2o3b2o5bobo19bo$
1076bo116b2o3b2o$1076bobo114bo5bo5b2o$1077b2o18bo79bo15bo5bo4bo2bo$
1095bo2bo65b3o9b3o26bobo$1095bo2bo66b3o35b2obo$1082bo5bo7bo106b3o$
1082bo5bo114b2o$1063b2o3b2o12b2o3b2o7bo121bo$1062bo7bo5bobo16bo2bo66b
3o48b3o$1065bobo8b2ob2o2b2ob2o2b3o2bo2bo65b3o9b3o36bo$1063b2o3b2o5bobo
19bo79bo37b2o$1082b2o3b2o$1082bo5bo5b2o71b2o32bo21bo$1066bo15bo5bo4bo
2bo69bo2bo32bo19bob2o$1053b3o9b3o26bobo69bobo2bo28b3o23bo$1054b3o35b2o
bo71bo23b3o28bo2bobo18b2o$1092b3o73b2obo19bo32bo2bo18b2o$1092b2o76bo
21bo32b2o$1107bo$1054b3o48b3o69b2o37bo$1053b3o9b3o36bo73bo36b3o9b3o$
1066bo37b2o69b3o48b3o$1175bo$1056b2o32bo21bo76b2o$1055bo2bo32bo19bob2o
73b3o$1055bobo2bo28b3o23bo29bo5bo35bob2o35b3o$1037b2o17bo23b3o28bo2bob
o28b2o3b2o34bobo26b3o9b3o$1037bobo17b2obo19bo32bo2bo28b2o3b2o34bo2bo4b
o5bo15bo$1040bo18bo21bo32b2o30bo3bo6b2o28b2o5bo5bo$1041bo115bo36b2o3b
2o$1042bo23b2o37bo49bobo27bo19bobo5b2o3b2o$1043bo23bo36b3o9b3o17bo18b
2o27bo2bo2b3o2b2ob2o2b2ob2o8bobo$1044bo19b3o48b3o17bo2bo13b2o30bo2bo
16bobo5bo7bo$1045bo18bo70bo2bo5b3o4bobo32bo7b2o3b2o12b2o3b2o$1046bo31b
2o57bo5bo3bo5bo40bo5bo$1047bo29b3o63bo3bo38bo7bo5bo$1048bo27bob2o35b3o
19bo5bo3bo16b2o3b2o13bo2bo$1049bo25bobo26b3o9b3o16bo2bo5b3o16bo7bo12bo
2bo$1050bo24bo2bo4bo5bo15bo29bo2bo13b3o11bobo16bo18b2o$1051bo24b2o5bo
5bo30bobo13bo7b3o17b2o3b2o33bobo$1052bo30b2o3b2o30b2o21bo3bo3bobo52bo$
1053bo20bo19bobo5b2o3b2o12bo16b2o3bo3bo2b2obo41bo3bo6b2o$1054bo18bo2bo
2b3o2b2ob2o2b2ob2o8bobo30bo2bo6bo2bo2bo10bo5bo23b2o3b2o$1046bo8bo17bo
2bo16bobo5bo7bo27bobo4b3o4b2o25b3o13b2o3b2o$1047b2o7bo18bo7b2o3b2o12b
2o3b2o29bob2o35b3o14bo5bo$1046b2o9bo25bo5bo49b3o$1058bo16bo7bo5bo50b2o
$1059bo13bo2bo49bo$1060bo12bo2bo49b3o35bo5bo6b3o$1061bo12bo54bo34bobob
obo7b3o$1062bo65b2o34bo5bo$1063bo103bo$1064bo19bo3bo32bo32b3o10bo8b2o$
1065bo17b2o3b2o29b2obo33bo10bo7bo2bo$1066bo16b2o3b2o28bo36bo17bo2bobo$
1067bo15bo5bo27bobo2bo17bo36bo$1068bo48bo2bo7bo10bo33bob2o$1069bo48b2o
8bo10b3o32bo$1070bo32bo24bo$1071bo29bobo21bo5bo34b2o$1072bo29b2o11b3o
7bobobobo34bo$1073bo42b3o6bo5bo35b3o$1074bo94bo$1075bo78b2o$1076bo77b
3o$1077bo38b3o35b2obo$1078bo36b3o25b2o4b3o4bobo$1079bo45bo5bo10bo2bo2b
o6bo2bo$1080bo61bob2o2bo3bo3b2o$1081bo60bobo3bo3bo$1082bo42b2o3b2o17b
3o7bo$1083bo43bobo11b3o13bo2bo$1084bo39bo7bo16b3o5bo2bo$1085bo32bo6b2o
3b2o16bo3bo5bo$1086bo29bobo29bo3bo$1087bo29b2o23bo5bo3bo5bo$1088bo53bo
bo4b3o5bo2bo$1089bo52b2o13bo2bo$1090bo68bo$1091bo$1092bo$1093bo51bo3bo
$1094bo49b2o3b2o$1095bo48b2o3b2o$1096bo47bo5bo$1097bo$1098bo$1099bo$
1100bo$1101bo$1102bo$1103bo$1104bo$1105bo$1106bo$1107bo$1108bo$1109bo$
1110bo$1111bo$1110b2o7$1118b2o$1118bobo$1121bo$1122bo$1123bo$1124bo$
1125bo$1126bo$1127bo$1128bo$1129bo$1130bo$1131bo$1132bo$1133bo$1134bo$
1135bo2b2o$1134b2o2b2o168$bo2722bo$obo2720bobo$2o2722b2o!

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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » May 7th, 2018, 4:38 am

Ripping some useful particles for signal circuitry from David Bell's article:

HighLife - An Interesting Variant of Life (part 1/3) - 7 May 1994)

Fig. 45

Code: Select all

#C B3aeijknqry6ci/S23aeijnqry - B34q5ckr67c/S234qy5eknr6an78
x = 23, y = 23, rule = B36/S2378
2bo$obo$b2o10bo$4b2o6bob2o$6bo4bo3bo$12bob2o$2bo10bo5b2o$bo17bobo$bo3b
o15bo$21b2o$2b3o$2bobo$2bobo$2b3o6$5b2o$5bo$6b3o$8bo!
Fig. 46

Code: Select all

#C B3aeijknqry6ci/S23aijnqry - B34kqz5cjkr67c/S234eqty5aeknr6akn78
x = 35, y = 13, rule = B36/S2378
15bo$13bobo$14b2o9bo$17bo3bo3bo$16bo2bo3b2obo$9bo11bo3bo$9bo3bo11bo5b
2o$8bob2o3bo2bo12bobo$9bo3bo3bo15bo$2b2o5bo23b2o$bobo$bo$2o!
Fig. 57a

Code: Select all

#C B36ckn/S23 - B34z5ek67e/S234cz5e6i8
x = 36, y = 27, rule = B36/S238
2o$2o2$16bo$15b3o$14b3obo$13b2o2b3o$12b2o3b2obo$11b3o2b2ob3o$12bob3ob
3obo$13b3ob2o2b3o$14bob2o3b2obo$15b3o2b2ob3o$16bob3ob3obo$17b3ob2o2b3o
$18bob2o3b2obo$19b3o2b2ob3o$20bob3ob3obo3bo$21b3ob2o2b3ob2o$22bob2o3b
2o2bobo$23b3o2b2o$24bob3o$25b3o$26bo2$25b2o$25b2o!
Fig. 57b

Code: Select all

#C B36ckn/S23 - B34z5ek67e8/S234cz5e6i7e8
x = 36, y = 27, rule = B368/S238
2o$2o2$16bo$15b3o$14b3obo$13b2o2b3o$12b2o3b2obo$11b3o2b2ob3o$12bob3ob
3obo$13b3ob2o2b3o$14bob2o3b2obo$15b3o2b2ob3o$16bob3ob3obo$17b3ob2o2b3o
$18bob2o3b2obo$19b3o2b2ob3o$20bob3ob3obo$21b3ob2o2b3ob3o$22bob2o3b2o2b
o$23b3o2b2o4bo$24bob3o$25b3o$26bo2$25b2o$25b2o!
Fig. 58

Code: Select all

#C B36ckn/S23aceijnqry - B34qz5ek67e8/S234cz5en6i7e8
x = 37, y = 27, rule = B368/S238
2o$2o$16bo$15b2o$14b2ob2o$13bo$12bo5bobo$11b2o$10b2o6bobobo$12bo4bo$
12bobobo5bobo2$14bobo5bobobo$21bo$16bobobo5bobo2$18bobo5bobobo$25bo4bo
$20bobobo6b2o$30b2o2b2o$22bobo5bo3bobo$29bo4bo$24b2ob2o$25bobo$24bo$
24bo2bo$25b2o!
Fig. 43 modified based on the article's instructions - become a signal duplicator

Code: Select all

#C B36cin/S23 - B34z5r6/S235r6n7e8
x = 44, y = 47, rule = B36/S238
21bo$19b3o$18bo$18b2o2$15b3o$14bo3bo$14bo3bo2$15b3o$15bobo$15bobo$15b
3o3$35b2o$2o33bo5bobo$bo31bobo5b2o$bobo29b2o7bo$2b2o3bo17b2ob3o$6b4obo
12b3obobo$5b2obobob2o11b2ob3o$6b4obo7bo$7bo9bobo$18b2o2$8bo$8b3o$11bo
13bo$10b2o11bobo$17bo2b2o2b2o$17bo4bo$17bo4bo$14b5o$17bobo$18b5o$14bo
4bo$14bo4bo$15b2o2bo5$29b2o$29bo$30b3o$32bo!
For later use, of course. Inserted all patterns with their longest compatible outer-totalistic rulestring.

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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » May 7th, 2018, 6:28 pm

Naszvadi wrote:...
Fig. 43 modified based on the article's instructions - become a signal duplicator

Code: Select all

#C B36cin/S23 - B34z5r6/S235r6n7e8
x = 44, y = 47, rule = B36/S238
21bo$19b3o$18bo$18b2o2$15b3o$14bo3bo$14bo3bo2$15b3o$15bobo$15bobo$15b
3o3$35b2o$2o33bo5bobo$bo31bobo5b2o$bobo29b2o7bo$2b2o3bo17b2ob3o$6b4obo
12b3obobo$5b2obobob2o11b2ob3o$6b4obo7bo$7bo9bobo$18b2o2$8bo$8b3o$11bo
13bo$10b2o11bobo$17bo2b2o2b2o$17bo4bo$17bo4bo$14b5o$17bobo$18b5o$14bo
4bo$14bo4bo$15b2o2bo5$29b2o$29bo$30b3o$32bo!
For later use, of course. Inserted all patterns with their longest compatible outer-totalistic rulestring.
Now, a p192 duplicator puzzled by me that supports more outer-totalistic rules - for comparison, near placed an inputless clone instance:

Code: Select all

#C B36ckn/S23 - B34z5ek67e8/S234c6i8
x = 180, y = 79, rule = B368/S238
o$b2o$2o4$97b2o$97bo$95bobo$95b2o10$45bo$45b3o$48bo$47b2o2$98b2o78b2o$
98b2o78b2o16$67b2o2bo75b2o2bo$66bo4bo74bo4bo$66bo4bo74bo4bo$70b5o75b5o
$69bobo77bobo$66b5o75b5o$69bo4bo74bo4bo$48bo20bo4bo74bo4bo$49b2o18bo2b
2o75bo2b2o$48b2o2$7b2o78b2o$7b2o78b2o$48b3o77b3o$50bo79bo$49bo79bo$51b
2o2bo75b2o2bo$26bo23bo4bo50bo23bo4bo$25bo24bo4bo49bo24bo4bo$26b3o25b5o
47b3o25b5o$26b4o23bobo50b4o23bobo$22bo2bo3bo20b5o47bo2bo3bo20b5o$21bob
2o28bo4bo42bob2o28bo4bo$23b2o6b2o20bo4bo44b2o6b2o20bo4bo$23b2o7b2o19bo
2b2o45b2o7b2o19bo2b2o$24b2o6b2o70b2o6b2o$32b2obo76b2obo$27bo3bo2bo72bo
3bo2bo$27b4o76b4o$28b3o9b2o66b3o9b2o$31bo8b2o69bo8b2o$30bo79bo$49b2o
78b2o$42bo6b2o71bo6b2o$40bobo77bobo$41bobo77bobo$32b2o7bo70b2o7bo$32b
2o78b2o!

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Redstoneboi
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Re: List of the Turing-complete totalistic life-like CA

Post by Redstoneboi » June 15th, 2018, 1:39 am

is this TC? (if everything is infinitely repeated along the x axis)
it's very similar to LWoD, though there is a 1 cell reflector, 1 cell ladder destroyer, and a splitter.

Code: Select all

x = 136, y = 141, rule = B3/S0123456
23bo8$128bo4$78bo2$104bo20$135bo4$39bo32$35bo4$15bo31$43bo4$43bo5$8b3o
$7b4o$7b6o$7bobo2bo$6b5ob2o$7bo2bobo$6b2ob5o$7bobo2bo$6b2obo2b2o9$50bo
2$obobo$8o$4bob3o$3ob5o$2b3ob3o$2bo3bo$7o$obobo!
c(>^w^<c)~*
This is 「Fluffy」
「Fluffy」is my sutando.
「Fluffy」has the ability to engineer r e p l i c a t o r s.
「Fluffy」likes to watch spaceship guns in Golly.
「Fluffy」knows Natsuki best girl.

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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » July 29th, 2018, 5:57 pm

4 rules between Highlife and LowDeath are Turing-complete. They are:
  • B36/S23
  • B368/S23
  • B36/S238
  • B368/S238
TODO: Printer, more checks, determine supporting isotropic rules.
Thanks: To the contributors of David Bell's HighLife.txt, many partials and reactions are from there.

Six unit cells in a 9-generations loop on a closed strip with initial pattern 111000 - each unit cell has period 2688 and height 584. Four very long boats mark corners (little bit skew), and two more inner very long boats denote a glider in an inverted glider stream, which absense in every 2688 generations means that the cell is ALIVE - dead otherwise.

Code: Select all

#C Naszvadi, Peter, 2014-2018. Polyglot Unit Cell for rules: B36[8]/S23[8], virtual pattern is (111000)
x = 400, y = 3504, rule = B36/S23:T0,3504
398b2o$2o395bobo$obo393bobo$bobo391bobo$2bobo391bo$3bo50$267b2o$267b2o
13$277bo$276b3o$275b2ob2o$274b2ob2o$273b2ob2o$274b3o$275bo2$285bo$284b
3o$283b2ob2o$282b2ob2o5b2o$281b2ob2o6b2o$282b3o$283bo24$296b2o$297bo$
294b3o$294bo74$397bo$395b2o$391b2o4b2o$391b2o3bo7$398b2o$398b2o7$380b
3o$376b2o5bo$378bo4bo$374bo8bo$374bo$375bo5bo$382bo$373bo8bo$373bo4bo$
373bo5b2o$374b3o$351bo$351b2o$350bobo11$179b2o$179b2o11$171b3o$170bo3b
o$170bo4bo$170bo2bo2bo$167b3obo4bo$166bo3bobo3bo172b2o$166bo4bob3o173b
2o$166bo2bo2bo$163b3obo4bo$162bo3bobo3bo$162bo4bob3o$162bo2bo2bo$159b
3obo4bo$158bo3bobo3bo$158bo4bob3o$158bo2bo2bo$159bo4bo$160bo3bo$161b3o
5$303bo$303b2o$302bobo3$62b2o$62b2o8$57bo72b2o$56b3o71b2o$55bob3o$54b
3o2b2o$55b2o3b2o$56b2o2b3o$57b3obo$58b3o$59bo72bo4b2o$132bobo2b2o6bobo
15b2o$131bobo12b2o15bo$133bo12bo14bobo$161b2o4$37b2o$37b2o$140bo$139bo
bo$140bobo35b2o$47bobo91bobo34b2o$48b2o92b2o$2o46bo$2o$146b3o$148bo$
147bo$281b2o$281b2o8bo$151b2o136b2o$19b3o129bobo137b2o$18bo3bo129bobo
135bo7b2o$17bo4bo130bobo142b2o$16bo2bo2bo131bo100bo$16bo4bob3o229b2o
32b2o$16bo3bobo3bo227bobo32b2o$17b3obo4bo$20bo2bo2bo$20bo4bo$20bo3bo
248b3o$21b3o26b2o220bo3bo$49bobo220bo4bo$49bo163b3o56bo2bo2bo11bo$48b
2o162bo56b3obo4bo12b2o$71bobo137bo3bobo50bo3bobo3bo11b2o$72b2o136bo57b
o4bob3o$72bo136bo7bobo48bo2bo2bo$25b2o182bo6bo48b3obo4bo$25b2o14b2o79b
3o84bobo3bo3bobo42bo3bobo3bo$40b2o82bo89bo6bo42bo4bob3o$42bo80bo87bobo
7bo42bo2bo2bo$220bo40b3obo4bo27b2o$213bobo3bo36b2o2bo3bobo3bo27b2o$
218bo37b2o2bo4bob3o$215b3o42bo2bo2bo$261bo4bo$262bo3bo$263b3o3$324bo$
235b2o86b3o$235b2o85b3obo$321b2o2b3o$320b2o3b2o$236bo82b3o2b2o$237b2o
81bob3o$235b2o84b3o$227b2o8bo84bo9bo$227b2o102b3o$330b3obo$329b2o2b3o$
65b2o31b3o227b2o3b2o$64b2o34bo226b3o2b2o$66bo32bo228bob3o$90b2o237b3o$
89bo3bo236bo$89bo6bo$90bo4bo$94b2o$292b2o53b2o$292b2o53b2o3$109b2o$
348b2o$348b2o2$105bo4b3o$105bo3bobo$109b2o237bo$109bo237b2o$346bobo$
345b3o2$351b3o$89b2o172b2o85bobo$88b2o175bo84b2o$90bo170b2ob2o84bo5bo$
261b2o2b2o88b2o$259bo6b3o85bobo$114b2o143bobo5bobo83b3o$114b2o144b3o6b
o$262b2o2b2o91b3o$263b2ob2o90bobo$263bo94b2o$264b2o92bo2$201b2o$201b2o
$242b2o129b2o$241bobo129b2o$243bo3b2o$249bo$221bo23b2ob2o$220b2o23b2o
2b2o$219b2ob2o19bo6b3o$218bo24bobo5bobo$217bo5bobo18b3o6bo$216b2o28b2o
2b2o$113b2o100b2o6bobobo19b2ob2o$112b2o103bo4bo4bo19bo$114bo102bobobo
6b2o18b2o$227b2o$219bobo5bo$226bo$221b2ob2o8b2o$223b2o9b2o$223bo$243b
2o$211b2o23bo6b2o$211b2o21bobo$235bobo11bo$226b2o7bo11b3o$226b2o18bo$
246b2o9$137b2o$136b2o$138bo$223bo$222b2o$221bobo$220b3o2$226b3o$225bob
o$225b2o$225bo10b2o$236b2o12$161b2o$160b2o$162bo$239bo$238b2o$212bo25b
obo$211bo$211b3o17$185b2o$184b2o$186bo$263bo$262b2o$262bobo$279bo$279b
obo$274b2o2bobo$199b2o73b2o4bo$199b2o5$180bo$180b2o99b2o$178b2ob2o98b
2o$183bo83b3o$176bobo5bo81bo3bo$184b2o80bo4bo$174bobobo6b2o79bo2bo2bo$
174bo4bo4bo82bo4bo$172b2o6bobobo41b2o2bo37bo3bo$173b2o50bo4bo38b3o$
174bo5bobo42bo4bo$175bo53b5o3b2o$176b2ob2o47bobo6b2o$177b2o46b5o$178bo
49bo4bo$228bo4bo$218b2o2bo5bo2b2o$217bo4bo$217bo4bo$174b2o45b5o$174b2o
44bobo$217b5o35b2o$220bo4bo$220bo4bo$220bo2b2o2$256b2o$256b2o9$212b2o$
212b2o58$396bo$3bo391bobo$2bobo391bobo$bobo393bobo$obo395b2o$2o$398b2o
$2o395bobo$obo393bobo$bobo391bobo$2bobo391bo$3bo50$267b2o$267b2o13$
277bo$276b3o$275b2ob2o$274b2ob2o$273b2ob2o$274b3o$275bo2$285bo$284b3o$
283b2ob2o$282b2ob2o5b2o$281b2ob2o6b2o$282b3o$283bo24$296b2o$297bo$294b
3o$294bo74$397bo$395b2o$391b2o4b2o$391b2o3bo7$398b2o$398b2o7$380b3o$
376b2o5bo$378bo4bo$374bo8bo$374bo$375bo5bo$382bo$373bo8bo$373bo4bo$
373bo5b2o$374b3o$351bo$351b2o$350bobo11$179b2o$179b2o11$171b3o$170bo3b
o$170bo4bo$170bo2bo2bo$167b3obo4bo$166bo3bobo3bo172b2o$166bo4bob3o173b
2o$166bo2bo2bo$163b3obo4bo$162bo3bobo3bo$162bo4bob3o$162bo2bo2bo$159b
3obo4bo$158bo3bobo3bo$158bo4bob3o$158bo2bo2bo$159bo4bo$160bo3bo$161b3o
5$303bo$303b2o$302bobo3$62b2o$62b2o8$57bo72b2o$56b3o71b2o$55bob3o$54b
3o2b2o$55b2o3b2o$56b2o2b3o$57b3obo$58b3o$59bo72bo4b2o$132bobo2b2o6bobo
15b2o$131bobo12b2o15bo$133bo12bo14bobo$161b2o4$37b2o$37b2o$140bo$139bo
bo$140bobo35b2o$47bobo91bobo34b2o$48b2o92b2o$2o46bo$2o$146b3o$148bo$
147bo$281b2o$281b2o8bo$151b2o136b2o$19b3o129bobo137b2o$18bo3bo129bobo
135bo7b2o$17bo4bo130bobo142b2o$16bo2bo2bo131bo100bo$16bo4bob3o229b2o
32b2o$16bo3bobo3bo227bobo32b2o$17b3obo4bo$20bo2bo2bo$20bo4bo$20bo3bo
248b3o$21b3o26b2o220bo3bo$49bobo220bo4bo$49bo163b3o56bo2bo2bo11bo$48b
2o162bo56b3obo4bo12b2o$71bobo137bo3bobo50bo3bobo3bo11b2o$72b2o136bo57b
o4bob3o$72bo136bo7bobo48bo2bo2bo$25b2o182bo6bo48b3obo4bo$25b2o14b2o79b
3o84bobo3bo3bobo42bo3bobo3bo$40b2o82bo89bo6bo42bo4bob3o$42bo80bo87bobo
7bo42bo2bo2bo$220bo40b3obo4bo27b2o$213bobo3bo36b2o2bo3bobo3bo27b2o$
218bo37b2o2bo4bob3o$215b3o42bo2bo2bo$261bo4bo$262bo3bo$263b3o3$324bo$
235b2o86b3o$235b2o85b3obo$321b2o2b3o$320b2o3b2o$236bo82b3o2b2o$237b2o
81bob3o$235b2o84b3o$227b2o8bo84bo9bo$227b2o102b3o$330b3obo$329b2o2b3o$
65b2o31b3o227b2o3b2o$64b2o34bo226b3o2b2o$66bo32bo228bob3o$90b2o237b3o$
89bo3bo236bo$89bo6bo$90bo4bo$94b2o$292b2o53b2o$292b2o53b2o3$109b2o$
348b2o$348b2o2$105bo4b3o$105bo3bobo$109b2o237bo$109bo237b2o$346bobo$
345b3o2$351b3o$89b2o172b2o85bobo$88b2o175bo84b2o$90bo170b2ob2o84bo5bo$
261b2o2b2o88b2o$259bo6b3o85bobo$114b2o143bobo5bobo83b3o$114b2o144b3o6b
o$262b2o2b2o91b3o$263b2ob2o90bobo$263bo94b2o$264b2o92bo2$201b2o$201b2o
$242b2o129b2o$241bobo129b2o$243bo3b2o$249bo$221bo23b2ob2o$220b2o23b2o
2b2o$219b2ob2o19bo6b3o$218bo24bobo5bobo$217bo5bobo18b3o6bo$216b2o28b2o
2b2o$113b2o100b2o6bobobo19b2ob2o$112b2o103bo4bo4bo19bo$114bo102bobobo
6b2o18b2o$227b2o$219bobo5bo$226bo$221b2ob2o8b2o$223b2o9b2o$223bo$243b
2o$211b2o23bo6b2o$211b2o21bobo$235bobo11bo$226b2o7bo11b3o$226b2o18bo$
246b2o9$137b2o$136b2o$138bo$223bo$222b2o$221bobo$220b3o2$226b3o$225bob
o$225b2o$225bo10b2o$236b2o12$161b2o$160b2o$162bo$239bo$238b2o$212bo25b
obo$211bo$211b3o17$185b2o$184b2o$186bo$263bo$262b2o$262bobo$279bo$279b
obo$274b2o2bobo$199b2o73b2o4bo$199b2o5$180bo$180b2o99b2o$178b2ob2o98b
2o$183bo83b3o$176bobo5bo81bo3bo$184b2o80bo4bo$174bobobo6b2o79bo2bo2bo$
174bo4bo4bo82bo4bo$172b2o6bobobo41b2o2bo37bo3bo$173b2o50bo4bo38b3o$
174bo5bobo42bo4bo$175bo53b5o3b2o$176b2ob2o47bobo6b2o$177b2o46b5o$178bo
49bo4bo$228bo4bo$218b2o2bo5bo2b2o$217bo4bo$217bo4bo$174b2o45b5o$174b2o
44bobo$217b5o35b2o$220bo4bo$220bo4bo$220bo2b2o2$256b2o$256b2o9$212b2o$
212b2o58$396bo$3bo391bobo$2bobo391bobo$bobo393bobo$obo395b2o$2o$398b2o
$2o395bobo$obo393bobo$bobo391bobo$2bobo391bo$3bo50$267b2o$267b2o13$
277bo$276b3o$275b2ob2o$274b2ob2o$273b2ob2o$274b3o$275bo2$285bo$284b3o$
283b2ob2o$282b2ob2o5b2o$281b2ob2o6b2o$282b3o$283bo24$296b2o$297bo$294b
3o$294bo74$397bo$395b2o$391b2o4b2o$391b2o3bo7$398b2o$398b2o7$380b3o$
376b2o5bo$378bo4bo$374bo8bo$374bo$375bo5bo$382bo$373bo8bo$373bo4bo$
373bo5b2o$374b3o$351bo$351b2o$350bobo11$179b2o$179b2o11$171b3o$170bo3b
o$170bo4bo$170bo2bo2bo$167b3obo4bo$166bo3bobo3bo172b2o$166bo4bob3o173b
2o$166bo2bo2bo$163b3obo4bo$162bo3bobo3bo$162bo4bob3o$162bo2bo2bo$159b
3obo4bo$158bo3bobo3bo$158bo4bob3o$158bo2bo2bo$159bo4bo$160bo3bo$161b3o
5$303bo$303b2o$302bobo3$62b2o$62b2o8$57bo72b2o$56b3o71b2o$55bob3o$54b
3o2b2o$55b2o3b2o$56b2o2b3o$57b3obo$58b3o$59bo72bo4b2o$132bobo2b2o6bobo
15b2o$131bobo12b2o15bo$133bo12bo14bobo$161b2o4$37b2o$37b2o$140bo$139bo
bo$140bobo35b2o$47bobo91bobo34b2o$48b2o92b2o$2o46bo$2o$146b3o$148bo$
147bo$281b2o$281b2o8bo$151b2o136b2o$19b3o129bobo137b2o$18bo3bo129bobo
135bo7b2o$17bo4bo130bobo142b2o$16bo2bo2bo131bo100bo$16bo4bob3o229b2o
32b2o$16bo3bobo3bo227bobo32b2o$17b3obo4bo$20bo2bo2bo$20bo4bo$20bo3bo
248b3o$21b3o26b2o220bo3bo$49bobo220bo4bo$49bo163b3o56bo2bo2bo11bo$48b
2o162bo56b3obo4bo12b2o$71bobo137bo3bobo50bo3bobo3bo11b2o$72b2o136bo57b
o4bob3o$72bo136bo7bobo48bo2bo2bo$25b2o182bo6bo48b3obo4bo$25b2o14b2o79b
3o84bobo3bo3bobo42bo3bobo3bo$40b2o82bo89bo6bo42bo4bob3o$42bo80bo87bobo
7bo42bo2bo2bo$220bo40b3obo4bo27b2o$213bobo3bo36b2o2bo3bobo3bo27b2o$
218bo37b2o2bo4bob3o$215b3o42bo2bo2bo$261bo4bo$262bo3bo$263b3o3$324bo$
235b2o86b3o$235b2o85b3obo$321b2o2b3o$320b2o3b2o$236bo82b3o2b2o$237b2o
81bob3o$235b2o84b3o$227b2o8bo84bo9bo$227b2o102b3o$330b3obo$329b2o2b3o$
98b3o227b2o3b2o$100bo226b3o2b2o$99bo228bob3o$90b2o237b3o$89bo3bo236bo$
89bo6bo$90bo4bo$94b2o$292b2o53b2o$292b2o53b2o3$109b2o$348b2o$348b2o2$
105bo4b3o$105bo3bobo$109b2o237bo$109bo237b2o$346bobo$345b3o2$351b3o$
89b2o172b2o85bobo$88b2o175bo84b2o$90bo170b2ob2o84bo5bo$261b2o2b2o88b2o
$259bo6b3o85bobo$114b2o143bobo5bobo83b3o$114b2o144b3o6bo$262b2o2b2o91b
3o$263b2ob2o90bobo$263bo94b2o$264b2o92bo2$201b2o$201b2o$242b2o129b2o$
241bobo129b2o$243bo3b2o$249bo$221bo23b2ob2o$220b2o23b2o2b2o$219b2ob2o
19bo6b3o$218bo24bobo5bobo$217bo5bobo18b3o6bo$216b2o28b2o2b2o$113b2o
100b2o6bobobo19b2ob2o$112b2o103bo4bo4bo19bo$114bo102bobobo6b2o18b2o$
227b2o$219bobo5bo$226bo$221b2ob2o8b2o$223b2o9b2o$223bo$243b2o$211b2o
23bo6b2o$211b2o21bobo$235bobo11bo$226b2o7bo11b3o$226b2o18bo$246b2o9$
137b2o$136b2o$138bo$223bo$222b2o$221bobo$220b3o2$226b3o$225bobo$225b2o
$225bo10b2o$236b2o12$161b2o$160b2o$162bo$239bo$238b2o$212bo25bobo$211b
o$211b3o17$185b2o$184b2o$186bo$263bo$262b2o$262bobo$279bo$279bobo$274b
2o2bobo$199b2o73b2o4bo$199b2o5$180bo$180b2o99b2o$178b2ob2o98b2o$183bo
83b3o$176bobo5bo81bo3bo$184b2o80bo4bo$174bobobo6b2o79bo2bo2bo$174bo4bo
4bo82bo4bo$172b2o6bobobo41b2o2bo37bo3bo$173b2o50bo4bo38b3o$174bo5bobo
42bo4bo$175bo53b5o3b2o$176b2ob2o47bobo6b2o$177b2o46b5o$178bo49bo4bo$
228bo4bo$218b2o2bo5bo2b2o$217bo4bo$217bo4bo$174b2o45b5o$174b2o44bobo$
217b5o35b2o$220bo4bo$220bo4bo$220bo2b2o2$256b2o$256b2o9$212b2o$212b2o
58$396bo$3bo391bobo$2bobo391bobo$bobo393bobo$obo395b2o$2o$398b2o$2o
395bobo$obo393bobo$bobo391bobo$2bobo391bo$3bo50$267b2o$267b2o13$277bo$
276b3o$275b2ob2o$274b2ob2o$273b2ob2o$274b3o$275bo2$285bo$284b3o$283b2o
b2o$282b2ob2o5b2o$281b2ob2o6b2o$282b3o$283bo24$296b2o$297bo$294b3o$
294bo74$397bo$395b2o$391b2o4b2o$391b2o3bo7$398b2o$398b2o7$380b3o$376b
2o5bo$378bo4bo$374bo8bo$374bo$375bo5bo$382bo$373bo8bo$373bo4bo$373bo5b
2o$374b3o$351bo$351b2o$350bobo11$179b2o$179b2o11$171b3o$170bo3bo$170bo
4bo$170bo2bo2bo$167b3obo4bo$166bo3bobo3bo172b2o$166bo4bob3o173b2o$166b
o2bo2bo$163b3obo4bo$162bo3bobo3bo$162bo4bob3o$162bo2bo2bo$159b3obo4bo$
158bo3bobo3bo$158bo4bob3o$158bo2bo2bo$159bo4bo$160bo3bo$161b3o5$303bo$
303b2o$302bobo3$62b2o$62b2o8$57bo72b2o$56b3o71b2o$55bob3o$54b3o2b2o$
55b2o3b2o$56b2o2b3o$57b3obo$58b3o$59bo72bo4b2o$132bobo2b2o6bobo15b2o$
131bobo12b2o15bo$133bo12bo14bobo$161b2o4$37b2o$37b2o$140bo$139bobo$
140bobo35b2o$47bobo91bobo34b2o$48b2o92b2o$2o46bo$2o$146b3o$148bo$147bo
$281b2o$281b2o8bo$151b2o136b2o$19b3o129bobo137b2o$18bo3bo129bobo135bo
7b2o$17bo4bo130bobo142b2o$16bo2bo2bo131bo100bo$16bo4bob3o229b2o32b2o$
16bo3bobo3bo227bobo32b2o$17b3obo4bo$20bo2bo2bo$20bo4bo$20bo3bo248b3o$
21b3o26b2o220bo3bo$49bobo220bo4bo$49bo163b3o56bo2bo2bo11bo$48b2o162bo
56b3obo4bo12b2o$71bobo137bo3bobo50bo3bobo3bo11b2o$72b2o136bo57bo4bob3o
$72bo136bo7bobo48bo2bo2bo$25b2o182bo6bo48b3obo4bo$25b2o14b2o79b3o84bob
o3bo3bobo42bo3bobo3bo$40b2o82bo89bo6bo42bo4bob3o$42bo80bo87bobo7bo42bo
2bo2bo$220bo40b3obo4bo27b2o$213bobo3bo36b2o2bo3bobo3bo27b2o$218bo37b2o
2bo4bob3o$215b3o42bo2bo2bo$261bo4bo$262bo3bo$263b3o3$324bo$235b2o86b3o
$235b2o85b3obo$321b2o2b3o$320b2o3b2o$236bo82b3o2b2o$237b2o81bob3o$235b
2o84b3o$227b2o8bo84bo9bo$227b2o102b3o$330b3obo$329b2o2b3o$98b3o227b2o
3b2o$100bo226b3o2b2o$99bo228bob3o$90b2o237b3o$89bo3bo236bo$89bo6bo$90b
o4bo$94b2o$292b2o53b2o$292b2o53b2o3$109b2o$348b2o$348b2o2$105bo4b3o$
105bo3bobo$109b2o237bo$109bo237b2o$346bobo$345b3o2$351b3o$89b2o172b2o
85bobo$88b2o175bo84b2o$90bo170b2ob2o84bo5bo$261b2o2b2o88b2o$259bo6b3o
85bobo$114b2o143bobo5bobo83b3o$114b2o144b3o6bo$262b2o2b2o91b3o$263b2ob
2o90bobo$263bo94b2o$264b2o92bo2$201b2o$201b2o$242b2o129b2o$241bobo129b
2o$243bo3b2o$249bo$221bo23b2ob2o$220b2o23b2o2b2o$219b2ob2o19bo6b3o$
218bo24bobo5bobo$217bo5bobo18b3o6bo$216b2o28b2o2b2o$113b2o100b2o6bobob
o19b2ob2o$112b2o103bo4bo4bo19bo$114bo102bobobo6b2o18b2o$227b2o$219bobo
5bo$226bo$221b2ob2o8b2o$223b2o9b2o$223bo$243b2o$211b2o23bo6b2o$211b2o
21bobo$235bobo11bo$226b2o7bo11b3o$226b2o18bo$246b2o9$137b2o$136b2o$
138bo$223bo$222b2o$221bobo$220b3o2$226b3o$225bobo$225b2o$225bo10b2o$
236b2o12$161b2o$160b2o$162bo$239bo$238b2o$212bo25bobo$211bo$211b3o17$
185b2o$184b2o$186bo$263bo$262b2o$262bobo$279bo$279bobo$274b2o2bobo$
199b2o73b2o4bo$199b2o5$180bo$180b2o99b2o$178b2ob2o98b2o$183bo83b3o$
176bobo5bo81bo3bo$184b2o80bo4bo$174bobobo6b2o79bo2bo2bo$174bo4bo4bo82b
o4bo$172b2o6bobobo41b2o2bo37bo3bo$173b2o50bo4bo38b3o$174bo5bobo42bo4bo
$175bo53b5o3b2o$176b2ob2o47bobo6b2o$177b2o46b5o$178bo49bo4bo$228bo4bo$
218b2o2bo5bo2b2o$217bo4bo$217bo4bo$174b2o45b5o$174b2o44bobo$217b5o35b
2o$220bo4bo$220bo4bo$220bo2b2o2$256b2o$256b2o9$212b2o$212b2o58$396bo$
3bo391bobo$2bobo391bobo$bobo393bobo$obo395b2o$2o$398b2o$2o395bobo$obo
393bobo$bobo391bobo$2bobo391bo$3bo50$267b2o$267b2o13$277bo$276b3o$275b
2ob2o$274b2ob2o$273b2ob2o$274b3o$275bo2$285bo$284b3o$283b2ob2o$282b2ob
2o5b2o$281b2ob2o6b2o$282b3o$283bo24$296b2o$297bo$294b3o$294bo74$397bo$
395b2o$391b2o4b2o$391b2o3bo7$398b2o$398b2o7$380b3o$376b2o5bo$378bo4bo$
374bo8bo$374bo$375bo5bo$382bo$373bo8bo$373bo4bo$373bo5b2o$374b3o$351bo
$351b2o$350bobo11$179b2o$179b2o11$171b3o$170bo3bo$170bo4bo$170bo2bo2bo
$167b3obo4bo$166bo3bobo3bo172b2o$166bo4bob3o173b2o$166bo2bo2bo$121bo
41b3obo4bo$119b2o41bo3bobo3bo$120b2o40bo4bob3o$162bo2bo2bo$159b3obo4bo
$158bo3bobo3bo$158bo4bob3o$158bo2bo2bo$159bo4bo$160bo3bo$161b3o5$303bo
$303b2o$302bobo3$62b2o$62b2o8$57bo72b2o$56b3o71b2o$55bob3o$54b3o2b2o$
55b2o3b2o$56b2o2b3o$57b3obo$58b3o$59bo72bo4b2o$132bobo2b2o6bobo15b2o$
131bobo12b2o15bo$133bo12bo14bobo$161b2o4$37b2o$37b2o$140bo$139bobo$
140bobo35b2o$47bobo91bobo34b2o$48b2o92b2o$2o46bo$2o$146b3o$148bo$147bo
$281b2o$281b2o8bo$151b2o136b2o$19b3o129bobo137b2o$18bo3bo129bobo135bo
7b2o$17bo4bo130bobo142b2o$16bo2bo2bo131bo100bo$16bo4bob3o229b2o32b2o$
16bo3bobo3bo227bobo32b2o$17b3obo4bo$20bo2bo2bo$20bo4bo$20bo3bo248b3o$
21b3o26b2o220bo3bo$49bobo220bo4bo$49bo163b3o56bo2bo2bo11bo$48b2o162bo
56b3obo4bo12b2o$71bobo137bo3bobo50bo3bobo3bo11b2o$72b2o136bo57bo4bob3o
$72bo136bo7bobo48bo2bo2bo$25b2o182bo6bo48b3obo4bo$25b2o14b2o79b3o84bob
o3bo3bobo42bo3bobo3bo$40b2o82bo89bo6bo42bo4bob3o$42bo80bo87bobo7bo42bo
2bo2bo$220bo40b3obo4bo27b2o$213bobo3bo36b2o2bo3bobo3bo27b2o$218bo37b2o
2bo4bob3o$215b3o42bo2bo2bo$261bo4bo$262bo3bo$263b3o3$324bo$235b2o86b3o
$235b2o85b3obo$321b2o2b3o$320b2o3b2o$236bo82b3o2b2o$237b2o81bob3o$235b
2o84b3o$227b2o8bo84bo9bo$227b2o102b3o$330b3obo$329b2o2b3o$65b2o31b3o
227b2o3b2o$64b2o34bo226b3o2b2o$66bo32bo228bob3o$90b2o237b3o$89bo3bo
236bo$89bo6bo$90bo4bo$94b2o$292b2o53b2o$292b2o53b2o3$109b2o$348b2o$
348b2o2$105bo4b3o$105bo3bobo$109b2o237bo$109bo237b2o$346bobo$345b3o2$
351b3o$89b2o172b2o85bobo$88b2o175bo84b2o$90bo170b2ob2o84bo5bo$261b2o2b
2o88b2o$259bo6b3o85bobo$114b2o143bobo5bobo83b3o$114b2o144b3o6bo$262b2o
2b2o91b3o$263b2ob2o90bobo$263bo94b2o$264b2o92bo2$201b2o$201b2o$242b2o
129b2o$241bobo129b2o$243bo3b2o$249bo$221bo23b2ob2o$220b2o23b2o2b2o$
219b2ob2o19bo6b3o$218bo24bobo5bobo$217bo5bobo18b3o6bo$216b2o28b2o2b2o$
113b2o100b2o6bobobo19b2ob2o$112b2o103bo4bo4bo19bo$114bo102bobobo6b2o
18b2o$227b2o$219bobo5bo$226bo$221b2ob2o8b2o$223b2o9b2o$223bo$243b2o$
211b2o23bo6b2o$211b2o21bobo$235bobo11bo$226b2o7bo11b3o$226b2o18bo$246b
2o9$137b2o$136b2o$138bo$223bo$222b2o$221bobo$220b3o2$226b3o$225bobo$
225b2o$225bo10b2o$236b2o12$161b2o$160b2o$162bo$239bo$238b2o$212bo25bob
o$211bo$211b3o17$185b2o$184b2o$186bo$263bo$262b2o$262bobo$279bo$279bob
o$274b2o2bobo$199b2o73b2o4bo$199b2o5$180bo$180b2o99b2o$178b2ob2o98b2o$
183bo83b3o$176bobo5bo81bo3bo$184b2o80bo4bo$174bobobo6b2o79bo2bo2bo$
174bo4bo4bo82bo4bo$172b2o6bobobo41b2o2bo37bo3bo$173b2o50bo4bo38b3o$
174bo5bobo42bo4bo$175bo53b5o3b2o$176b2ob2o47bobo6b2o$177b2o46b5o$178bo
49bo4bo$228bo4bo$218b2o2bo5bo2b2o$217bo4bo$217bo4bo$174b2o45b5o$174b2o
44bobo$217b5o35b2o$220bo4bo$220bo4bo$220bo2b2o2$256b2o$256b2o9$212b2o$
212b2o58$396bo$3bo391bobo$2bobo391bobo$bobo393bobo$obo395b2o$2o$398b2o
$2o395bobo$obo393bobo$bobo391bobo$2bobo391bo$3bo50$267b2o$267b2o13$
277bo$276b3o$275b2ob2o$274b2ob2o$273b2ob2o$274b3o$275bo2$285bo$284b3o$
283b2ob2o$282b2ob2o5b2o$281b2ob2o6b2o$282b3o$283bo24$296b2o$297bo$294b
3o$294bo74$397bo$395b2o$391b2o4b2o$391b2o3bo7$398b2o$398b2o7$380b3o$
376b2o5bo$378bo4bo$374bo8bo$374bo$375bo5bo$382bo$373bo8bo$373bo4bo$
373bo5b2o$374b3o$351bo$351b2o$350bobo11$179b2o$179b2o11$171b3o$170bo3b
o$170bo4bo$170bo2bo2bo$167b3obo4bo$166bo3bobo3bo172b2o$166bo4bob3o173b
2o$166bo2bo2bo$163b3obo4bo$162bo3bobo3bo$162bo4bob3o$162bo2bo2bo$159b
3obo4bo$158bo3bobo3bo$158bo4bob3o$158bo2bo2bo$159bo4bo$160bo3bo$161b3o
5$303bo$303b2o$302bobo3$62b2o$62b2o8$57bo72b2o$56b3o71b2o$55bob3o$54b
3o2b2o$55b2o3b2o$56b2o2b3o$57b3obo$58b3o$59bo72bo4b2o$132bobo2b2o6bobo
15b2o$131bobo12b2o15bo$133bo12bo14bobo$161b2o4$37b2o$37b2o$140bo$139bo
bo$140bobo35b2o$47bobo91bobo34b2o$48b2o92b2o$2o46bo$2o$146b3o$148bo$
147bo$281b2o$281b2o8bo$151b2o136b2o$19b3o129bobo137b2o$18bo3bo129bobo
135bo7b2o$17bo4bo130bobo142b2o$16bo2bo2bo131bo100bo$16bo4bob3o229b2o
32b2o$16bo3bobo3bo227bobo32b2o$17b3obo4bo$20bo2bo2bo$20bo4bo$20bo3bo
248b3o$21b3o26b2o220bo3bo$49bobo220bo4bo$49bo163b3o56bo2bo2bo11bo$48b
2o162bo56b3obo4bo12b2o$71bobo137bo3bobo50bo3bobo3bo11b2o$72b2o136bo57b
o4bob3o$72bo136bo7bobo48bo2bo2bo$25b2o182bo6bo48b3obo4bo$25b2o14b2o79b
3o84bobo3bo3bobo42bo3bobo3bo$40b2o82bo89bo6bo42bo4bob3o$42bo80bo87bobo
7bo42bo2bo2bo$220bo40b3obo4bo27b2o$213bobo3bo36b2o2bo3bobo3bo27b2o$
218bo37b2o2bo4bob3o$215b3o42bo2bo2bo$261bo4bo$262bo3bo$263b3o3$324bo$
235b2o86b3o$235b2o85b3obo$321b2o2b3o$320b2o3b2o$236bo82b3o2b2o$237b2o
81bob3o$235b2o84b3o$227b2o8bo84bo9bo$227b2o102b3o$330b3obo$329b2o2b3o$
65b2o31b3o227b2o3b2o$64b2o34bo226b3o2b2o$66bo32bo228bob3o$90b2o237b3o$
89bo3bo236bo$89bo6bo$90bo4bo$94b2o$292b2o53b2o$292b2o53b2o3$109b2o$
348b2o$348b2o2$105bo4b3o$105bo3bobo$109b2o237bo$109bo237b2o$346bobo$
345b3o2$351b3o$89b2o172b2o85bobo$88b2o175bo84b2o$90bo170b2ob2o84bo5bo$
261b2o2b2o88b2o$259bo6b3o85bobo$114b2o143bobo5bobo83b3o$114b2o144b3o6b
o$262b2o2b2o91b3o$263b2ob2o90bobo$263bo94b2o$264b2o92bo2$201b2o$201b2o
$242b2o129b2o$241bobo129b2o$243bo3b2o$249bo$221bo23b2ob2o$220b2o23b2o
2b2o$219b2ob2o19bo6b3o$218bo24bobo5bobo$217bo5bobo18b3o6bo$216b2o28b2o
2b2o$113b2o100b2o6bobobo19b2ob2o$112b2o103bo4bo4bo19bo$114bo102bobobo
6b2o18b2o$227b2o$219bobo5bo$226bo$221b2ob2o8b2o$223b2o9b2o$223bo$243b
2o$211b2o23bo6b2o$211b2o21bobo$235bobo11bo$226b2o7bo11b3o$226b2o18bo$
246b2o9$137b2o$136b2o$138bo$223bo$222b2o$221bobo$220b3o2$226b3o$225bob
o$225b2o$225bo10b2o$236b2o12$161b2o$160b2o$162bo$239bo$238b2o$212bo25b
obo$211bo$211b3o17$185b2o$184b2o$186bo$263bo$262b2o$262bobo$279bo$279b
obo$274b2o2bobo$199b2o73b2o4bo$199b2o5$180bo$180b2o99b2o$178b2ob2o98b
2o$183bo83b3o$176bobo5bo81bo3bo$184b2o80bo4bo$174bobobo6b2o79bo2bo2bo$
174bo4bo4bo82bo4bo$172b2o6bobobo41b2o2bo37bo3bo$173b2o50bo4bo38b3o$
174bo5bobo42bo4bo$175bo53b5o3b2o$176b2ob2o47bobo6b2o$177b2o46b5o$178bo
49bo4bo$228bo4bo$218b2o2bo5bo2b2o$217bo4bo$217bo4bo$174b2o45b5o$174b2o
44bobo$217b5o35b2o$220bo4bo$220bo4bo$220bo2b2o2$256b2o$256b2o9$212b2o$
212b2o58$396bo$3bo391bobo$2bobo391bobo$bobo393bobo$obo395b2o$2o!

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Re: List of the Turing-complete totalistic life-like CA

Post by AforAmpere » July 30th, 2018, 12:22 pm

I don't know if this is off-topic, but is there any way we can prove that certain rules are not Turing-complete? B1 rules are trivially not Turing-complete, because every pattern expands at light speed, and so can't do the computation necessary (I believe). Is there some way to prove that any non-exploding rules are not Turing-complete?
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

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Macbi
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Re: List of the Turing-complete totalistic life-like CA

Post by Macbi » July 30th, 2018, 2:11 pm

AforAmpere wrote:I don't know if this is off-topic, but is there any way we can prove that certain rules are not Turing-complete? B1 rules are trivially not Turing-complete, because every pattern expands at light speed, and so can't do the computation necessary (I believe). Is there some way to prove that any non-exploding rules are not Turing-complete?
It depends on exactly how you define universal. For example universal computation in a B1 rule might occur on the exploding edge, the edge evolving in a certain way that corresponds to the operation of a Turing machine.

The problem of how to define when a cellular automaton (or automaton more generally) is universal has been studied in the literature, but I've never seen a satisfactory answer. The problem is that the input to the automaton has to be encoded in some way, and the output decoded. But if you allow the input encoding to be arbitrary then all automata become universal, because you can just allow the encoding function to do all of the computation. So you've got to choose a definition broad enough to allow all the kinds of encodings you want, while not allowing literally all computable functions.

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Re: List of the Turing-complete totalistic life-like CA

Post by Apple Bottom » July 31st, 2018, 5:28 am

AforAmpere wrote:I don't know if this is off-topic, but is there any way we can prove that certain rules are not Turing-complete? B1 rules are trivially not Turing-complete, because every pattern expands at light speed, and so can't do the computation necessary (I believe). Is there some way to prove that any non-exploding rules are not Turing-complete?
A general avenue for proving non-universality might be, I think, proving simulatibility (I sure hope that's a word!) in some other model of computation that is known to not be Turing-complete. Whether that's feasible for 2-dimensional CAs on infinite grids (outer-totalistic or not) is another question.
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Re: List of the Turing-complete totalistic life-like CA

Post by calcyman » July 31st, 2018, 5:41 am

Macbi wrote:The problem of how to define when a cellular automaton (or automaton more generally) is universal has been studied in the literature, but I've never seen a satisfactory answer. The problem is that the input to the automaton has to be encoded in some way, and the output decoded. But if you allow the input encoding to be arbitrary then all automata become universal, because you can just allow the encoding function to do all of the computation. So you've got to choose a definition broad enough to allow all the kinds of encodings you want, while not allowing literally all computable functions.
The input to the CA should be a finite pattern, and there should be a deterministic guaranteed-to-terminate algorithm for translating any Turing machine into an equivalent input pattern.

So yes, Banks-I is not universal whereas Banks-III is. You need sliding-block memory or equivalent
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Re: List of the Turing-complete totalistic life-like CA

Post by Macbi » July 31st, 2018, 5:56 am

calcyman wrote:
Macbi wrote:The problem of how to define when a cellular automaton (or automaton more generally) is universal has been studied in the literature, but I've never seen a satisfactory answer. The problem is that the input to the automaton has to be encoded in some way, and the output decoded. But if you allow the input encoding to be arbitrary then all automata become universal, because you can just allow the encoding function to do all of the computation. So you've got to choose a definition broad enough to allow all the kinds of encodings you want, while not allowing literally all computable functions.
The input to the CA should be a finite pattern, and there should be a deterministic guaranteed-to-terminate algorithm for translating any Turing machine into an equivalent input pattern.

So yes, Banks-I is not universal whereas Banks-III is. You need sliding-block memory or equivalent
So, for example, Rule 110 isn't universal (because the input requires an infinite background agar)?

Also, you need to specify what kind of rules are allowed for determining when the Turing machine has halted, and what its output is.

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Re: List of the Turing-complete totalistic life-like CA

Post by calcyman » July 31st, 2018, 9:42 am

Okay, to formalise this fully:

Let T be the set of Turing machines, and P be the set of finite patterns in a CA. Then the CA with rule R : P --> P is universal if there exist computable functions:

f : T --> P
g : P --> bool

such that for all T, we have:

(exists i : T halts at time i) <==> (exists j : g(R^j(f(T))) is true)

Edit: The reason I insist on a finite pattern is to avoid all of the debacle surrounding Alex Smith's Turing machine. Periodic background would also be okay, as would specifying a predicate phi(x,y) in first-order Presburger arithmetic describing whether cell (x,y) is on or not.
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77topaz
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Re: List of the Turing-complete totalistic life-like CA

Post by 77topaz » August 1st, 2018, 11:00 pm

Maybe a good way of summarising that would be to say that the input pattern should have finite complexity?

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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » August 2nd, 2018, 3:00 am

calcyman wrote:...
So yes, Banks-I is not universal whereas ...
Really?

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Re: List of the Turing-complete totalistic life-like CA

Post by Macbi » August 2nd, 2018, 3:57 am

77topaz wrote:Maybe a good way of summarising that would be to say that the input pattern should have finite complexity?
That's not useful unless you have a rigorous definition of complexity. One option is to use Kolmogorov complexity, but in fact that won't work. A pattern with finite Kolmogorov complexity is just any computable one. But then we can do things like let f be the function that prints out the entire evolution of T (in some format) from left to right in generation 0. Then even the CA "shift one to the left each generation" would be universal, since we could just let g check near the origin to see if the Turing machine had halted on that step.

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Re: List of the Turing-complete totalistic life-like CA

Post by calcyman » August 4th, 2018, 7:49 am

Naszvadi wrote:
calcyman wrote:...
So yes, Banks-I is not universal whereas ...
Really?
Implementing an arbitrary Turing machine in Banks-I would need a non-finitely-supported initial configuration to contain the tape. You have to be very careful about which configurations should be allowed, as otherwise Macbi's "shift to the left" is universal. This debate is exactly why Alex Smith's solution to the Wolfram prize is controversial.

The most parsimonious solution is to only allow finitely-supported initial configurations. Otherwise, you need to decide which infinite patterns are permissible, and moreover describe them by finite descriptions. If you want Banks-I and Rule 110 to be universal, then specifying the pattern as a predicate in Presburger arithmetic is one solution, but it feels very arbitrary.
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Re: List of the Turing-complete totalistic life-like CA

Post by Macbi » August 4th, 2018, 9:28 am

Suppose we let the initial configuration be described by a function f(T,x,y), where T is a Turing machine and x and y are coordinates. Then the evil f I described above (that just prints out the entire evolution of T in the first generation) is EXPSPACE-complete. So maybe the principled rule is to allow any computable f so long as it isn't EXPSPACE-hard. Would that work?

I'm also worried about only letting g only see one generation. I can imagine a proof of universality where we say something like "consider the machine to have halted if this spaceship is ever deleted". Given a single generation we wouldn't necessarily know where that spaceship was supposed to be, so we can't tell if it has been deleted. But someone watching from generation 0 would have been able to track the spaceship and would know which location they were supposed to be checking.

EDIT: I changed PSPACE to EXPSPACE, since the amount of space is polynomial in x and y, and hence exponential in the lengths of x and y.

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Re: List of the Turing-complete totalistic life-like CA

Post by Macbi » August 4th, 2018, 11:41 am

To argue in the other direction, I think your original definition
calcyman wrote:Let T be the set of Turing machines, and P be the set of finite patterns in a CA. Then the CA with rule R : P --> P is universal if there exist computable functions:

f : T --> P
g : P --> bool

such that for all T, we have:

(exists i : T halts at time i) <==> (exists j : g(R^j(f(T))) is true)
is too generous. Consider any CA which allows a "timer" and "data storage". Then let f be a program that stores T in the data storage and starts the timer, and let g be the program that reads the timer and the data storage and runs T for t seconds, outputting True iff it halts in that time. For example B12345678/S012345678 is universal, because if you store data like this:

Code: Select all

x = 14, y = 14, rule = B12345678/S012345678
13bo2$11bo$10bo$9bo2$7bo2$5bo$4bo2$2bo$bo$o!
it's easy to read out the data and the time from the pattern at generation t.

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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » August 7th, 2018, 7:55 am

Naszvadi wrote:4 rules between Highlife and LowDeath are Turing-complete. They are:
  • B36/S23
  • B368/S23
  • B36/S238
  • B368/S238
TODO: Printer
...
Added a "printer".

Changes in the unit cell's alive state notation: two inner very long boats denote a glider, which appereance in every 2688 generations means that the cell is ALIVE - dead otherwise.

Code: Select all

#C Naszvadi, Peter, 2014-2018. Polyglot Unit Cell for rules: B36[8]/S23[8]
#C virtual pattern is (001000), evolves to (111000) and loops in 9 virtual generations
#C Printer added, period is 2688, height 584
#C [[ AUTOSTART STEP 48 THEME 9 ]]
x = 511, y = 3504, rule = B36/S23:T0,3504
509b2o$2o506bobo$obo504bobo$bobo502bobo$2bobo502bo$3bo50$267b2o$267b2o
6$268b3o$267bo2bo$266bo3bo$266bo2bo$266b3o4$276b3o$275bo2bo$274bo3bo$
274bo2bo$274b3o6$292b2o$292b2o26$296b2o$297bo$294b3o$294bo61$206b2o$
206b2o8bo$214b2o$216b2o$215bo3$214b2o$207bobo4b2o$208b2o$208bo3$396bo$
396bobo$391b2o2bobo$391b2o4bo6$389bo$385bo3bo8b2o$385bo3bo8b2o$385bob
6o$389bo$381b3o5bo2$383bo5b3o$383bo$362b3o15b6obo$364bo18bo3bo$175b2o
2bo183bo19bo3bo$174bo4bo203bo$174bo4bo$178b5o$177bobo$174b5o194bo$177b
o4bo186bo3bo$177bo4bo186bo3bo$177bo2b2o187bob6o$373bo$365b3o5bo2$367bo
5b3o$367bo$364b6obo$367bo3bo$157b2o208bo3bo$157b2o208bo5$179b2o$179b2o
74bobo$256b2o$256bo$180bo$179b3o$178b2ob2o$179b2ob2o$176bo3b2ob2o$175b
3o3b3o$174b2ob2o3bo$175b2ob2o$172bo3b2ob2o$171b3o3b3o$170b2ob2o3bo$
171b2ob2o$168bo3b2ob2o$167b3o3b3o173b2o$166b2ob2o3bo174b2o$167b2ob2o$
164bo3b2ob2o$163b3o3b3o$162b2ob2o3bo$163b2ob2o$160bo3b2ob2o145b3o$159b
3o3b3o148bo$158b2ob2o3bo148bo$159b2ob2o$156bo3b2ob2o$155b3o3b3o$154b2o
b2o3bo$155b2ob2o$152bo3b2ob2o$151b3o3b3o$150b2ob2o3bo$151b2ob2o$152b2o
b2o$153b3o$154bo2$62b2o$62b2o5$61b2o3$130b2o171bobo$130b2o172b2o$304bo
6$133bo3b2o$48b3o80b2o4b2o24b2o$47bo3bo81b2o28bo$47bo4bo79bo28bobo$47b
o2bo2bo107b2o$48bo4bo$49bo3bo111bo$50b3o111bobo$37b2o124bobo$37b2o123b
obo$162b2o2$178b2o$178b2o2$2o10bo253b3o$2o9b3o254bo$10b2ob2o252bo$9b2o
b2o139b2o$8b2ob2o3bo135bobo$9b3o3b3o133bobo127b2o$10bo3b2ob2o131bobo
128b2o7bo$13b2ob2o133bo138bobo$12b2ob2o272bobo$13b3o44bo221bo8bo6b2o$
14bo46bo219b3o14b2o$33bo25b3o218b2ob2o$33b2o171bo74b2ob2o3b2o$32bobo
170b3o70bo3b2ob2o2b2o$134b2o68b3obo68b3o3b3o$135b2o66b2o2b3o66b2ob2o3b
o$134bo67b2o3b2obo66b2ob2o$201b3o2b2ob3o62bo3b2ob2o$50b2o150bob3ob3obo
60b3o3b3o$49bobo151b3ob2o2b3o58b2ob2o3bo$49bo154bob2o3b2o60b2ob2o$48b
2o155b3o2b2o58bo3b2ob2o$206bob3o58b3o3b3o$207b3o58b2ob2o3bo$208bo60b2o
b2o$25b2o243b2ob2o76bobo$25b2o244b3o78b2o$272bo79bo$222bo$221b3o$220b
3obo31b2o$219b2o2b3o30b2o57b3o$218b2o3b2obo87bo3bo$84bo132b3o2b2ob3o
85bo4bo$85bo132bob3ob3obo83bo2bo2bo$83b3o133b3ob2o2b3o82bo4bo$220bob2o
3b2o83bo3bo$221b3o2b2o85b3o$53b2o55b2o110bob3o$53bobo55b2o110b3o9b2o
86b3o$53bo56bo113bo10b2o85bo3bo$321bo4bo$320bo2bo2bo$237bo82bo4bo$235b
obo82bo3bo$236bobo82b3o$227b2o7bo$227b2o102b3o$330bo3bo$329bo4bo$328bo
2bo2bo$328bo4bo$328bo3bo$329b3o$89b2o$89b2o248b3o$338bo3bo$337bo4bo$
102b3o187b2o42bo2bo2bo4b2o$101bo5b2o183b2o42bo4bo5b2o$101bo4bo229bo3bo
$101bo235b3o$77b2o$77bobo23bo244b2o$77bo24bo245b2o$102bo$271bo$271b2o$
269b2ob2o$118bo150bo4bo$118bo148b2o6bo$117bo150b2o5b2o$269bo6b2o$114b
2o3bo150bo4bo123bobo$113bo4b2o151b2ob2o124b2o58b2o$112b2o4b2o152b2o
126bo50bo8b2o$113b2o158bo86bo91b2o$113b3o239b3o3bo88b2o$114b2o238bo97b
o$113bo2bo237bo$114b2o238bo2bo2bo$360bo91b2o$360bo91b2o$353bo3b3o$354b
o13bo$212b3o148b3o3bo$101b2o98b2o8bo150bo$101bobo97b2o7bo3bobo26b2o
117bo105bo$101bo107bo33b2o117bo2bo2bo4b2o92b2o$208bo7bobo149bo4b2o91bo
bo$208bo6bo152bo96b3o$208bobo3bo3bobo140bo3b3o$213bo6bo141bo108b3o$
210bobo7bo249bobo$219bo250b2o$212bobo3bo251bo5bo$217bo257b2o$214b3o
257bobo$473b3o2$230bo248b3o$230b2o246bobo$229bobo246b2o$478bo$234b2o$
234b2o2$243b2o144b2o$211b2o22bo7b2o144b2o$211b2o23b2o$125b2o107b2o13bo
$125bobo98b2o8bo10b3o$125bo100b2o18bo182bo$246b2o179b2o$428b2o$387b3o$
383b2o5bo$219bo147b2o16bo4bo$214b3o3bo146b2o12bo8bo$213bo167bo$213bo
168bo5bo$213bo2bo2bo169bo57bobo$219bo160bo8bo58b2o$219bo160bo4bo62bo
60b2o$212bo3b3o161bo5b2o121b2o$213bo167b3o7$364b2o$236b2o126b2o$149b2o
85b2o$149bobo$149bo226bo$377bo$375b3o$225bo$223b2o142bo3b2o$224b2o139b
2o4b2o$367b2o$366bo6$368b2o41b5o$368b2o40bo4bo$415bo$410bo3bo$412bo5$
173b2o$173bobo$173bo2$250b3o$201bo48bo$199b2o50bo$200b2o9$404bo$403b2o
$280bo121bobo$278b2o121b3o$187b3o84b2o4b2o$190bo8b2o73b2o3bo127b3o$
185bobo3bo7b2o205bobo$192bo213b2o$183bobo7bo212bo$186bo6bo$181bobo3bo
3bobo230bo$181bo6bo236bo$181bo7bobo82b3o4b2o140b3o$182bo91bo6b2o$183bo
3bobo85bo$184bo$185b3o4$432b2o$432bo$237b2o21bo172b3o$237b2o20b3o173bo
$258b2ob2o154b2o$259b2ob2o153b2o$221bo38b2ob2o$219bo2bo38b3o$218b4o40b
o$217b5o$174b2o42b2o2bo2bo$174b2o40bob2o3b2obo$217bo2bo2b2o$221b5o$
213bo7b4o$211bo2bo5bo2bo$210b4o7bo$209b5o42b2o$210b2o2bo2bo38b2o$208bo
b2o3b2obo$209bo2bo2b2o$213b5o$213b4o$212bo2bo$213bo3$212b2o$212b2o58$
507bo$3bo502bobo$2bobo502bobo$bobo504bobo$obo506b2o$2o$509b2o$2o506bob
o$obo504bobo$bobo502bobo$2bobo502bo$3bo50$267b2o$267b2o6$268b3o$267bo
2bo$266bo3bo$266bo2bo$266b3o4$276b3o$275bo2bo$274bo3bo$274bo2bo$274b3o
6$292b2o$292b2o26$296b2o$297bo$294b3o$294bo61$206b2o$206b2o8bo$214b2o$
216b2o$215bo3$214b2o$207bobo4b2o$208b2o$208bo3$396bo$396bobo$391b2o2bo
bo$391b2o4bo6$389bo$385bo3bo8b2o$385bo3bo8b2o$385bob6o$389bo$381b3o5bo
2$383bo5b3o$383bo$362b3o15b6obo$364bo18bo3bo$175b2o2bo183bo19bo3bo$
174bo4bo203bo$174bo4bo$178b5o$177bobo$174b5o194bo$177bo4bo186bo3bo$
177bo4bo186bo3bo$177bo2b2o187bob6o$373bo$365b3o5bo2$367bo5b3o$367bo$
364b6obo$367bo3bo$157b2o208bo3bo$157b2o208bo5$179b2o$179b2o74bobo$256b
2o$256bo$180bo$179b3o$178b2ob2o$179b2ob2o$176bo3b2ob2o$175b3o3b3o$174b
2ob2o3bo$175b2ob2o$172bo3b2ob2o$171b3o3b3o$170b2ob2o3bo$171b2ob2o$168b
o3b2ob2o$167b3o3b3o173b2o$166b2ob2o3bo174b2o$167b2ob2o$164bo3b2ob2o$
163b3o3b3o$162b2ob2o3bo$163b2ob2o$160bo3b2ob2o145b3o$159b3o3b3o148bo$
158b2ob2o3bo148bo$159b2ob2o$156bo3b2ob2o$155b3o3b3o$154b2ob2o3bo$155b
2ob2o$152bo3b2ob2o$151b3o3b3o$150b2ob2o3bo$151b2ob2o$152b2ob2o$153b3o$
154bo2$62b2o$62b2o5$61b2o3$130b2o171bobo$130b2o172b2o$304bo6$133bo3b2o
$48b3o80b2o4b2o24b2o$47bo3bo81b2o28bo$47bo4bo79bo28bobo$47bo2bo2bo107b
2o$48bo4bo$49bo3bo111bo$50b3o111bobo$37b2o124bobo$37b2o123bobo$162b2o
2$178b2o$178b2o2$2o10bo253b3o$2o9b3o254bo$10b2ob2o252bo$9b2ob2o139b2o$
8b2ob2o3bo135bobo$9b3o3b3o133bobo127b2o$10bo3b2ob2o131bobo128b2o7bo$
13b2ob2o133bo138bobo$12b2ob2o272bobo$13b3o44bo221bo8bo6b2o$14bo46bo
219b3o14b2o$33bo25b3o218b2ob2o$33b2o171bo74b2ob2o3b2o$32bobo170b3o70bo
3b2ob2o2b2o$134b2o68b3obo68b3o3b3o$135b2o66b2o2b3o66b2ob2o3bo$134bo67b
2o3b2obo66b2ob2o$201b3o2b2ob3o62bo3b2ob2o$50b2o150bob3ob3obo60b3o3b3o$
49bobo151b3ob2o2b3o58b2ob2o3bo$49bo154bob2o3b2o60b2ob2o$48b2o155b3o2b
2o58bo3b2ob2o$206bob3o58b3o3b3o$207b3o58b2ob2o3bo$208bo60b2ob2o$25b2o
243b2ob2o76bobo$25b2o244b3o78b2o$272bo79bo$222bo$221b3o$220b3obo31b2o$
219b2o2b3o30b2o57b3o$218b2o3b2obo87bo3bo$84bo132b3o2b2ob3o85bo4bo$85bo
132bob3ob3obo83bo2bo2bo$83b3o133b3ob2o2b3o82bo4bo$220bob2o3b2o83bo3bo$
221b3o2b2o85b3o$53b2o55b2o110bob3o$53bobo55b2o110b3o9b2o86b3o$53bo56bo
113bo10b2o85bo3bo$321bo4bo$320bo2bo2bo$237bo82bo4bo$235bobo82bo3bo$
236bobo82b3o$227b2o7bo$227b2o102b3o$330bo3bo$329bo4bo$328bo2bo2bo$328b
o4bo$328bo3bo$329b3o$89b2o$89b2o248b3o$338bo3bo$337bo4bo$102b3o187b2o
42bo2bo2bo4b2o$101bo5b2o183b2o42bo4bo5b2o$101bo4bo229bo3bo$101bo235b3o
$77b2o$77bobo23bo244b2o$77bo24bo245b2o$102bo$271bo$271b2o$269b2ob2o$
118bo150bo4bo$118bo148b2o6bo$117bo150b2o5b2o$269bo6b2o$114b2o3bo150bo
4bo123bobo$113bo4b2o151b2ob2o124b2o58b2o$112b2o4b2o152b2o126bo50bo8b2o
$113b2o158bo86bo91b2o$113b3o239b3o3bo88b2o$114b2o238bo97bo$113bo2bo
237bo$114b2o238bo2bo2bo$360bo91b2o$360bo91b2o$353bo3b3o$354bo13bo$212b
3o148b3o3bo$101b2o98b2o8bo150bo$101bobo97b2o7bo3bobo26b2o117bo105bo$
101bo107bo33b2o117bo2bo2bo4b2o92b2o$208bo7bobo149bo4b2o91bobo$208bo6bo
152bo96b3o$208bobo3bo3bobo140bo3b3o$213bo6bo141bo108b3o$210bobo7bo249b
obo$219bo250b2o$212bobo3bo251bo5bo$217bo257b2o$214b3o257bobo$473b3o2$
230bo248b3o$230b2o246bobo$229bobo246b2o$478bo$234b2o$234b2o2$243b2o
144b2o$211b2o22bo7b2o144b2o$211b2o23b2o$125b2o107b2o13bo$125bobo98b2o
8bo10b3o$125bo100b2o18bo182bo$246b2o179b2o$428b2o$387b3o$383b2o5bo$
219bo147b2o16bo4bo$214b3o3bo146b2o12bo8bo$213bo167bo$213bo168bo5bo$
213bo2bo2bo169bo57bobo$219bo160bo8bo58b2o$219bo160bo4bo62bo60b2o$212bo
3b3o161bo5b2o121b2o$213bo167b3o7$364b2o$236b2o126b2o$149b2o85b2o$149bo
bo$149bo226bo$377bo$375b3o$225bo$223b2o142bo3b2o$224b2o139b2o4b2o$367b
2o$366bo6$368b2o41b5o$368b2o40bo4bo$415bo$410bo3bo$412bo5$173b2o$173bo
bo$173bo2$250b3o$201bo48bo$199b2o50bo$200b2o9$404bo$403b2o$280bo121bob
o$278b2o121b3o$187b3o84b2o4b2o$190bo8b2o73b2o3bo127b3o$185bobo3bo7b2o
205bobo$192bo213b2o$183bobo7bo212bo$186bo6bo$181bobo3bo3bobo230bo$181b
o6bo236bo$181bo7bobo82b3o4b2o140b3o$182bo91bo6b2o$183bo3bobo85bo$184bo
$185b3o4$432b2o$432bo$237b2o21bo172b3o$237b2o20b3o173bo$258b2ob2o154b
2o$259b2ob2o153b2o$221bo38b2ob2o$219bo2bo38b3o$218b4o40bo$217b5o$174b
2o42b2o2bo2bo$174b2o40bob2o3b2obo$217bo2bo2b2o$221b5o$213bo7b4o$211bo
2bo5bo2bo$210b4o7bo$209b5o42b2o$210b2o2bo2bo38b2o$208bob2o3b2obo$209bo
2bo2b2o$213b5o$213b4o$212bo2bo$213bo3$212b2o$212b2o58$507bo$3bo502bobo
$2bobo502bobo$bobo504bobo$obo506b2o$2o$509b2o$2o506bobo$obo504bobo$bob
o502bobo$2bobo502bo$3bo50$267b2o$267b2o6$268b3o$267bo2bo$266bo3bo$266b
o2bo$266b3o4$276b3o$275bo2bo$274bo3bo$274bo2bo$274b3o6$292b2o$292b2o
26$296b2o$297bo$294b3o$294bo61$206b2o$206b2o8bo$214b2o$216b2o$215bo3$
214b2o$207bobo4b2o$208b2o$208bo3$396bo$396bobo$391b2o2bobo$391b2o4bo6$
389bo$385bo3bo8b2o$385bo3bo8b2o$385bob6o$389bo$381b3o5bo2$383bo5b3o$
383bo$362b3o15b6obo$364bo18bo3bo$175b2o2bo183bo19bo3bo$174bo4bo203bo$
174bo4bo$178b5o$177bobo$174b5o194bo$177bo4bo186bo3bo$177bo4bo186bo3bo$
177bo2b2o187bob6o$373bo$365b3o5bo2$367bo5b3o$367bo$364b6obo$367bo3bo$
157b2o208bo3bo$157b2o208bo5$179b2o$179b2o74bobo$256b2o$256bo$180bo$
179b3o$178b2ob2o$179b2ob2o$176bo3b2ob2o$175b3o3b3o$174b2ob2o3bo$175b2o
b2o$172bo3b2ob2o$171b3o3b3o$170b2ob2o3bo$171b2ob2o$168bo3b2ob2o$167b3o
3b3o173b2o$166b2ob2o3bo174b2o$167b2ob2o$164bo3b2ob2o$163b3o3b3o$162b2o
b2o3bo$163b2ob2o$160bo3b2ob2o145b3o$159b3o3b3o148bo$158b2ob2o3bo148bo$
159b2ob2o$156bo3b2ob2o$155b3o3b3o$154b2ob2o3bo$155b2ob2o$152bo3b2ob2o$
151b3o3b3o$150b2ob2o3bo$151b2ob2o$152b2ob2o$153b3o$154bo2$62b2o$62b2o
5$61b2o3$130b2o171bobo$130b2o172b2o$304bo6$133bo3b2o$48b3o80b2o4b2o24b
2o$47bo3bo81b2o28bo$47bo4bo79bo28bobo$47bo2bo2bo107b2o$48bo4bo$49bo3bo
111bo$50b3o111bobo$37b2o124bobo$37b2o123bobo$162b2o2$158bo19b2o$159bo
18b2o$157b3o$2o10bo253b3o$2o9b3o254bo$10b2ob2o252bo$9b2ob2o139b2o$8b2o
b2o3bo135bobo$9b3o3b3o133bobo127b2o$10bo3b2ob2o131bobo128b2o7bo$13b2ob
2o133bo138bobo$12b2ob2o272bobo$13b3o44bo221bo8bo6b2o$14bo46bo219b3o14b
2o$33bo25b3o218b2ob2o$33b2o171bo74b2ob2o3b2o$32bobo170b3o70bo3b2ob2o2b
2o$134b2o68b3obo68b3o3b3o$135b2o66b2o2b3o66b2ob2o3bo$134bo67b2o3b2obo
66b2ob2o$201b3o2b2ob3o62bo3b2ob2o$50b2o150bob3ob3obo60b3o3b3o$49bobo
151b3ob2o2b3o58b2ob2o3bo$49bo154bob2o3b2o60b2ob2o$48b2o155b3o2b2o58bo
3b2ob2o$206bob3o58b3o3b3o$207b3o58b2ob2o3bo$208bo60b2ob2o$25b2o243b2ob
2o76bobo$25b2o244b3o78b2o$272bo79bo$222bo$221b3o$220b3obo31b2o$219b2o
2b3o30b2o57b3o$218b2o3b2obo87bo3bo$84bo132b3o2b2ob3o85bo4bo$85bo132bob
3ob3obo83bo2bo2bo$83b3o133b3ob2o2b3o82bo4bo$220bob2o3b2o83bo3bo$221b3o
2b2o85b3o$53b2o55b2o110bob3o$53bobo55b2o110b3o9b2o86b3o$53bo56bo113bo
10b2o85bo3bo$321bo4bo$320bo2bo2bo$237bo82bo4bo$235bobo82bo3bo$236bobo
82b3o$227b2o7bo$227b2o102b3o$330bo3bo$329bo4bo$328bo2bo2bo$328bo4bo$
328bo3bo$329b3o$89b2o$89b2o248b3o$338bo3bo$337bo4bo$102b3o187b2o42bo2b
o2bo4b2o$101bo5b2o183b2o42bo4bo5b2o$101bo4bo229bo3bo$101bo235b3o$77b2o
$77bobo23bo244b2o$77bo24bo245b2o$102bo$271bo$271b2o$269b2ob2o$118bo
150bo4bo$118bo148b2o6bo$117bo150b2o5b2o$269bo6b2o$114b2o3bo150bo4bo
123bobo$113bo4b2o151b2ob2o124b2o58b2o$112b2o4b2o152b2o126bo50bo8b2o$
113b2o158bo86bo91b2o$113b3o239b3o3bo88b2o$114b2o238bo97bo$113bo2bo237b
o$114b2o238bo2bo2bo$360bo91b2o$360bo91b2o$353bo3b3o$354bo13bo$212b3o
148b3o3bo$101b2o98b2o8bo150bo$101bobo97b2o7bo3bobo26b2o117bo105bo$101b
o107bo33b2o117bo2bo2bo4b2o92b2o$208bo7bobo149bo4b2o91bobo$208bo6bo152b
o96b3o$208bobo3bo3bobo140bo3b3o$213bo6bo141bo108b3o$210bobo7bo249bobo$
219bo250b2o$212bobo3bo251bo5bo$217bo257b2o$214b3o257bobo$473b3o2$230bo
248b3o$230b2o246bobo$229bobo246b2o$478bo$234b2o$234b2o2$243b2o144b2o$
211b2o22bo7b2o144b2o$211b2o23b2o$125b2o107b2o13bo$125bobo98b2o8bo10b3o
$125bo100b2o18bo182bo$246b2o179b2o$428b2o$387b3o$383b2o5bo$219bo147b2o
16bo4bo$214b3o3bo146b2o12bo8bo$213bo167bo$213bo168bo5bo$213bo2bo2bo
169bo57bobo$219bo160bo8bo58b2o$219bo160bo4bo62bo60b2o$212bo3b3o161bo5b
2o121b2o$213bo167b3o7$364b2o$236b2o126b2o$149b2o85b2o$149bobo$149bo
226bo$377bo$375b3o$225bo$223b2o142bo3b2o$224b2o139b2o4b2o$367b2o$366bo
6$368b2o41b5o$368b2o40bo4bo$415bo$410bo3bo$412bo5$173b2o$173bobo$173bo
2$250b3o$201bo48bo$199b2o50bo$200b2o9$404bo$403b2o$280bo121bobo$278b2o
121b3o$187b3o84b2o4b2o$190bo8b2o73b2o3bo127b3o$185bobo3bo7b2o205bobo$
192bo213b2o$183bobo7bo212bo$186bo6bo$181bobo3bo3bobo230bo$181bo6bo236b
o$181bo7bobo82b3o4b2o140b3o$182bo91bo6b2o$183bo3bobo85bo$184bo$185b3o
4$432b2o$432bo$237b2o21bo172b3o$237b2o20b3o173bo$258b2ob2o154b2o$259b
2ob2o153b2o$221bo38b2ob2o$219bo2bo38b3o$218b4o40bo$217b5o$174b2o42b2o
2bo2bo$174b2o40bob2o3b2obo$217bo2bo2b2o$221b5o$213bo7b4o$211bo2bo5bo2b
o$210b4o7bo$209b5o42b2o$210b2o2bo2bo38b2o$208bob2o3b2obo$209bo2bo2b2o$
213b5o$213b4o$212bo2bo$213bo3$212b2o$212b2o58$507bo$3bo502bobo$2bobo
502bobo$bobo504bobo$obo506b2o$2o$509b2o$2o506bobo$obo504bobo$bobo502bo
bo$2bobo502bo$3bo50$267b2o$267b2o6$268b3o$267bo2bo$266bo3bo$266bo2bo$
266b3o4$276b3o$275bo2bo$274bo3bo$274bo2bo$274b3o6$292b2o$292b2o26$296b
2o$297bo$294b3o$294bo61$206b2o$206b2o8bo$214b2o$216b2o$215bo3$214b2o$
207bobo4b2o$208b2o$208bo3$396bo$396bobo$391b2o2bobo$391b2o4bo6$389bo$
385bo3bo8b2o$385bo3bo8b2o$385bob6o$389bo$381b3o5bo2$383bo5b3o$383bo$
362b3o15b6obo$364bo18bo3bo$175b2o2bo183bo19bo3bo$174bo4bo203bo$174bo4b
o$178b5o$177bobo$174b5o194bo$177bo4bo186bo3bo$177bo4bo186bo3bo$177bo2b
2o187bob6o$373bo$365b3o5bo2$367bo5b3o$367bo$364b6obo$367bo3bo$157b2o
208bo3bo$157b2o208bo5$179b2o$179b2o74bobo$256b2o$256bo$180bo$179b3o$
178b2ob2o$179b2ob2o$176bo3b2ob2o$175b3o3b3o$174b2ob2o3bo$175b2ob2o$
172bo3b2ob2o$171b3o3b3o$170b2ob2o3bo$171b2ob2o$168bo3b2ob2o$167b3o3b3o
173b2o$166b2ob2o3bo174b2o$167b2ob2o$164bo3b2ob2o$163b3o3b3o$162b2ob2o
3bo$163b2ob2o$160bo3b2ob2o145b3o$159b3o3b3o148bo$158b2ob2o3bo148bo$
159b2ob2o$156bo3b2ob2o$155b3o3b3o$154b2ob2o3bo$155b2ob2o$152bo3b2ob2o$
151b3o3b3o$150b2ob2o3bo$151b2ob2o$152b2ob2o$153b3o$154bo2$62b2o$62b2o
5$61b2o3$130b2o171bobo$130b2o172b2o$304bo6$133bo3b2o$48b3o80b2o4b2o24b
2o$47bo3bo81b2o28bo$47bo4bo79bo28bobo$47bo2bo2bo107b2o$48bo4bo$49bo3bo
111bo$50b3o111bobo$37b2o124bobo$37b2o123bobo$162b2o2$178b2o$178b2o2$2o
10bo253b3o$2o9b3o254bo$10b2ob2o252bo$9b2ob2o139b2o$8b2ob2o3bo135bobo$
9b3o3b3o133bobo127b2o$10bo3b2ob2o131bobo128b2o7bo$13b2ob2o133bo138bobo
$12b2ob2o272bobo$13b3o44bo221bo8bo6b2o$14bo46bo219b3o14b2o$33bo25b3o
218b2ob2o$33b2o171bo74b2ob2o3b2o$32bobo170b3o70bo3b2ob2o2b2o$134b2o68b
3obo68b3o3b3o$135b2o66b2o2b3o66b2ob2o3bo$134bo67b2o3b2obo66b2ob2o$201b
3o2b2ob3o62bo3b2ob2o$50b2o150bob3ob3obo60b3o3b3o$49bobo151b3ob2o2b3o
58b2ob2o3bo$49bo154bob2o3b2o60b2ob2o$48b2o155b3o2b2o58bo3b2ob2o$206bob
3o58b3o3b3o$207b3o58b2ob2o3bo$208bo60b2ob2o$25b2o243b2ob2o76bobo$25b2o
244b3o78b2o$272bo79bo$222bo$221b3o$220b3obo31b2o$219b2o2b3o30b2o57b3o$
218b2o3b2obo87bo3bo$84bo132b3o2b2ob3o85bo4bo$85bo132bob3ob3obo83bo2bo
2bo$83b3o133b3ob2o2b3o82bo4bo$220bob2o3b2o83bo3bo$221b3o2b2o85b3o$53b
2o55b2o110bob3o$53bobo55b2o110b3o9b2o86b3o$53bo56bo113bo10b2o85bo3bo$
321bo4bo$320bo2bo2bo$237bo82bo4bo$235bobo82bo3bo$236bobo82b3o$227b2o7b
o$227b2o102b3o$330bo3bo$329bo4bo$328bo2bo2bo$328bo4bo$328bo3bo$329b3o$
89b2o$89b2o248b3o$338bo3bo$337bo4bo$102b3o187b2o42bo2bo2bo4b2o$101bo5b
2o183b2o42bo4bo5b2o$101bo4bo229bo3bo$101bo235b3o$77b2o$77bobo23bo244b
2o$77bo24bo245b2o$102bo$271bo$271b2o$269b2ob2o$118bo150bo4bo$118bo148b
2o6bo$117bo150b2o5b2o$269bo6b2o$114b2o3bo150bo4bo123bobo$113bo4b2o151b
2ob2o124b2o58b2o$112b2o4b2o152b2o126bo50bo8b2o$113b2o158bo86bo91b2o$
113b3o239b3o3bo88b2o$114b2o238bo97bo$113bo2bo237bo$114b2o238bo2bo2bo$
360bo91b2o$360bo91b2o$353bo3b3o$354bo13bo$212b3o148b3o3bo$101b2o98b2o
8bo150bo$101bobo97b2o7bo3bobo26b2o117bo105bo$101bo107bo33b2o117bo2bo2b
o4b2o92b2o$208bo7bobo149bo4b2o91bobo$208bo6bo152bo96b3o$208bobo3bo3bob
o140bo3b3o$213bo6bo141bo108b3o$210bobo7bo249bobo$219bo250b2o$212bobo3b
o251bo5bo$217bo257b2o$214b3o257bobo$473b3o2$230bo248b3o$230b2o246bobo$
229bobo246b2o$478bo$234b2o$234b2o2$243b2o144b2o$211b2o22bo7b2o144b2o$
211b2o23b2o$125b2o107b2o13bo$125bobo98b2o8bo10b3o$125bo100b2o18bo182bo
$246b2o179b2o$428b2o$387b3o$383b2o5bo$219bo147b2o16bo4bo$214b3o3bo146b
2o12bo8bo$213bo167bo$213bo168bo5bo$213bo2bo2bo169bo57bobo$219bo160bo8b
o58b2o$219bo160bo4bo62bo60b2o$212bo3b3o161bo5b2o121b2o$213bo167b3o7$
364b2o$236b2o126b2o$149b2o85b2o$149bobo$149bo226bo$377bo$375b3o$225bo$
223b2o142bo3b2o$224b2o139b2o4b2o$367b2o$366bo6$368b2o41b5o$368b2o40bo
4bo$415bo$410bo3bo$412bo5$173b2o$173bobo$173bo2$250b3o$201bo48bo$199b
2o50bo$200b2o9$404bo$403b2o$280bo121bobo$278b2o121b3o$187b3o84b2o4b2o$
190bo8b2o73b2o3bo127b3o$185bobo3bo7b2o205bobo$192bo213b2o$183bobo7bo
212bo$186bo6bo$181bobo3bo3bobo230bo$181bo6bo236bo$181bo7bobo82b3o4b2o
140b3o$182bo91bo6b2o$183bo3bobo85bo$184bo$185b3o4$432b2o$432bo$237b2o
21bo172b3o$237b2o20b3o173bo$258b2ob2o154b2o$259b2ob2o153b2o$221bo38b2o
b2o$219bo2bo38b3o$218b4o40bo$217b5o$174b2o42b2o2bo2bo$174b2o40bob2o3b
2obo$217bo2bo2b2o$221b5o$213bo7b4o$211bo2bo5bo2bo$210b4o7bo$209b5o42b
2o$210b2o2bo2bo38b2o$208bob2o3b2obo$209bo2bo2b2o$213b5o$213b4o$212bo2b
o$213bo3$212b2o$212b2o58$507bo$3bo502bobo$2bobo502bobo$bobo504bobo$obo
506b2o$2o$509b2o$2o506bobo$obo504bobo$bobo502bobo$2bobo502bo$3bo50$
267b2o$267b2o6$268b3o$267bo2bo$266bo3bo$266bo2bo$266b3o4$276b3o$275bo
2bo$274bo3bo$274bo2bo$274b3o6$292b2o$292b2o26$296b2o$297bo$294b3o$294b
o61$206b2o$206b2o8bo$214b2o$216b2o$215bo3$214b2o$207bobo4b2o$208b2o$
208bo3$396bo$396bobo$391b2o2bobo$391b2o4bo6$389bo$385bo3bo8b2o$385bo3b
o8b2o$385bob6o$389bo$381b3o5bo2$383bo5b3o$383bo$362b3o15b6obo$364bo18b
o3bo$175b2o2bo183bo19bo3bo$174bo4bo203bo$174bo4bo$178b5o$177bobo$174b
5o194bo$177bo4bo186bo3bo$177bo4bo186bo3bo$177bo2b2o187bob6o$373bo$365b
3o5bo2$367bo5b3o$367bo$364b6obo$367bo3bo$157b2o208bo3bo$157b2o208bo5$
179b2o$179b2o74bobo$256b2o$256bo$180bo$179b3o$178b2ob2o$179b2ob2o$176b
o3b2ob2o$175b3o3b3o$174b2ob2o3bo$175b2ob2o$172bo3b2ob2o$171b3o3b3o$
170b2ob2o3bo$171b2ob2o$168bo3b2ob2o$167b3o3b3o173b2o$166b2ob2o3bo174b
2o$167b2ob2o$164bo3b2ob2o$163b3o3b3o$162b2ob2o3bo$163b2ob2o$160bo3b2ob
2o145b3o$159b3o3b3o148bo$158b2ob2o3bo148bo$159b2ob2o$156bo3b2ob2o$155b
3o3b3o$154b2ob2o3bo$155b2ob2o$152bo3b2ob2o$151b3o3b3o$150b2ob2o3bo$
151b2ob2o$152b2ob2o$153b3o$154bo2$62b2o$62b2o5$61b2o3$130b2o171bobo$
130b2o172b2o$304bo6$133bo3b2o$48b3o80b2o4b2o24b2o$47bo3bo81b2o28bo$47b
o4bo79bo28bobo$47bo2bo2bo107b2o$48bo4bo$49bo3bo111bo$50b3o111bobo$37b
2o124bobo$37b2o123bobo$162b2o2$178b2o$178b2o2$2o10bo253b3o$2o9b3o254bo
$10b2ob2o252bo$9b2ob2o139b2o$8b2ob2o3bo135bobo$9b3o3b3o133bobo127b2o$
10bo3b2ob2o131bobo128b2o7bo$13b2ob2o133bo138bobo$12b2ob2o272bobo$13b3o
44bo221bo8bo6b2o$14bo46bo219b3o14b2o$33bo25b3o218b2ob2o$33b2o171bo74b
2ob2o3b2o$32bobo170b3o70bo3b2ob2o2b2o$134b2o68b3obo68b3o3b3o$135b2o66b
2o2b3o66b2ob2o3bo$134bo67b2o3b2obo66b2ob2o$201b3o2b2ob3o62bo3b2ob2o$
50b2o150bob3ob3obo60b3o3b3o$49bobo151b3ob2o2b3o58b2ob2o3bo$49bo154bob
2o3b2o60b2ob2o$48b2o155b3o2b2o58bo3b2ob2o$206bob3o58b3o3b3o$207b3o58b
2ob2o3bo$208bo60b2ob2o$25b2o243b2ob2o76bobo$25b2o244b3o78b2o$272bo79bo
$222bo$221b3o$220b3obo31b2o$219b2o2b3o30b2o57b3o$218b2o3b2obo87bo3bo$
84bo132b3o2b2ob3o85bo4bo$85bo132bob3ob3obo83bo2bo2bo$83b3o133b3ob2o2b
3o82bo4bo$220bob2o3b2o83bo3bo$221b3o2b2o85b3o$53b2o55b2o110bob3o$53bob
o55b2o110b3o9b2o86b3o$53bo56bo113bo10b2o85bo3bo$321bo4bo$320bo2bo2bo$
237bo82bo4bo$235bobo82bo3bo$236bobo82b3o$227b2o7bo$227b2o102b3o$330bo
3bo$329bo4bo$328bo2bo2bo$328bo4bo$328bo3bo$329b3o$89b2o$89b2o248b3o$
338bo3bo$337bo4bo$102b3o187b2o42bo2bo2bo4b2o$101bo5b2o183b2o42bo4bo5b
2o$101bo4bo229bo3bo$101bo235b3o$77b2o$77bobo23bo244b2o$77bo24bo245b2o$
102bo$271bo$271b2o$269b2ob2o$118bo150bo4bo$118bo148b2o6bo$117bo150b2o
5b2o$269bo6b2o$114b2o3bo150bo4bo123bobo$113bo4b2o151b2ob2o124b2o58b2o$
112b2o4b2o152b2o126bo50bo8b2o$113b2o158bo86bo91b2o$113b3o239b3o3bo88b
2o$114b2o238bo97bo$113bo2bo237bo$114b2o238bo2bo2bo$360bo91b2o$360bo91b
2o$353bo3b3o$354bo13bo$212b3o148b3o3bo$101b2o98b2o8bo150bo$101bobo97b
2o7bo3bobo26b2o117bo105bo$101bo107bo33b2o117bo2bo2bo4b2o92b2o$208bo7bo
bo149bo4b2o91bobo$208bo6bo152bo96b3o$208bobo3bo3bobo140bo3b3o$213bo6bo
141bo108b3o$210bobo7bo249bobo$219bo250b2o$212bobo3bo251bo5bo$217bo257b
2o$214b3o257bobo$473b3o2$230bo248b3o$230b2o246bobo$229bobo246b2o$478bo
$234b2o$234b2o2$243b2o144b2o$211b2o22bo7b2o144b2o$211b2o23b2o$125b2o
107b2o13bo$125bobo98b2o8bo10b3o$125bo100b2o18bo182bo$246b2o179b2o$428b
2o$387b3o$383b2o5bo$219bo147b2o16bo4bo$214b3o3bo146b2o12bo8bo$213bo
167bo$213bo168bo5bo$213bo2bo2bo169bo57bobo$219bo160bo8bo58b2o$219bo
160bo4bo62bo60b2o$212bo3b3o161bo5b2o121b2o$213bo167b3o7$364b2o$236b2o
126b2o$149b2o85b2o$149bobo$149bo226bo$377bo$375b3o$225bo$223b2o142bo3b
2o$224b2o139b2o4b2o$367b2o$366bo6$368b2o41b5o$368b2o40bo4bo$415bo$410b
o3bo$412bo5$173b2o$173bobo$173bo2$250b3o$201bo48bo$199b2o50bo$200b2o9$
404bo$403b2o$280bo121bobo$278b2o121b3o$187b3o84b2o4b2o$190bo8b2o73b2o
3bo127b3o$185bobo3bo7b2o205bobo$192bo213b2o$183bobo7bo212bo$186bo6bo$
181bobo3bo3bobo230bo$181bo6bo236bo$181bo7bobo82b3o4b2o140b3o$182bo91bo
6b2o$183bo3bobo85bo$184bo$185b3o4$432b2o$432bo$237b2o21bo172b3o$237b2o
20b3o173bo$258b2ob2o154b2o$259b2ob2o153b2o$221bo38b2ob2o$219bo2bo38b3o
$218b4o40bo$217b5o$174b2o42b2o2bo2bo$174b2o40bob2o3b2obo$217bo2bo2b2o$
221b5o$213bo7b4o$211bo2bo5bo2bo$210b4o7bo$209b5o42b2o$210b2o2bo2bo38b
2o$208bob2o3b2obo$209bo2bo2b2o$213b5o$213b4o$212bo2bo$213bo3$212b2o$
212b2o58$507bo$3bo502bobo$2bobo502bobo$bobo504bobo$obo506b2o$2o$509b2o
$2o506bobo$obo504bobo$bobo502bobo$2bobo502bo$3bo50$267b2o$267b2o6$268b
3o$267bo2bo$266bo3bo$266bo2bo$266b3o4$276b3o$275bo2bo$274bo3bo$274bo2b
o$274b3o6$292b2o$292b2o26$296b2o$297bo$294b3o$294bo61$206b2o$206b2o8bo
$214b2o$216b2o$215bo3$214b2o$207bobo4b2o$208b2o$208bo3$396bo$396bobo$
391b2o2bobo$391b2o4bo6$389bo$385bo3bo8b2o$385bo3bo8b2o$385bob6o$389bo$
381b3o5bo2$383bo5b3o$383bo$362b3o15b6obo$364bo18bo3bo$175b2o2bo183bo
19bo3bo$174bo4bo203bo$174bo4bo$178b5o$177bobo$174b5o194bo$177bo4bo186b
o3bo$177bo4bo186bo3bo$177bo2b2o187bob6o$373bo$365b3o5bo2$367bo5b3o$
367bo$364b6obo$367bo3bo$157b2o208bo3bo$157b2o208bo5$179b2o$179b2o74bob
o$256b2o$256bo$180bo$179b3o$178b2ob2o$179b2ob2o$176bo3b2ob2o$175b3o3b
3o$174b2ob2o3bo$175b2ob2o$172bo3b2ob2o$171b3o3b3o$170b2ob2o3bo$171b2ob
2o$168bo3b2ob2o$167b3o3b3o173b2o$166b2ob2o3bo174b2o$167b2ob2o$164bo3b
2ob2o$163b3o3b3o$162b2ob2o3bo$163b2ob2o$160bo3b2ob2o145b3o$159b3o3b3o
148bo$158b2ob2o3bo148bo$159b2ob2o$156bo3b2ob2o$155b3o3b3o$154b2ob2o3bo
$155b2ob2o$152bo3b2ob2o$151b3o3b3o$150b2ob2o3bo$151b2ob2o$152b2ob2o$
153b3o$154bo2$62b2o$62b2o5$61b2o3$130b2o171bobo$130b2o172b2o$304bo6$
133bo3b2o$48b3o80b2o4b2o24b2o$47bo3bo81b2o28bo$47bo4bo79bo28bobo$47bo
2bo2bo107b2o$48bo4bo$49bo3bo111bo$50b3o111bobo$37b2o124bobo$37b2o123bo
bo$162b2o2$178b2o$178b2o2$2o10bo253b3o$2o9b3o254bo$10b2ob2o252bo$9b2ob
2o139b2o$8b2ob2o3bo135bobo$9b3o3b3o133bobo127b2o$10bo3b2ob2o131bobo
128b2o7bo$13b2ob2o133bo138bobo$12b2ob2o272bobo$13b3o44bo221bo8bo6b2o$
14bo46bo219b3o14b2o$33bo25b3o218b2ob2o$33b2o171bo74b2ob2o3b2o$32bobo
170b3o70bo3b2ob2o2b2o$134b2o68b3obo68b3o3b3o$135b2o66b2o2b3o66b2ob2o3b
o$134bo67b2o3b2obo66b2ob2o$201b3o2b2ob3o62bo3b2ob2o$50b2o150bob3ob3obo
60b3o3b3o$49bobo151b3ob2o2b3o58b2ob2o3bo$49bo154bob2o3b2o60b2ob2o$48b
2o155b3o2b2o58bo3b2ob2o$206bob3o58b3o3b3o$207b3o58b2ob2o3bo$208bo60b2o
b2o$25b2o243b2ob2o76bobo$25b2o244b3o78b2o$272bo79bo$222bo$221b3o$220b
3obo31b2o$219b2o2b3o30b2o57b3o$218b2o3b2obo87bo3bo$84bo132b3o2b2ob3o
85bo4bo$85bo132bob3ob3obo83bo2bo2bo$83b3o133b3ob2o2b3o82bo4bo$220bob2o
3b2o83bo3bo$221b3o2b2o85b3o$53b2o55b2o110bob3o$53bobo55b2o110b3o9b2o
86b3o$53bo56bo113bo10b2o85bo3bo$321bo4bo$320bo2bo2bo$237bo82bo4bo$235b
obo82bo3bo$236bobo82b3o$227b2o7bo$227b2o102b3o$330bo3bo$329bo4bo$328bo
2bo2bo$328bo4bo$328bo3bo$329b3o$89b2o$89b2o248b3o$338bo3bo$337bo4bo$
102b3o187b2o42bo2bo2bo4b2o$101bo5b2o183b2o42bo4bo5b2o$101bo4bo229bo3bo
$101bo235b3o$77b2o$77bobo23bo244b2o$77bo24bo245b2o$102bo$271bo$271b2o$
269b2ob2o$118bo150bo4bo$118bo148b2o6bo$117bo150b2o5b2o$269bo6b2o$114b
2o3bo150bo4bo123bobo$113bo4b2o151b2ob2o124b2o58b2o$112b2o4b2o152b2o
126bo50bo8b2o$113b2o158bo86bo91b2o$113b3o239b3o3bo88b2o$114b2o238bo97b
o$113bo2bo237bo$114b2o238bo2bo2bo$360bo91b2o$360bo91b2o$353bo3b3o$354b
o13bo$212b3o148b3o3bo$101b2o98b2o8bo150bo$101bobo97b2o7bo3bobo26b2o
117bo105bo$101bo107bo33b2o117bo2bo2bo4b2o92b2o$208bo7bobo149bo4b2o91bo
bo$208bo6bo152bo96b3o$208bobo3bo3bobo140bo3b3o$213bo6bo141bo108b3o$
210bobo7bo249bobo$219bo250b2o$212bobo3bo251bo5bo$217bo257b2o$214b3o
257bobo$473b3o2$230bo248b3o$230b2o246bobo$229bobo246b2o$478bo$234b2o$
234b2o2$243b2o144b2o$211b2o22bo7b2o144b2o$211b2o23b2o$125b2o107b2o13bo
$125bobo98b2o8bo10b3o$125bo100b2o18bo182bo$246b2o179b2o$428b2o$387b3o$
383b2o5bo$219bo147b2o16bo4bo$214b3o3bo146b2o12bo8bo$213bo167bo$213bo
168bo5bo$213bo2bo2bo169bo57bobo$219bo160bo8bo58b2o$219bo160bo4bo62bo
60b2o$212bo3b3o161bo5b2o121b2o$213bo167b3o7$364b2o$236b2o126b2o$149b2o
85b2o$149bobo$149bo226bo$377bo$375b3o$225bo$223b2o142bo3b2o$224b2o139b
2o4b2o$367b2o$366bo6$368b2o41b5o$368b2o40bo4bo$415bo$410bo3bo$412bo5$
173b2o$173bobo$173bo2$250b3o$201bo48bo$199b2o50bo$200b2o9$404bo$403b2o
$280bo121bobo$278b2o121b3o$187b3o84b2o4b2o$190bo8b2o73b2o3bo127b3o$
185bobo3bo7b2o205bobo$192bo213b2o$183bobo7bo212bo$186bo6bo$181bobo3bo
3bobo230bo$181bo6bo236bo$181bo7bobo82b3o4b2o140b3o$182bo91bo6b2o$183bo
3bobo85bo$184bo$185b3o4$432b2o$432bo$237b2o21bo172b3o$237b2o20b3o173bo
$258b2ob2o154b2o$259b2ob2o153b2o$221bo38b2ob2o$219bo2bo38b3o$218b4o40b
o$217b5o$174b2o42b2o2bo2bo$174b2o40bob2o3b2obo$217bo2bo2b2o$221b5o$
213bo7b4o$211bo2bo5bo2bo$210b4o7bo$209b5o42b2o$210b2o2bo2bo38b2o$208bo
b2o3b2obo$209bo2bo2b2o$213b5o$213b4o$212bo2bo$213bo3$212b2o$212b2o58$
507bo$3bo502bobo$2bobo502bobo$bobo504bobo$obo506b2o$2o!

Naszvadi
Posts: 388
Joined: May 7th, 2016, 8:53 am
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Re: List of the Turing-complete totalistic life-like CA

Post by Naszvadi » December 27th, 2018, 6:37 am

calcyman wrote:...
If you want Banks-I and Rule 110 to be universal, then specifying the pattern as a predicate in Presburger arithmetic is one solution, but it feels very arbitrary.
Suggesting that Cook's result (tag systems in Rule-110) needs clarification or revocation? I've heard on internets that you are a mathematician withOUT any pejorative prefixes like appl./programmer etc. :) Just like me.

In order to raise all your 2cents, according to your interpretations and assumptions: even rule-72 is universal, if a binary fraction constant "z" is known, where its nth digit is 1 if and only if the nth Turing machine halts on the empty input. The cellspace is initially filled with ones in all (4*k)th positions if z's kth digit is 1. Then let the initial generation be altered in position ((4*n)+1). So the fate of any kind of pattern is equivalent to determine a Turing machine's execution finiteness.

What if I told you - a rule-110 simulation also means that logic gates do exist in the host cellular automata. If someone got stuck with finding a universal subset of logical functions, bat^Wrule-110 logo would have to be shown onto the sky: ../forums/viewtopic.php?f=11&t=803&start=1200#p66774

Code: Select all

#C Naszvadi, Peter, 2018, one Christmas afternoon
x = 336, y = 91, rule = 01234-ci5aiknq/5einy6e7e/3:T336,0
94.A.5A.A103.A.5A.A103.A.5A.A2$94.A.5A.A103.A.5A.A103.A.5A.A$94.A.A3.
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A48.A.A3.A.A$38.A.A2.A.A48.A.A3.A.A47.A.A2.A.A48.A.A3.A.A47.A.A2.A.A
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4A.A2.A.12A.4A.3A.4A.4A.3A.4A.A2.A.A2.A.A3.A.10A$89.A.A2.A.A104.A.A2.
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I think these sort of "proofs" are simplifying Banks'-like constructions and verifications of logic gates and their connections, delays etc.

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calcyman
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Re: List of the Turing-complete totalistic life-like CA

Post by calcyman » December 27th, 2018, 4:02 pm

Naszvadi wrote:
calcyman wrote:...
If you want Banks-I and Rule 110 to be universal, then specifying the pattern as a predicate in Presburger arithmetic is one solution, but it feels very arbitrary.
Suggesting that Cook's result (tag systems in Rule-110) needs clarification or revocation?
Cook's paper is absolutely fine; he specifically writes:
Matthew Cook wrote:given a fixed repeating pattern to the left and right, it is undecidable whether a given finite initial condition will lead to periodicity in Rule 110’s behavior
My criticism is not with Cook's result, but with people who go on to say "rule 110 is universal" without explaining what "universal" means in this context.
Naszvadi wrote:In order to raise all your 2cents, according to your interpretations and assumptions: even rule-72 is universal, if a binary fraction constant "z" is known, where its nth digit is 1 if and only if the nth Turing machine halts on the empty input. The cellspace is initially filled with ones in all (4*k)th positions if z's kth digit is 1. Then let the initial generation be altered in position ((4*n)+1). So the fate of any kind of pattern is equivalent to determine a Turing machine's execution finiteness.
Yes, that's why it's necessary to restrict the function mapping a Turing machine to the input pattern.

That function should be computable (as otherwise it could determine directly whether the TM halts), which implies that the output must be a finite description. The simplest set of finitely-describable patterns are the finite patterns themselves. You could, as Cook does, use a more complex definition such as 'patterns which agree with a periodic background in all but finitely many cells', but this needs specifying explicitly to contrast it with the stronger notion of universality that Banks-IV, JVN29, Codd, and B3/S23 all possess.

As far as I know, it's unsolved whether Rule 110 is universal in the stronger sense.
I've heard on internets that you are a mathematician withOUT any pejorative prefixes like appl./programmer etc. :) Just like me.
Indeed -- which is perhaps why I'm very cautious about ensuring that when we use 'universal', everyone agrees what it means. I recall that there was (maybe in the 1800s) a mathematical journal that published (inter alia) two papers on real analysis, where the result of the first directly contradicted the result of the second; specifically, the word 'function' hadn't been properly defined at that point, and the two authors were using different definitions.

And in classical logic, a single contradiction causes everything to collapse: https://en.wikipedia.org/wiki/Principle_of_explosion
What do you do with ill crystallographers? Take them to the mono-clinic!

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