Golly 2.8 has been released

[rowett]

If original rule has B0 and S8:

• Such rules don't strobe, so we just want to invert all the cells. The trick is to do both changes: invert the isotropic bits, and swap B[digit][alpha] for S[8-digit][alpha], plus the special 4-neighbor isotropic bit swap shown in the above table.

And based on this would you expect:

Code: Select all

rule: B0124cik/S1c258  becomes: B12457-c8/S01234-etk5

[dvgrn]

If original rule has B0 and S8:

• Such rules don't strobe, so we just want to invert all the cells. The trick is to do both changes: invert the isotropic bits, and swap B[digit][alpha] for S[8-digit][alpha], plus the special 4-neighbor isotropic bit swap shown in the above table.

And based on this would you expect:

Code: Select all

rule: B0124cik/S1c258  becomes: B12457-c8/S01234-etk5

Let's see... B0124cik inverts to B34-cik5678, and swapping to S[8-digit] you get S01234-etk5 -- check.
And S1c258 inverts to S01-c3467, and swapping to B[8-digit] you get... B12457-c8. Check again!

Seems like black magic -- I hope this all actually works.

[rowett]

Seems like black magic -- I hope this all actually works.

You can try it here. Copy and paste from the pattern below.

B0 without S8:

Code: Select all

x = 1, y = 1, rule = B01c23/S1234kt5
o!

[dvgrn]

Seems like black magic -- I hope this all actually works.

You can try it here. Copy and paste from the pattern below.

B0 without S8:

Code: Select all

x = 1, y = 1, rule = B01c23/S1234kt5
o!

Ha -- looks good so far! Golly, via isotropic-rule-gen.py, reports (after a lot of flickering) that generation 128 of the above pattern is

Code: Select all

x = 129, y = 129, rule = B01c23/S1234kt5
obobo119bobobo$2b2o2bo3bobo15bobobo21bobobo11bobobo21bobobo15bobo3bo2b
2o$2ob2o24b2o21bo2b2o15b2o2bo21b2o24b2ob2o$b2obo4bob2o11bo3b2ob2o21b2o
b2o11b2ob2o21b2ob2o3bo11b2obo4bob2o$ob2ob2o2bobo10bobo3bob2o19bo2bob2o
13b2obo2bo19b2obo3bobo10bobo2b2ob2obo$4bo3bo3bo5b2o4bo4b2obo22b2obo11b
ob2o22bob2o4bo4b2o5bo3bo3bo$bo2bobobob2o2bo2bobobobo7bo25bo13bo25bo7bo
bobobo2bo2b2obobobo2bo$7b3o6bobo2bobo7bo25bo13bo25bo7bobo2bobo6b3o$5b
3o8bo2bobobo15bobo45bobo15bobobo2bo8b3o$3b2o2bo2b3o3bo3b2obo17bo10bo
23bo10bo17bob2o3bo3b3o2bo2b2o$bo4bo2bo29b2o10bob2o19b2obo10b2o29bo2bo
4bo$3b2obo2bobobo4bobo2bobo3bobobo6b2obo9bobo17bobo9bob2o6bobobo3bobo
2bobo4bobobo2bob2o$bobobo3bo4bo8bo7bo7bob2o3b2o5bobo3bobobobobobo3bobo
5b2o3b2obo7bo7bo8bo4bo3bobobo$11bo6bo3b2obo3b2ob2o6bo10bobob2obob2o5b
2obob2obobo10bo6b2ob2o3bob2o3bo6bo$6bo5bo2b2o8bo6bo9bo3b3o9bo4bobo4bo
9b3o3bo9bo6bo8b2o2bo5bo$14bo3b3obo2bo7bo15bo2b2ob3o2bo7bo2b3ob2o2bo15b
o7bo2bob3o3bo$7b3o4bo6bo3bo16bo4b3o8b2o9b2o8b3o4bo16bo3bo6bo4b3o$6bo
12bobo3bobobo3b2o5bo7b8o17b8o7bo5b2o3bobobo3bobo12bo$5bobo3bobobo11bob
obo7bo6b3o31b3o6bo7bobobo11bobobo3bobo$5b2obo6bobo7bobo4bobo5b2obo5b7o
8bo8b7o5bob2o5bobo4bobo7bobo6bob2o$9bobo3bo9b3ob3o7b2o4bo3bo29bo3bo4b
2o7b3ob3o9bo3bobo$6b4o6b2o6bo7b2o7bo2b2o4b6obo5bobo5bob6o4b2o2bo7b2o7b
o6b2o6b4o$4bo8bobo9bo13bo10bo4b2obo4bobo4bob2o4bo10bo13bo9bobo8bo$6b4o
b3o18bo11bo6b4ob3obo3bo3bob3ob4o6bo11bo18b3ob4o$3b3o15bo25b4o4b2o5bobo
bo5b2o4b4o25bo15b3o$11bob5ob2obo9bobo16bo6bo11bo6bo16bobo9bob2ob5obo$
20bo11bobo6bo4b3o2bo5b2o4b3o4b2o5bo2b3o4bo6bobo11bo$17b4o9bob2obo6bo6b
2o8bo9bo8b2o6bo6bob2obo9b4o$bob2o23bo2bobobo9b5o7b2o4b3o4b2o7b5o9bobob
o2bo23b2obo$2b2obo5bobo3b2obo8bobobobobo6bo4bo29bo4bo6bobobobobo8bob2o
3bobo5bob2o$b2ob2o7bo6bo6bo3bobobobo4bob4obo29bob4obo4bobobobo3bo6bo6b
o7b2ob2o$3b2ob2o3b2o5bobo7b4obobobo4bo6bo29bo6bo4bobobob4o7bobo5b2o3b
2ob2o$bobobo7b2o4bobobob3o5bobobobo3b3obobo6b2o13b2o6bobob3o3bobobobo
5b3obobobo4b2o7bobobo$11bobobobo3bo5b8obo8bobobobo25bobobobo8bob8o5bo
3bobobobo$17bobo5b2o6b2obo6bo2bo9bo4bobobobo4bo9bo2bo6bob2o6b2o5bobo$
27b6o10b2obobo10bo2b2ob2o2bo10bobob2o10b6o$33b2o6bo2bo4bobo10bobobo10b
obo4bo2bo6b2o$29b4o10bo18bobobo18bo10b4o$49bobo9bobobobo9bobo$8bobobo
5bobobo9bo12bo2bo14bobo14bo2bo12bo9bobobo5bobobo$10b2obo3bob2o23bo18bo
bo18bo23b2obo3bob2o$8b2ob2o6bobo4bo9bo6bobob2o7bo6bobo6bo7b2obobo6bo9b
o4bobo6b2ob2o$12bobobo10bo2b2o15bo15bobo15bo15b2o2bo10bobobo$11bo7bo
12bob2obo3bo2b2obo13bo5bo13bob2o2bo3bob2obo12bo7bo$21bobo5b2obo2b2o3bo
2bob2o10bo3bo2bo2bo3bo10b2obo2bo3b2o2bob2o5bobo$20b2o6bobob2o5bobob2ob
2o10bobob2ob2obobo10b2ob2obobo5b2obobo6b2o$12bobo3bo7bobobo3b2o8b2o3bo
bo3bo2bobo3bo3bobo2bo3bobo3b2o8b2o3bobobo7bo3bobo$12bobobobo5bobobobob
2o7b3obobo11b3obobob3o11bobob3o7b2obobobobo5bobobobo$14bob3o5bobobo6bo
3bobo7b4o5b2obob3obob2o5b4o7bobo3bo6bobobo5b3obo$15b3ob2o3bo2b7o2bobo
7bobo6bobo4bobobo4bobo6bobo7bobo2b7o2bo3b2ob3o$17bobob2obo2bo20bobob3o
7bobobo7b3obobo20bo2bob2obobo$4bo5bo2bo3bobobobob2o6bo2bobo7bobo7bo2bo
9bo2bo7bobo7bobo2bo6b2obobobobo3bo2bo5bo$2bo6bo5bobobobobo24bobo3bo9bo
9bo3bobo24bobobobobo5bo6bo$10b4obobobobobo26bo7b2ob2obob2ob2o7bo26bobo
bobobob4o$bob2o5bo6bobobobo26bobo23bobo26bobobobo6bo5b2obo$2b2obo5b3ob
obobob2obo21bo2bo9bob7obo9bo2bo21bob2obobobob3o5bob2o$b2ob2o7bobo6b3o
7bobo6bo9bo25bo9bo6bobo7b3o6bobo7b2ob2o$3b2ob2o7bo5bobo2bobo3bo11bo4bo
10b9o10bo4bo11bo3bobo2bobo5bo7b2ob2o$bobobo7b2obo5b2ob2obo16b2obo4bo
21bo4bob2o16bob2ob2o5bob2o7bobobo$12bo3bo10bo7bo11b2o2bobobo5bob3obo5b
obobo2b2o11bo7bo10bo3bo$13bobo7bo21b3o9bo13bo9b3o21bo7bobo$12b2o20bo3b
o4b2o2b2o4bobobobo4bo4bobobobo4b2o2b2o4bo3bo20b2o$24bo10b3o7bo3b2o2bob
obo4bobobo4bobobo2b2o3bo7b3o10bo$12bobo6b2o3bobo5b2o2b5o2bob2o6bobobo
4bo4bobobo6b2obo2b5o2b2o5bobo3b2o6bobo$19bo3b2obobo7b2o6bobob3ob2obobo
bob3ob3obobobob2ob3obobo6b2o7bobob2o3bo$12bobo6b2o3bobo5b2o2b5o2bob2o
6bobobo4bo4bobobo6b2obo2b5o2b2o5bobo3b2o6bobo$24bo10b3o7bo3b2o2bobobo
4bobobo4bobobo2b2o3bo7b3o10bo$12b2o20bo3bo4b2o2b2o4bobobobo4bo4bobobob
o4b2o2b2o4bo3bo20b2o$13bobo7bo21b3o9bo13bo9b3o21bo7bobo$12bo3bo10bo7bo
11b2o2bobobo5bob3obo5bobobo2b2o11bo7bo10bo3bo$bobobo7b2obo5b2ob2obo16b
2obo4bo21bo4bob2o16bob2ob2o5bob2o7bobobo$3b2ob2o7bo5bobo2bobo3bo11bo4b
o10b9o10bo4bo11bo3bobo2bobo5bo7b2ob2o$b2ob2o7bobo6b3o7bobo6bo9bo25bo9b
o6bobo7b3o6bobo7b2ob2o$2b2obo5b3obobobob2obo21bo2bo9bob7obo9bo2bo21bob
2obobobob3o5bob2o$bob2o5bo6bobobobo26bobo23bobo26bobobobo6bo5b2obo$10b
4obobobobobo26bo7b2ob2obob2ob2o7bo26bobobobobob4o$2bo6bo5bobobobobo24b
obo3bo9bo9bo3bobo24bobobobobo5bo6bo$4bo5bo2bo3bobobobob2o6bo2bobo7bobo
7bo2bo9bo2bo7bobo7bobo2bo6b2obobobobo3bo2bo5bo$17bobob2obo2bo20bobob3o
7bobobo7b3obobo20bo2bob2obobo$15b3ob2o3bo2b7o2bobo7bobo6bobo4bobobo4bo
bo6bobo7bobo2b7o2bo3b2ob3o$14bob3o5bobobo6bo3bobo7b4o5b2obob3obob2o5b
4o7bobo3bo6bobobo5b3obo$12bobobobo5bobobobob2o7b3obobo11b3obobob3o11bo
bob3o7b2obobobobo5bobobobo$12bobo3bo7bobobo3b2o8b2o3bobo3bo2bobo3bo3bo
bo2bo3bobo3b2o8b2o3bobobo7bo3bobo$20b2o6bobob2o5bobob2ob2o10bobob2ob2o
bobo10b2ob2obobo5b2obobo6b2o$21bobo5b2obo2b2o3bo2bob2o10bo3bo2bo2bo3bo
10b2obo2bo3b2o2bob2o5bobo$11bo7bo12bob2obo3bo2b2obo13bo5bo13bob2o2bo3b
ob2obo12bo7bo$12bobobo10bo2b2o15bo15bobo15bo15b2o2bo10bobobo$8b2ob2o6b
obo4bo9bo6bobob2o7bo6bobo6bo7b2obobo6bo9bo4bobo6b2ob2o$10b2obo3bob2o
23bo18bobo18bo23b2obo3bob2o$8bobobo5bobobo9bo12bo2bo14bobo14bo2bo12bo
9bobobo5bobobo$49bobo9bobobobo9bobo$29b4o10bo18bobobo18bo10b4o$33b2o6b
o2bo4bobo10bobobo10bobo4bo2bo6b2o$27b6o10b2obobo10bo2b2ob2o2bo10bobob
2o10b6o$17bobo5b2o6b2obo6bo2bo9bo4bobobobo4bo9bo2bo6bob2o6b2o5bobo$11b
obobobo3bo5b8obo8bobobobo25bobobobo8bob8o5bo3bobobobo$bobobo7b2o4bobob
ob3o5bobobobo3b3obobo6b2o13b2o6bobob3o3bobobobo5b3obobobo4b2o7bobobo$
3b2ob2o3b2o5bobo7b4obobobo4bo6bo29bo6bo4bobobob4o7bobo5b2o3b2ob2o$b2ob
2o7bo6bo6bo3bobobobo4bob4obo29bob4obo4bobobobo3bo6bo6bo7b2ob2o$2b2obo
5bobo3b2obo8bobobobobo6bo4bo29bo4bo6bobobobobo8bob2o3bobo5bob2o$bob2o
23bo2bobobo9b5o7b2o4b3o4b2o7b5o9bobobo2bo23b2obo$17b4o9bob2obo6bo6b2o
8bo9bo8b2o6bo6bob2obo9b4o$20bo11bobo6bo4b3o2bo5b2o4b3o4b2o5bo2b3o4bo6b
obo11bo$11bob5ob2obo9bobo16bo6bo11bo6bo16bobo9bob2ob5obo$3b3o15bo25b4o
4b2o5bobobo5b2o4b4o25bo15b3o$6b4ob3o18bo11bo6b4ob3obo3bo3bob3ob4o6bo
11bo18b3ob4o$4bo8bobo9bo13bo10bo4b2obo4bobo4bob2o4bo10bo13bo9bobo8bo$
6b4o6b2o6bo7b2o7bo2b2o4b6obo5bobo5bob6o4b2o2bo7b2o7bo6b2o6b4o$9bobo3bo
9b3ob3o7b2o4bo3bo29bo3bo4b2o7b3ob3o9bo3bobo$5b2obo6bobo7bobo4bobo5b2ob
o5b7o8bo8b7o5bob2o5bobo4bobo7bobo6bob2o$5bobo3bobobo11bobobo7bo6b3o31b
3o6bo7bobobo11bobobo3bobo$6bo12bobo3bobobo3b2o5bo7b8o17b8o7bo5b2o3bobo
bo3bobo12bo$7b3o4bo6bo3bo16bo4b3o8b2o9b2o8b3o4bo16bo3bo6bo4b3o$14bo3b
3obo2bo7bo15bo2b2ob3o2bo7bo2b3ob2o2bo15bo7bo2bob3o3bo$6bo5bo2b2o8bo6bo
9bo3b3o9bo4bobo4bo9b3o3bo9bo6bo8b2o2bo5bo$11bo6bo3b2obo3b2ob2o6bo10bob
ob2obob2o5b2obob2obobo10bo6b2ob2o3bob2o3bo6bo$bobobo3bo4bo8bo7bo7bob2o
3b2o5bobo3bobobobobobo3bobo5b2o3b2obo7bo7bo8bo4bo3bobobo$3b2obo2bobobo
4bobo2bobo3bobobo6b2obo9bobo17bobo9bob2o6bobobo3bobo2bobo4bobobo2bob2o
$bo4bo2bo29b2o10bob2o19b2obo10b2o29bo2bo4bo$3b2o2bo2b3o3bo3b2obo17bo
10bo23bo10bo17bob2o3bo3b3o2bo2b2o$5b3o8bo2bobobo15bobo45bobo15bobobo2b
o8b3o$7b3o6bobo2bobo7bo25bo13bo25bo7bobo2bobo6b3o$bo2bobobob2o2bo2bobo
bobo7bo25bo13bo25bo7bobobobo2bo2b2obobobo2bo$4bo3bo3bo5b2o4bo4b2obo22b
2obo11bob2o22bob2o4bo4b2o5bo3bo3bo$ob2ob2o2bobo10bobo3bob2o19bo2bob2o
13b2obo2bo19b2obo3bobo10bobo2b2ob2obo$b2obo4bob2o11bo3b2ob2o21b2ob2o
11b2ob2o21b2ob2o3bo11b2obo4bob2o$2ob2o24b2o21bo2b2o15b2o2bo21b2o24b2ob
2o$2b2o2bo3bobo15bobobo21bobobo11bobobo21bobobo15bobo3bo2b2o$obobo119b
obobo!
#C [[ THUMBNAIL ]]

-- and Molly agrees with that, cell for cell, using the flicker-avoidance algorithm.

An asymmetric starting pattern would probably make for a marginally better test. I'll try that with a random selection of other rules and see how it goes.

-- I can't copy an evolved pattern out of Molly as RLE, right? The Help doesn't seem to give me any save or copy options. Copying out as a bitmap doesn't quite work in Internet Explorer 11; a lot of gray pixels sneak in and mess things up. But in Chrome it works perfectly. Not that I needed any more reasons to avoid IE -- it look like even Molly's keyboard shortcuts don't respond in IE.

EDIT: Okay, now it's looking even better. This starting soup --

Code: Select all

x = 20, y = 20, rule = B02ce3aeqk4ynktec5krcyjni6ikc7c8_S01c2a3ayeq4krjzc5krqcei6ic7e
o2b4o6b7o$obob3o2b3ob3obo$3bo3b5obobob2o$bo2b2ob3o2bo4bo$obob2obobo3b
2o3b2o$2ob2obob4o$2o2bob2o2b2o2b3obo$4o4b2ob2obo$bobo3b3o2b2ob5o$6o4b
2ob3o2b2o$o2b2o3b3o3b5o$2b2obob2o4bob5o$4b3o2bobob2o2bobo$ob3ob4obo2b
2o3bo$2o2b2obob2o4bob3o$3bob2obobob3o3b2o$bo2bobo4b2obo3b2o$2ob2o3bo5b
o$bo4bo2b2o7bo$3b2o4b3o2bob4o!

produces the following in Molly after 128 ticks:

Code: Select all

x = 296, y = 296, rule = B02ce3aeqk4ynktec5krcyjni6ikc7c8_S01c2a3ayeq4krjzc5krqcei6ic7e
296o$296o$296o$296o$296o$296o$296o$296o$296o$296o$138o7b6o7b138o$138o
3bo3b6o3bo3b138o$136o4bobo4bo2bo2bobo4b136o$136o2bo10b2ob3o2bo2b136o$
134o2b2ob2obo2b2o3b2o2b3ob138o$138o2b2o2bob2ob2ob3ob2ob137o$135ob6ob2o
bob2o4bobobob136o$132ob4obo4b2ob4o3bob2obob2ob133o$131ob4obobobo2b6obo
b3o5b135o$131o2b6o3b2ob3ob4obo2b4ob3ob130o$128o2b4ob2o2bo3b2ob3ob2ob2o
4b2ob4ob129o$128o2b2obo2b2ob4o2bobob4o2b2ob7obob128o$129ob3obo2b8o4b3o
3b10ob2ob127o$130o2b4o3b2o4b3o2bo2bobob2obo2bo2b3ob126o$125o2b4ob2ob9o
b4obo3bo2bo2b4o2bob128o$124o2b2ob11obob3o5b2ob2o2b2ob2ob2o3b2ob124o$
124o2bo3bo2b2ob2obo2b2o4b3o5b3ob2o2bo6b125o$124ob2obobobob2o2bob2o2b2o
bobob2o2b2obobo2b4o4b125o$120obo3b3o2b2ob2obo2b2o4bob4o3bob2obob2obob
2ob2o4b121o$120o5b2o2bob5o2b3o9b4o3bob2ob2obo2bob2o2bob120o$118ob2obo
2b2obob2ob5ob4obob2obo4bob2ob3obob8o2b121o$120ob3obob2obobo2bob3o2bob
5o2b3obob4ob3o2b2obobo3bob118o$119obob6o2b3o2b4ob3obo3b3o2b2ob6ob4obo
3b2o2b2ob117o$119o2bo2b6obo2bo2bo2b4obob3o6b2o2bob3ob8obob119o$116o3b
2ob5o2b2obo3bo6bob2ob2obobobob5o2b2o4b7ob118o$115o3b7o3bobo2bobobo3bo
4b2o2b2o3b2o2bob2obo2bobob2obobob118o$115o6bobo2bob7o2b3o6b5obobob2o2b
3o2b2obo2b2ob122o$112ob4o6b3obobobo3b2obob5ob3ob5o2b2o4bo2b2ob2obobob
2ob3ob113o$115o4bo2b3ob3obo3bob2ob2o2b6o3b2ob4ob3obob3o2bobo2b2o2bobo
2b111o$114o5bob7o2b2o5b2o2b2ob4o2b3o4b4ob2ob4o4bo2b2ob4o3b110o$109o2b
2ob2o2bob3o2bo4bo3bo2bobob4ob2obob2obob5o4b5o2bobo2bo2b6ob109o$108obo
2b2ob7o2bo2b2o2bob2o3b3ob2ob8ob4o2b4o3bo2bobob2ob5o3bob109o$108o2bo3b
5obo2b2ob2obo5bob2ob5ob2o2b2obob5o2b3ob2obobo6b4obo4b108o$106o3b7obob
3obo3b2obobo2b2o2b3ob5ob3o3b2obo3b4o3b2o5bo2b4ob3o3b106o$106o2b5o3bob
5ob3o2b2obo3bo2b2ob12ob4o3b2o3b2ob5o4bob4ob3o2b105o$106o2bobo2b3ob7ob
4o5b3ob2obo2b7obo4b2ob3ob7ob2o2bob2ob3o3b2o2b105o$103ob6o5bo2bo3bob2ob
o4b3obob6o2bo2b3o3b3o2b3o2b3ob6o3bo2b3ob3obob105o$102ob4ob2ob3o4b4ob6o
b3obo2b2obob3o3bobob15ob4obo2bob2ob3ob6o3b102o$101ob5o2b4obo4bob2o3b4o
b2obo2b3ob3obo2b2ob4o2b7obo3b2o2bob2obobob3obo2b4o2b101o$100ob4o2b5obo
2bo3bo3b3obob3o2b3o2bob3obob8ob2obob4o2b2o4bobo2b3o2b2ob7o2b100o$101o
2bo2b6o3bobob3ob12o3b2ob2ob3o4bobo2b2o3bob2ob8ob2o2b4o3b2ob2ob3o2b99o$
103ob2ob4obobo2b2obo3b8obo2b2obobob3ob3ob3o2bobob3o2bob3obob2o2b6ob3ob
2ob6ob98o$99ob7o3bo2bobo2b2o2bo3bobob2o2b5o2b5o3bo2bobo3b2o2bo3b2ob3ob
ob2ob5o2b2ob4obob101o$96obobobob5obobob15ob5o2b3ob3ob5o2bo3b2obobo3b2o
2bob2ob3ob3obobob5o2bob4ob97o$95ob3obo2bob5o2bo2bobo2bo3bo3bobob2o2b3o
bo2b3o2bo2b4ob9obob2o2bob2o6b7ob5ob2o3b95o$94o3bobo2bo2b11ob2obob2o5bo
b6o2b2obo2b3o3b2obob4o3b4obob4o2bo2bo4b2o3b2ob2o3b99o$93obobo2b7obob2o
b3obob3ob2obo2b2ob3obo3b2o2bo2b3obobobobo4b2obo2bobo3b2o2b5o2b2ob2ob2o
3bo2bo2bob93o$94obo2bobobobobo2b2obob2o2bo5b4o2b10o2bo2bobobo2bob2ob3o
b5obob3obobo2b4o2b2ob2ob5o3bob3ob92o$92ob5o3bobobo2bob2ob3o2bo3bob7ob
2o2bobob2obo2bobob3o2b3ob2obo2bobobo2bobo2bo2bo5b2o4b7obobob92o$90o2bo
bo2b3o3b5ob2obob2o4b2ob4o2bobob3o3bobob2o4bob3obob3ob3ob4o2b2obo2b2o2b
ob6o2b2ob2o6b94o$89ob5obo2b3obo4bobo3b2ob4ob2obob3o5b4ob2ob2ob3obob2o
2b2obo3b4o2b6obob3o2b9o2bobob2ob95o$88ob2ob2o3bo3bobobo5b6ob4o2bo2b3ob
o2b5obo2bobo2b3ob3o2b8obobo2b4ob2obob4ob3obo2bob2ob5obob90o$87o2bob7ob
2ob2o3b4o3b2obo2b12obobob2ob3ob4o3bo4bob2o2b4ob2o2bob5obo3bo3b3o3b6o2b
2ob2ob89o$86obobobob3o2bo4b2o3b2o2b7ob3o3bobob2ob3o2b5o4bob2o2b6ob7o3b
ob8obob2ob4obo3b2ob6o3b89o$86o2b2o2b4obo2b2o2bo2b2ob3obob3o2bobobo2bo
6bob4obobob2ob3ob4ob2o2b3ob3ob5obo2bob3ob4o2bobo4b3o3b2o2bo2b85o$84o2b
ob4obob2ob6ob5o3bob3o2b2obobobobob2ob2o2b2obob2o2b3ob6obobo4b2obobob3o
2b5ob7obobob2ob2o2b2ob2o3bob84o$83ob6ob11ob3ob2o2b2o2bo3bob6o2b2ob2o3b
2ob6ob3obobo2bo2b2obobob8obo4b4o3b3o2bo2b3ob2o3bo2bobo3b83o$82o3b2obo
3b2o3bo2b4o2b6obobobo2bob5ob3obo3bo2b2o2b3ob4ob5o4bob4ob3o3b4o2b3obo2b
4obobob4ob2o3bobob86o$81obo2b2obob3o4b4obob5ob2o3b2obo3b6o2b2o2b2ob4ob
3obo2bobobob2o5b5obob4ob3o2b3o2b2ob3obobob5o3b5o6b81o$80ob2ob2obo3b2ob
ob2obo3b2ob6obobobo2b4o3bo2bo3b2o3bob2ob2o2b8o2b3ob2obob2ob2ob2ob2ob7o
b3ob5o2b4obo2bo2bobo4b80o$80o2b3obobob2ob2ob2ob4ob8ob3o2bob3ob3o2b10ob
2obo3b2ob2o2bobo3b3o2b4obob3o2bobo2bob4o4b3ob2ob2o2bobo5b3o3b79o$78ob
7ob2obob3ob8ob7obob7obo2b2ob2ob3obo4b2obobob2obo2b4o3bobob3o2b2obo3b2o
b2obob2obobob2o2bobob9ob3o4b79o$77o3bob2ob2ob9ob2obob5o2bob2o2b3o2bo2b
7ob2o2b3ob3ob2obob12o2bob2o2b5ob2ob2obob2o2b2ob2o3b7obob3ob3ob3o3b77o$
76o2b2ob8o3b4o2bobobo3b5ob2obob3obob2o4b2o2b7o2b3obo2bo2b10o3b7ob4obob
3obobob2ob3obo2b3obobob4o2bo2b2obob76o$78ob4ob3obob2ob3o2b5obobo4b5o2b
9obo2bobo2b3ob6o2bo2bob6o3bob2obobob7o4bobo2b2obob3o2b2ob2o4b3o2b2obo
2bo2b76o$75obobob2ob3obob3o2b3o2b2ob3ob4o2b2ob3obob6o4bobob2obob4ob4o
3b3obo2bob4o3b5o2b2ob2obob2ob6o2bob3o3b2o3bobo3b2o2b3o2b74o$73ob2obo2b
3obo2bobo2bo2bo2b4ob4o2bo6bob13o2b2obo3b3o3bobo2bobob3o2b3o2b3o2b5obo
2b3o6bo2b3ob7o2bo2bobobobo3b2o4b73o$72o3bo10b3ob3o2bobobobob3obob5o2b
2ob3ob4o2bobo2b2obobob4obo2bo4bob2ob2ob3o6bo3bob2o2b7obobob3ob4obo5b3o
bobobo3b2o2b72o$71o4b3ob3obo4b2ob2ob9ob3obobob8o3bobob4ob6obob2ob5obob
ob2ob2o4b17ob2obob2ob8o2b3ob6ob2ob5o3b2o2b71o$70obob3o4bo2b6o2bo3b5ob
5o2bob4ob6o5b4ob4o2b2o5b6obobo4b3ob2obob3o2b7ob4obo2b2ob8o4bobobob2obo
bo4bo3b73o$69o2bo2b7obo3b3ob2ob6o3b3o4b2ob2ob6ob2o2bo2b2o2b2obo4bo2bob
3ob2ob2ob2ob6obobo2b3obo3bo3bob2o3bo2bob9obo2bobo4b4o2bobobob69o$68obo
3bo2bo3b2obob2ob2ob3ob4o2b5o3bob3ob2ob3o2b2ob3ob8ob6o2bob3o3bobo3bob2o
bo3bob6ob2ob2ob4o2b4obob2o3b2o2bobo2bo2b3obo5bo2b68o$67o5b4obob2o3b4ob
2ob5ob3ob9ob2ob6ob3o2b5o2b2obobobob2ob3ob3obob3obob6obob5o2b4ob2o2b7o
2bob2ob3o2bo2b8ob2o3b3ob69o$70ob2o5b4ob3ob7obobobo2b5obobob6ob4obo4b2o
2bo2bob2obobobo2b2o3b2o4bob3ob15obobo2bobo3b4obob3ob2o2b2o2bo2b5o2b8ob
66o$65obobobob3obob2o2b8o2bobob2o2bo2b2o2bobo2b2ob3obobo2b2ob10o2bobo
2bob2obob3obob5ob2ob2ob2ob2obobobob11obo2bob2obo2bo2bob2o2bob2obo2bob
2ob4ob65o$64ob4o2b2ob6obob3o2b2obobobo2b3obob3ob3o2bobobob2o2b3o2bo2b
2o3bo2b3ob2o2b3ob6ob5o2bo2b9o2bo3bob5o2b5obobob3ob2obo2b3o3b4o2b5obob
64o$63ob2ob2obob6obob2obobob2ob3o2bobo3bobobo2b4ob9ob3obo4bob3obo2b2ob
2obob5ob3ob3o2bob3o2bo2bo2bo13b2ob2obobob2o2b2o3b3o2bobo3bo2b3obobob
63o$62o4bobo2bo2b4o2b2ob4o2bo2bo3b2ob4o2bo2bobo2b3obob3o4b2o2b3obobob
3o3bo2bo3b4ob2ob3obob3ob6ob2obobobobo2b3ob2obo2b5obo2bo2bob4ob3o3b3o4b
ob64o$61obo3b4ob4ob10obob2ob7obo3bobo2b2ob5ob3o2b2ob6ob4ob4obob5obo2bo
bob3o4bob2o2b2o4b2ob3ob3ob2ob2ob2ob2ob4o2bob2o2b2obob2o3bo2b3o5b63o$
60obo3bobob3ob2ob8o2b2o4bo5bob2o2b2o2bob8obobo2bo3b3o2bobob2obo4bobo2b
5obob6o2b2ob2o2b3ob4o3bo5b4obobobo7b2o2bob7obobobo2b5o3b60o$59ob3ob2ob
2ob2obo2b3o2bobo3bob3ob2obobobobo3bo2b13obob3obob2o2b2ob3o2bo2b3ob3ob
3obob2ob2o2b2ob4obo3bobob2obob5ob2ob4o2b2ob3ob2o2b2ob5o2bobo2bo2b4ob
59o$61ob2ob3ob4o2bob2obo2b5o2b4o2b2o3b2ob3ob2ob2o2b2o2b3ob6ob2ob6obob
2obo2bob2obobo2b4obo2bob6ob3obo2bo2bob5o3b2ob6ob5ob2o8b2o4bobob5o2b58o
$61ob5o5b3ob3obobobobobobob2o5bo3b4obob2obobo3b3o2bobob2o2b2obobob2ob
4obobob5obob2ob2obobo5b2obob4obo2bo2b2o2bobo2bo5b5o2b3ob11o4bob6ob57o$
56o8b2o6bobo2bo3bob3obob2o4b3o3b5obob2ob5obo2b7ob2o2b2ob3ob2ob6o2b2ob
3ob2obobob2ob2ob7o2bo3b2obo4bo4b4o3bo2b2ob5o4bo4b3o2bo2b64o$55o3bob3ob
2ob4o3bob5ob3o4bo2b2obob8ob4obo2b2o2bo3bo2b12ob4obobobob4o3bo2b7ob6o3b
2obo2b2obobobobo4b2obo2b3o3b5obob3o2bob2o2bobobo5b2o2b55o$54ob2ob2ob4o
bob3o3b3obobobobob2o2b5ob2ob2ob2ob5o3b2ob2o2bob7o4bo2bo4b6obobob2o3bob
o2b4o4bo2b2obobobob2obo4b4obob2o2b2o2bob2ob5ob2o2b8ob3obob61o$53obob3o
b2o3bo3bo2b2obo2b10obob3obo2bob2ob4o3bobo4b7ob2o4b2ob3ob3ob10obobob5o
2b3obo2bo2b2o2b5obo2b7ob3ob5o2bobob2ob3obo3bob3obob2o2bob3o2b56o$52ob
7ob4ob3obobobo2bob5ob6o2bobob2ob2ob3ob2obob2o2bo2b6ob3ob2obo2bobob2ob
4o2b4o3b2ob3obob3obob2ob3o2bobo2b2o3b2o4bobo2b6obo3bo2bo4bo2b4obo2bob
2ob61o$51ob2o6b2obobo4bo2bo2bo2bo2b11ob4ob2ob7obob4o2b6o2b3o2bob3obo2b
ob2o4b6o2bob9ob5ob6ob3o2b5ob2o2bobo2b2ob2ob3ob2o2b3ob5o2bobo2b2ob2o2b
5ob52o$50o2bo3b3obob2o2bob5obo2bob5o3b4ob5ob2o2b5o3b2obo2bob3o3bo3b2o
5bo2b2ob2ob2ob2ob7o2bobobo2b3obo2b3o2bobob3ob3ob3ob4obo2b4ob2o3b3o2bob
7o2b2o6bo5bob52o$49o2bobob2o4bob3ob4ob4ob3obobo2b4ob2o2bobob4o2b2ob2ob
5obo2b2ob4ob5ob2o5b3ob2obobobo3bobob4obobobob2ob3ob8obobo2bobob2ob4obo
bo2b3obob2o2b3ob2obob2o2b2obo4bob2o2b50o$48ob2o2bo3bo2bob6obob9o3b12ob
10ob2o3bobo2b3o8b2obobob4o3bo4b3ob3o3b3obob7obobob3ob4o3b5ob6o2b2ob2ob
ob3o2b5ob3ob3ob2obo2bo2bobobobob2ob49o$47o6bobo3bo4b3obo2bobo3b2o3b2o
2b2ob3obobobo2bo2b2ob2obo2b4ob3o3b2o2b3ob3obob3ob5o2bob2obobobob2ob2ob
obo2b3obo2bob3ob2obobobo2b2ob2obo2bob2o2b9obob2ob2o2b5o2b2o2bobo2b2obo
b48o$46o3bo2bob4ob4ob2o2bo2b3ob3ob6o2b5ob4ob2ob3obob2obo3bobobo2b2ob5o
2b2ob4o3bob2ob2o2bo2b2o3b2o4bo2b3obob3ob2ob2obobo4b4o2b2obob3ob7o2b2ob
3ob2o2b2o3bobo5b2obo3bobob47o$45o3b3ob6obo5bo2b3o3b2ob3ob5o4bob10obo2b
3ob2o3bo3b4o2bob2ob2o2bo3b2ob3obobo2b2o4b2ob5o3b6ob4o3b2obobo2b2ob5obo
3b9ob5obo2b2o2b3obo2b3ob8ob2o2b47o$44o3b2o2b2obobob2o2b2o3b2obo2b4ob3o
2bobo2bob3obobob2ob5ob2ob3ob2o5bobo2b2obobob2ob2o2b3o2bo2b2obobo4bob2o
b2o2b2ob5o3b4obobob2ob4ob2o3b3ob3o2bobobob2obobob5o2b3o2b3o2bo2b5ob2ob
45o$43o4b3o2b2obobob2obob2o2b5obo2b2ob5o3bobobo4b8ob2ob3ob4obobo3bo3b
3ob2o3b5o2bobob6o2b8o2b2obob2ob5obob3obob2ob2o3b2obo6b5ob3o4bobo2bob
10ob2ob4o2b4o2b44o$43o2bo2b3obob4obobob7o5b2o3b2obo2bobo2b2obobo3b3o4b
o2bobo2b3obobobo2b3o2bo2bob3ob2o2b2ob2o2bo2b2o3bo2bob3ob2obobo3bob4o2b
ob5obobob3o3b4obobo2b8o2b7o2b4ob2obobob2obobobob43o$41o2b2ob2o2b10obob
2obobo2b4o2bo2b3ob2obo3b2ob7obob6o2b2ob2obo6bob2obob4o3bob3obo3b3ob2o
2b2o2b8o4bob6o2bob2ob4o3bob5o2b4ob3obo2bo2b4ob2ob10o2b2obob2ob2obo2b
43o$40obob3ob7ob3o2bob3obo2bo2bo2b2o2bo3b6obob3ob3obo2b4o2b5o2b5obobob
2ob6o2b5o2bobo5b3ob5o3bobob5o2b3o2b2obo2b6obob3ob5ob2obo3bo4b2o2b5ob3o
2b4obo2b2o3b2ob2o2b44o$40o2b3ob3o2b2obob4ob3ob2o3b4ob3o2b3obob9o3b2o3b
3ob2o2bo2b3o3b2o2bo2b2o2b2ob4obo4bo3b2obo2bobobo2b2ob4o2bo2bo4b2ob3o4b
2o4b3obo4bobob8o2b2o4bob5o2bo2b4ob3obobo4bob2ob40o$41o3b2ob2ob2o3bo2b
3ob4obobob2o3b2obo3bo2b3ob2o4bob2o2bo2b2o3b3o4b3obob3o3bo2b4ob3o2bo4bo
2bob3o2bob2o4b2o3b2obo2bob3ob2o4b3obo2bobo2bob4o3b5o4b4o2bobo2bob8ob2o
2b2o2b2ob2ob2ob39o$37o5b2ob3o3b3obobob4o5bobob2ob3ob5ob4obo2b3ob2ob2ob
5o3bob4o3bobo2b3o2bobobo3b4obobob3o4b2obo2bo3bobo2bo2bobo5bobob2ob3ob
2obob2o2bobo2b2o3b2obob2o2b3o2bob2o3bob2ob4ob3o3bobo4b3ob38o$40o2b2o3b
ob5ob3ob3o3b2o2bobo2bobobob3o3bo2bob6ob3ob5ob2o2b3obo4b2o2b3ob2ob2ob3o
b5ob4o3bob2ob2o2b4obob2ob3obo2b2ob8o3b2ob2obob5ob2obob5o2b2o3b4o2bob2o
b8o2b4obo5bo3b37o$39ob5o2bo2bob4obobo3bobo2bo2b2ob4o6b2o4b6ob5ob3ob2o
4bo2bob7obobo2b2ob2o2bobob2o2bobo2bob2obo4b3ob5obo2bob9o5bo2bob2obo2bo
b2obob4o4bob2ob2obo2b2obobo3bo2bo2bobob6o2b3o3b36o$35o2b3o2b2obo2b3o3b
2o2b3ob6ob4ob2ob2ob2o3bob13o4b4obob3o2b4o5b3ob2o4b4ob5ob3o3b2o2bo3b6ob
8ob4ob4o2bobob2obo2bob2obobob4obobobobo2b3ob3ob3o2b2ob2o3bo3b4obo2b43o
$34ob5o2bob4o5b2obo4b8o2b2o2b5ob2ob2ob3ob2ob2obo2b2o2bo4b2o2b7ob2o3b5o
b4obobo3b2obobobo3b2obobob2ob3ob3ob4obo4b4o2b3ob2ob5ob5o2b4o2b4ob10obo
2b3obobo2bo3b2obobob5o4b34o$33ob2o3bob7ob2obo2bob3o2bo2b2o3b3o3b2o3bob
4ob2ob2obobob4ob2o3bo3b2o2bo2b5o3b3o2b2ob2o3b6ob3o2b2obobo2b2o3bo3b2ob
3o2b3obo3bobob4o3bob3obobo3b3obo2bob7ob2ob3ob2o2b2o2bobob5o2bob5obob
35o$32o2bo2bob4ob2obob3obo3b3ob4o3bo2b2obo3bobob4ob2o4b2ob2ob5ob2o6b2o
b4o3b5o2bo2bob2ob2obobobobob2ob2o3b4o2bob2obo2bob2o2b4ob4ob3ob5obo2bo
2b2obobob3obo3b2obobob3obob6obo3bo2b5ob2o2bo3bobo2b32o$34obobo3b2o2b5o
b5o2bob4o3b3o3bob7o6b2obob7o2bob3o2b3ob2o3b2ob2o2bob2ob3ob3obo2b4ob3ob
o6b2obo2b2ob5ob3ob3obob2o3bobobo2b2o3bobob2obobo2b6ob7obobob2ob3ob2obo
bob7o2b3obobobo3b31o$30obob9o2b5obobobo7b7obo6b14ob3ob3o3b4o2b2ob4ob3o
4bo3bobo2bobo2b2ob2obob3ob3o3b3ob3o3bo4b11o2b2o7bob2o2b9ob4ob6o3b3o2bo
bob3obobobo2b3ob3ob4obob3ob3ob31o$29ob2o3bob4o2bob2o3b7o3bobo2b4ob3ob
3o2bob3o2bobob3o3b5o2b5o2b2obo2b2ob3obob4o2b4o2bobobo2bo2b2o2b3ob4o2bo
b4obob2o2b3o2b2ob2obobob2ob4o7b5ob3o3b6o2b3ob8ob3ob6o3bobob8o2b33o$28o
2bob3obobob2o3bo3b3ob6ob4obo2b5o2bo2b3ob2o2b2o2bo2b5obo2b3ob3o2b2o3b2o
4b5ob4o5bobob3ob5ob3obobo3b4ob19ob5o2b8ob6ob2ob2o2bobo2b4obobob3o2b2o
2bob5o3b2o3b2o2bobo2b33o$29o2b3ob9o5b2o2b4ob7ob3ob3ob5obobo2bo2b11obo
3b2o2b2ob2o3bo3bo2bo2bob4obo3b2ob2ob2obobo2b4ob2ob2obob2ob2o3b9ob2o2b
6ob3ob2o2b2ob11obo2b3ob4ob3obo4bob2ob5ob3o6bo2bo2b2o2b29o$26o2b2ob6obo
b2ob2o2bo2b4obob2ob10ob7obob10obobo2bobo2b3o2b4obob4o2b3obob3o2bob3o2b
obob3o2b2obobob2ob2obo2b2obob3obobo2b2obo2b4ob9o3bo2b3o3b2o2b4o2b2obo
2bo2b2obob2obob5ob6obob6obo3b32o$25o4bo5bobob3o2bo4b4obob2obob8obobobo
b5o2bob5ob3obobo4b2o2b2obob3ob5obo5b2obob2o5bobobob6o2bobobobobo2b3o2b
2o3b2ob5o2bobo3b8ob6ob2ob2obobo2bo2b6o2b2ob3o2b3ob4ob2ob4o3bob2obo2b3o
3b27o$24obobob2o2bo2bobo3bob3ob2ob3obobob3ob3o2bo2b3o2b2ob2obo2b11ob5o
b3o2b2o2bob2o2bob2o2b2o3b3obob3o2b15o2bob2o2bob6o2bo2bobo2b5o2bo7bob2o
bo2b4ob2ob5o2b3obobob3obobo3b2ob2obob3obob2obob4obobo4bob26o$23o3bob3o
b4obob2o2bo2b6ob4ob3o3b3o2b7o5b2ob6ob7obob2ob4o4b2o2b3o2bo2b9o4bo2bob
2obobob2ob4o2b3ob4ob2o3bo2b2ob2ob4obobo2bobo3bob4ob2o2b4obo2bob2obobob
o3b4ob5ob2obobob4ob2obobo2bobobo6b25o$22o3bob3o2bobobobob2o2bo3b3ob2ob
4obobo2b2ob3ob4ob2o2bob3ob7obob6ob3ob3o2bo2bob3ob6ob3o4b5o3b3o2b4ob5ob
o2bobobo2b3obob4o2b5o2b2ob3obob2obob3obobobo4b10o2b2ob6obo2bo2b2ob2o2b
3o2b3o6b4o2b25o$25o3b2obob2o3b2ob2ob2ob2obobob6obob2o3b4obo2bob2o3bobo
b8ob5o2bo3b4obo2b8ob4o2bo6bo2bo2bobob5o5b3obo2b3o2b2o2bo3b5ob2ob5ob2ob
3ob4ob7o2b4ob2o2bobo2b2ob4ob7ob3obo2bo2b3ob2ob2o2bobob2o3b23o$22ob2o2b
5ob3o3b2o2bo8bo2b4o2b3obobo2bob2obob3o2b2o2bobo2bob2o2bob7obobob3o2b2o
b4ob2o3bob3ob5ob2o2b2o3b3o2b2o2b3obo2b3ob3o2b3ob2obo2b3ob5ob4o2b3o2b2o
4b3o2b4ob5ob2o3b5ob2obob3o3b2ob3o2b3o3b2ob4o3b22o$21ob3ob2o3b3ob3o4b3o
b9ob2o3b10ob2o3b2o2bo2bob2ob2o2b4o2bo2b2o2bobo3bobo2b6ob2obob4ob3o3b3o
2b3o3b4o2b6obo3b7obobob3o3b3o4bob4obob2ob8ob4o3b7o3b6obobobob2ob2obob
2obo2bo2bo2b4obo2bo2b21o$19ob4o3b2o3bobo2b2obo7bobo4bo2b4o4b4ob2ob3obo
b2ob3o5b6o3bob2ob3o2b4obob3o2bob4obo2b2obobob2obo3b2ob2o2b4obobo3bo2bo
2b3ob5obo3bobo2bo7bob3ob2ob2ob4obob2o3b3ob3obo2bob8ob7o2b7ob3obob3ob4o
2b20o$16o3bo2b8ob4ob3o3bob3o2b3ob3obobobo3b2obob3obo2b4ob10obob4o2b12o
bobo6bob3o3bo2bob7ob2obobob6ob2ob4obob2o2b2o5b6obobo5b6o5b2o2b2obob2ob
3o2b2ob2o6b3o2b3o3b3obo4bob2obobob3ob5o3b2ob19o$29ob7ob5o2bobob3obob2o
6b5o2b2ob6obob3ob3ob4o3bobo3bobob5o2b2obob4o3b4ob6obob2ob5obobob4o3bob
3o3bob2obob2o5b2ob2o2b3obob2ob5ob2obobobobob5obob3o2b3obob5o3b4ob7o3b
3o3bob4ob5obob18o$14obo2b4ob2o2b3o2b2ob4obobo2bo2bobo3bob8ob2ob2o2bob
2obobobob5o2b2o2bob5ob2obo2bob2o2b2obobobo3b4obobob2o2b2o3b4o2b2ob11ob
2obob2ob3ob2o2b3ob3o2bob2o3bo3b5ob3ob3ob3o3bobob5obobo3bo2b2o2b6ob5obo
2b2obobo3b2ob2o2b21o$20o2b3obob5ob2obo3bob6o2bo2b4ob2o3b3o3b2ob3ob2ob
2ob3ob2ob2obob3obob2obob3o2bobo5b3obobo2bo3b2obob2ob3obob2ob2o4b4obob
2ob3ob9ob3o2bobobob2o2bo3b3obo2b7ob3o2b6ob5ob12ob4o2b4obo2b2obob2ob2o
4b3ob3ob16o$12o2bobo2bo6b5o2b4ob2o4bobob2ob6o2bob2o3bo3bobob8ob2ob3ob
2o2b4o2bo2b6obobo2b5o6b3ob2o2b5ob4o2bobob3o3bob3obob2obob7obob2o5b2o2b
8obo5bobob9ob2o2bob3ob2ob2o3bo2b3ob2obobob3o4b2obobo2b2ob2o2bob2o2bob
15o$16o2bobo2bob3obob4obo3bob4o2b7o2b4ob3obo6b4o2b9o4bobo2bo2b4o2b2ob
4obobob4o3b2obo7b4obo2b5ob4o3b2ob3obob5o2bob3ob3ob2ob3obob3obo3bo3b3ob
ob2obo3bob2o3b6o3bob2ob2obob5o2b3obob2ob6ob6obob3o2bob14o$14obob5ob2o
2b2obo3bo2bob2obo2bo2b3ob2obo2bobobobo3b3obob2obo4bobob3o4bob2obobo2b
5obobo2b5ob5o2b7ob8obobobo2b2obo2bob2ob4o2bob3o2b3o3b2o2b4ob13o3b2ob5o
b5o5b3obo3b3obob5obob2ob3o2bob2o6bobo2b3o2b2o2bob15o$10ob2obo3b2o2b4ob
2o2bob2obob2obo2b2ob3ob2ob3ob3o2b3o4bob3ob4ob3obo2b3ob6obobobobob2obo
2bob2obo2b3obo6b2o2bob2ob2o2b4obo3bobob2obob5obob5obob2ob8obo2bobobob
5o2b2obo3b5o2bobob4ob4ob6obob3obo2b3o2b5o3bobobo2bob3ob3ob15o$14obobob
2o2b3ob6obo2b2o3b3o3bob2obobo2b3ob3obobobob4o5b9o2b3obo3bobo3bob6o2bob
3ob10o4b4o2bob6o2bo2bo2b4o2bob2ob2obo3bobo2b5obobo5bo2b2o2bo2b7ob2obo
2bo3b3o2b2ob3ob4obo2b3obob3ob2o2b3ob2o2bob3ob3o2b2o4b14o$14ob2ob5ob5o
4b2o3b2obobo2b2obo2bo2b4ob4ob3obob3o3bo3bo2b4obo8bobobob3o2b2obo2b2ob
2ob4ob5obobob5o2bobo2b4obob3o2b3ob3o3bo2b2o2bob3obob2obobo5b4obo2b3o2b
3ob6o3bobob3ob3o2b5o3bob4obob2obo5b5ob2ob3ob2ob4o2b13o$14o2b9o2bo2bobo
b2obob4o6b2obob2obo2b3ob4ob2obob5o2b4obo2bobob2o2bo4b3ob8ob3ob2ob2o2bo
b3o2bobob3obobo2bob5ob4o2b3obo2bob2obob3o2b2o2b2o2bob3o3b6o2b3ob3ob2ob
2o2b5ob3obo4b2o2b2ob2ob3obob4obobobo2b2ob6ob2obo3b2obo2b12o$15o2b4ob9o
b2obo2b6obo2b2o2b2ob2ob3o2b2ob2o2b2obob5ob3o3bo2b2ob4o2bo2bo5b2obobob
4ob4ob2obob2o2bo4b2ob2obob3o2b2o2bob3obo2bob7o2bo3b3ob2obobob2o3b2ob3o
4bobo3b2o2b2ob6obo4bobo2bo2b4o2b4obo3b6obo3bo3b3ob3ob4obob12o$16o2bob
6obo4b2obo2b2obo2bo2bobo2bo2bob4o2b2o2b2o5b2ob8o6bob5obobobob2ob2obobo
bob7o2b2obob2ob3obobobob3obob5o3b2obo3b3ob4o2bo2bob2ob2ob4obo4b3o2bob
2obobo2bobobo3bobo2b2o4bob2o2bo2bo2bo2b9o2b2o4bob2o4bob7ob2ob13o$16o2b
3ob2obobo3b3ob3o3b2ob3ob3ob4ob2obobob3ob11o2b2obob5obob4ob4obob3ob2ob
2ob3ob5ob2o2b9ob2o2b2ob5ob4obob3ob2ob5ob2o2b4o5b3o6b8o2b3obo2b4o6b2ob
2o2bob2ob3obo3bo2bob3ob5o6b5obobo4bo2b2ob3o2b10o$16o4b3o3b2obobobobo2b
2o3bobob4obob5obo3b8o4b2ob3o3bo2b2o2b2o2bob2o3b6ob2ob5ob3ob8o2bob3o2bo
bo2b2o2b2obobob7ob4o2bobo2bo3bob3ob2ob2o3b2obob2obobobob2obob5o2bob4ob
4o3bo3b3ob5ob2ob4obo2bobo2b3obob4ob5o4bob11o$17obobob7ob3o3b3o2bo3b2ob
4o2bob2obo2b11ob2obob2obo3b2obob4ob2o2b3obo3bob3ob3ob2obo2b3o2bob2ob4o
2bob2ob4obob2obo2bob3ob3o2b2obo2bob3o2b4ob2o4bobobob4ob2ob10ob4ob3ob3o
2b2o3bob3o2b3ob2ob2ob4o4bob18o2b12o$18o2b2ob7obob8o2bobo2b3o2bo3b3o3b
3o5bo2b2o2b3o6b2obo2b7obob2o2b6obo2b2o4bo3bob5ob3o2b3obob2obobobob4obo
b3obob3o2bob2o2bob2ob2ob2o4b2ob2ob2obo5b2ob2ob2obob6ob3o2b2ob2o2bob2o
2bobob2o2b3obo2b4ob3ob2o2bo2bob3ob15o$15obo3b3o2b3ob3o4b3o3bobobob2ob
2o5bo2bobob2o2b2obobo2bobo5bobobob13o2b3ob2obob2o2b5o2bobo2b3ob2ob5ob
2obob2o2bo2b3o2b2ob3o3bo2bo2b2o2b8o2bobob2ob2o3b2ob2ob2ob2obob2o2bo6b
4obo2bo3bob9o2bob2ob4obob3o2bo3b2obobobob14o$14o2b2o2b3obob2o2b2o2b2ob
ob3o3b3ob2obobobob11o2bob2obo7b2o3b2ob8obo2b4ob2o2bo2bob7ob3obobo2bob
2ob2obo4bobo5bob3o2b3obo3bob8ob2ob4o2b6ob3ob4ob7obob2o4bo2b2o4b4ob3o2b
obob2o3bob2ob2ob2obob2ob3ob2ob2obob17o$19ob6o2b4obob2ob7o2b2ob2obo3bo
3b3obo2bobobob2o2bo3b2obob5obobo2b3obobo3b2ob3o2bob7ob2o2b3obobobobob
12o2bob5ob5o2bob5o2b2obo4bo3b2ob3o2bobo2bobo2b4ob2o2bob2obo3b4obob2ob
6o2bobo4bobob4obobob3obob5obobob14o$15o4b2obob3ob7o2bob2obo2bo2bob7ob
2ob2o2b3obobobob4o3b2o2bob6o2b6ob2o2bobobo2b2o4bobob2obob2o2bobo2bo2bo
bo2b6obo2b2o4bobo3b2o3bob2obobob3o6b2o3bob2obo2bo7bo2b8ob5o4bob2o2b4o
5bobo2b3obo3b6ob6o3b2ob16o$12o2b3ob2ob4obob7obob2ob2ob2obob3ob2o2b3o2b
ob7o3b3ob2o3b3ob2o2b2ob3obobobo3b2o4b2obob3obobob2obo2b2o6b3o2b5obob4o
b6ob3obo5bo2bob2obobo3b2ob2o3b3o6b4obo2b3ob7ob4o3b3ob2ob3o2b2o2bobobo
3b2o2bob2o3b6obo3bob16o$13o2b2ob2o3b10obobo2b3o2b5o4bob4o2b3o3bo2b2o4b
4ob4ob2ob4ob2obo2b2ob2ob2o4b2o2bobob5o3b10ob3o5bob4ob2obob2obobo2bob2o
bo3bo2b2obo3b3ob4o2bob7ob4obob2ob3ob3ob7ob5o2b5o2bo2bo4b4ob2o2b2o3b3ob
3ob3ob2o2b12o$14ob2o3b2o2bob2ob4o2b2obo3b2obobobobob2ob3o2b4ob4obobob
2o3b2obobo2bob4o2b4o2bo2bo2bob4ob3ob3o2b2ob14ob3obo4bobobob3o3b2obob3o
2bo3b4obob2o4b2ob3o4b8o2b5ob2o4b2obo2b3o3b2ob2ob3obo3bobob4obo3bobob2o
2bob6ob2o3b13o$19o2bobo2b5o3b2obob4obob3o2b2ob2obo2bob6o3b2obob5o2b2ob
3o2bobo2bo3bob5obobobob3ob2o2bob7ob2o2b2o4bob2obo3b2obob3obo2b3ob3obob
obo3b2obobo3b2obo5b2ob3o3b3o2b2o2bob2ob3ob2o3bobo3b2obo2bo3bobo3b3o2bo
bo5b3o3b2obo2b20o$16o3b2o3b2obob8ob3ob3ob2o3b3obobobo2bobo2b7ob2obo4bo
b5ob3obo2b3o2b5obobob4o2bobobo2b8o2b2ob3obob2o2b2obo6bob2o2bobob6obo2b
ob2o2b5o2bobob2obo2b5o3b2o2b3obo4b3obob2obo2b3ob5o2b5o3b2o4bo2bo3b2o4b
ob5ob15o$18o2bo2b2o2bo4b6ob4o5b4ob3ob3o3bo3bobobob2o2b6o3b9obo2bobobob
3ob4obob2ob3ob2ob2obo2b3ob3ob2o4b6ob2o2b2ob3o3bo2b4o4b4o3bob2obob2obob
2o3b4ob2obo3bobo13bobo2bobobo2b8obobob2ob2o2bo2bobobob5obobob16o$18ob
3o5b3ob4obobob2ob3ob4obobobo2b2obo2b2obobob3o5b3ob3o2bob4obo3bob3o2b2o
bo2b4obob2o2b9ob3ob5o2bob3o2b7obo2b2o3b3ob3o3bo3b5o2bob2ob3ob5ob8o2b2o
3bo2bo5b2ob4ob8ob2obobob2ob3obo3b2o2bob4ob2obob17o$19obob2ob2o2b2ob2o
2bobobobo5b5obob2ob7obob2ob10ob4obobo2bob2obob2obobob5o2b2o2b2ob7obob
2o3b5ob3o2bo3bo2bo3b3ob2obobob6o2bob13o3bobo2b2o2bo2bob5ob3o2bo4bobobo
bob6ob3obob6o2bob3obo3b2ob3ob4o3b18o$20ob2ob2ob2o2b4o3bob7ob8o2bo4bo3b
obo4bo2bob9ob2obo2bo2bobobob3ob6ob3o2bobob4o4bo3b4o2b4ob2o2b2ob2ob5ob
3ob4obobobob4ob2obo2b2obobob2obobo2bobob2ob2o2bo2bo2b3ob6obo2bobob2obo
bo2bob2o2b3o2b9obob4o3b19o$21obob4o3bo2b3ob3o6bo5b5o2bob2o2b2o3b4ob8ob
5obo4b4o2b3ob3o3bo6b5ob8o5b2ob2ob3ob3ob2obob4obob8o2b4ob6obob2obob4o2b
3o2bobobobob4obo3bo2bo2b2o3bobo2bobo4b2obobob2ob2obob3o2bo2bob2ob3ob
20o$22o2bo3b5ob6o2bob8o2b9ob3ob4o2b3obob2ob2ob3ob2o2b2o2bobobobob2o3b
3o3bo3bob6o2b2o3bobob2obob3obo2b2o2bo2b2ob3ob3ob3o4bob4ob6o4b2o4bob2ob
obobo2bo2bob2o2b2ob4ob3o2b2ob6ob4o3bo2bo3b5o2bob7ob21o$23obo2b4o6bobo
2b2o2b5ob3obo3bob3o2b4ob2ob3obo2bo4b2o2b5ob3obob2obobobobo2b11ob3o3bo
2b3ob6o2b3obobobobo2b3ob3o2b3ob2ob3ob3ob2ob2ob2ob3obo3b2ob2ob5o2b4o2bo
b2ob2ob2ob2obobo2b2o3bo2bob2ob3o2b4ob2obo3bob24o$25obob7o3bob4obobob2o
3bob4ob2ob4o2bo2b3obo4bo2bo2b3o4b4ob3o2b2o2bob2obobobo2bobobob2o4bo4bo
3b2o4bo2bo4bob8obob6obo2b2o2b2ob3obo2bobobobo2b9o2bobo2b8o2b2ob2obo6b
3o3bo2b2o2bo3bo3b3ob3o4b23o$25obobob18o3b2o2b2o3b5o8b4o2bob2ob4ob2o2b
2ob4o3bo3b2o2bob2ob3ob2ob4obob4ob3obobo2b7o2b2ob2ob4obob3o2b4ob4o3b3o
2bobo2b2ob3o3b2ob5o2b7o2b5o2bo2b2obo6bobo2bo2bob3obobobo3b2obob2ob25o$
26obob2obo2bo3b2o2bobob6obo4b2obobo2b2o2b2obob2ob2ob3o3bobob2o3b2obobo
b2o4b3o6bob7obobob3o2bo2bobo3b3ob2obobo2b5obobo3b2o2b8o2bob2o5bob2ob3o
b2obob5ob9obob2o2b2obo3bo2b3ob3ob2o3bobo10b2obob25o$27ob4ob2ob11ob2ob
2obo2bob3obob2ob2obob2obob7obob2ob2o2b6o3bob6o5bob2obo3b4ob2o4b2o2bobo
2b2o3b2o5bobob4ob5obobo2b2ob4ob2ob2ob2ob10obob3o2b2o2b3o2bob2obobobob
5o4b2o3bob6ob2obo2b2ob2obob26o$28obobob2o4b2o2bo3b3o3b2o3b2o2b2o2bo2b
4ob3obob5o2bo3b3ob2ob3o4bob3obob4ob2ob2o2bob3ob3ob2ob5o2b3o2b3obobo2bo
b2ob4ob3o2b2obob9o2b2o2bobobo3bob2obo2b5ob4obob6ob3o2bobobobob3o2b2ob
2obobob2ob2o2b3ob27o$29o3b5o4b3o2b2ob3ob2obo3bobobob2ob3o2bo3b4ob2ob7o
bobobo2b3o8b3ob7ob2obob5ob18ob4obo2b10obob4o2b4ob6ob3o2bo2bobo4b5ob11o
2bo3b2ob2o3bo2b8o3bob8obob30o$30o2bo3b2obo6b3o6bobobob4ob6o2bob3ob3obo
b2obobob4o2bo2b9o2b4ob4ob3ob4ob3obob3ob9o4b3o7bob2o2b3o2b5ob2obobob2ob
6ob11o2bob2obob2ob4o3b3obo2b2o2b3o3bobo3bobob2o2b2o2bob30o$31ob2o2bob
2o4b3ob3obob2ob8o2b7ob3obobob8obob2obob2obo2b5o3b3o2bob2o3b4o2b2o3b2o
2b3obobobob3o2b3o3b6obo2b2ob4ob2o2bo2b2obobo2bobobob3ob2obo2b6o2b3ob2o
3bo4b4obo2bobobob2o2bobobobo3b36o$35o2b4o2bob3ob5ob2o2b2o2bobob2ob3o5b
o4bo2bob5o3b6obob2o2bob2o2b5ob5ob2ob7ob5o3bo2b4o4bob3o2b2obob2ob2ob5o
2b2ob2ob5ob2o3b5ob2ob4obo2b2ob2obo5bo2b2o2b2ob2o2b3o2b8obo2bob35o$36ob
ob7o2b4ob2o3bobo3bo2b3o3b2ob3ob2o2b4ob8ob3o2bobob2obo2b4o3bobob3ob2o3b
ob3o8b2obo4bobob4obobobobo4b4obo2b6ob3ob2o2b5ob4o2bobo2bo2b3o2b3obob4o
b3ob2o2b3ob6obob2obob3o2b32o$34ob2ob2ob3o2bob4ob4o2bob2obob3obob2o5b2o
bob5o3bobo3bo2b2ob6obobob4ob2ob2o2bo2bo4bob3ob4o2b3o2b2o2b2ob4o2b2o2b
3o3b8o2bob3ob2obob3o3bobobobob2obob2obobobo2bob5o2b2o2bobo6b5o2b2obob
2o2b33o$35ob6obob3o2bob2ob4ob3ob2obobob2ob2obo2b3o2bob2o3b2obo2bo5bo2b
o3b11o2b2o2b2obo2b5o3bo2bob2obob5o3b4ob2ob2o6bo3bo4b11o2b2o2b2obo2bob
3obo3bob4obob2obo3b3ob2ob2o2b2o6b2ob3o3b34o$36o3b2ob2ob2ob2obob5ob9obo
3bo2bo2b2o3bob2obob3obo2bobobobob3obobo2bo2b3obobo3b2o2bob5o3bob4o3b2o
4b3o4b5ob2o2bo2bob2o3bo2bo6bobo2b9o2b5o2b7o4bobo2bob2ob2o2b3o2bo2bo2bo
b2o4b35o$39obob2o2b3o2b2ob4ob2ob2ob2o2b6o2b2ob6ob2ob4ob2obob2ob2o2b12o
3bo2b8obo2bo5b6o2b3ob2o2bobo2b4o2bo2b2ob2ob3o2bobo2b6o2b2obob4obo4b2o
2b3ob2obo2b3o2b2o2bob2ob4ob2o3bo3b2ob2ob36o$41obob3o3b6ob3o3b3obo3bobo
b2o4bob5ob4ob2ob3o2b5obo2b9ob3ob4obob5ob5obo2b3ob2o3b2o3b6obob3o2bobob
ob3o2b2obob3o2b3o4b2o2b3obob3ob3o2b2obob3obo2bob4o2b4o2b2o2b5ob38o$38o
3bo2b3ob6o3b4o2bobob2ob2o2bobobobob2ob2ob4obo2b2obo2b5obob2o2b3ob2o4b
6obobob5o3b6ob3o2b2ob2o2b4obobobob4o2bob4ob2o2b2o2b3o2bo2bobo4bob3o2bo
b3ob2o4bob2obob3obo2b2o3b2o2b6ob38o$47ob3ob2o2b7ob5o3b2ob3o2b2o2b2ob4o
bob4ob3ob11ob3ob7ob2o3b5ob2ob5ob3o3b2o2bo2bob2o2b2ob7ob3obobobo2b5obo
2b2o2bobobob2o3bo3bob3obo2b4o3bo2b2obobo4b2o2bob5o3b37o$45obob4o3b4obo
3b4ob2obob2ob3obobo2b2ob3ob2o2b4obobob2o2b5ob2ob2obobo2bobo2b3obob4ob
4o2b3ob5o2b11ob5ob2ob2ob4ob10obobo4b2ob8ob2o2b3o2b2obob6o3b5ob4obo2b
40o$39o2b8o3b5ob2o3b2obo2b7obobob11obobob2o4b3ob5ob5o2b11obob2o2bobob
2ob3o2b4o2b3ob3ob3o4b5ob2obob2ob2obo2b2ob2ob2obo3bobobobo7b5obo2bo2bob
o2b2o3b8ob2ob2obob39o$40o2bob3o4bo3b2obob3obobobobob3o3b2obo2b2obobo4b
3o2b3obob2ob2ob2ob2ob3ob2ob3ob4o3bobob3obob2ob5ob4o4b3o2bobob3o2b6obob
2o4bo7b3ob5o3b3o5bo4b4ob4obob2obob2ob3o2bo2b44o$41obob4obo3bob3ob3obo
2bob3o2bo4bo4b2ob14o2bo4bob3ob2o2b5ob3obo6b3o2b3o3b4o2b2ob4o2b2ob4ob3o
bob3o2b3ob6o2b5o2bobob4ob2ob3ob4o3bob3obobo2bo2bo4bobobo2b3ob3ob41o$
42obo4bob8ob2o2bo3bo2bobob2obo4bob2ob2obo4bobobobobo4bob2o2bo4b3o3b2o
5b2o4b2o2b2o2b2ob7o2bo2b7obob2o3b2ob7o5bo2b4ob8o6bo3b2obo2b2o3b4o3bobo
bob4ob2ob4ob42o$44o2bo2b2o2b2ob3ob2o2bo2bo2b6ob4obo3bob2o2bo2b3obo6b2o
3b5o2b5ob2o4bobob2o2bobo2b2obob2ob3ob2obobo2b2ob2o2bo2b6ob5obob2ob2obo
2bo4b3o2b2ob5ob4o2b2o2bobo4b2o5b3ob2o2bob46o$44o7b3o2b2ob3o2b3o2b4ob4o
bo2b2obob5obo4bo2bob2ob4ob4o2b4ob3obobob3o2b3obobob3ob5ob3obobo2bo3b2o
bob14obo5bo6b3ob4obo2b2ob2ob2ob2obob3o6b3ob2ob4o2b4ob44o$47o9bobobo2b
3obo2b3o3b3o2b2obob4ob4ob2o2bob3ob2obo3b5ob2obo3bob3o2bob3o2b3ob3o2b2o
bo3b2o2bo2bo3b3ob3obobobobobo3b6obobob2ob2obob2o2bo2b5ob2obo2b2obobobo
b3o2b2obob2obo3b45o$47o2b2ob6o3b6o2b2o4bobo2bob2o2bo2bob2ob3ob4ob3o2b
4obob2o4b11ob3ob2o2bob2ob5o4bo2bo2b3obo2b2ob4obobobo3b10o3b6ob4o5bob5o
b2obo2bobob3o3bo2b2ob4ob48o$52ob2obob4ob4o2bo3b2ob6o2bobo3bo3b2o2bob7o
bo4b3obobobo3b6o2b3ob3o2bo2b6o3b2ob4obob2obob8o3bo2bo2b4o2bo2b3o2b2obo
3b3ob3obo2b4obo2b3obo2bob2ob58o$49ob2o2b5obo2bobob2o2b2o2b3o3b7ob2ob3o
2b3ob2obo2bob2o3bo2bo3b2obob5ob3ob5ob3o3bob2ob4o4b2o3b5ob10o2b5obob3o
5b11obo5b5o3b3o2bo4bo2b2obob52o$49o2bobo2b3ob8o4b7obob6o3b3ob4ob3o2b
11o2bobobobo3bob7ob2o2bob3o2bobob4ob2obob2o2bo2bob6ob2o2bo3bobo6bo2b4o
bo2b2obob5ob4o2bo2b8o2bo2bo2b3ob49o$50obobo2b3ob4o2b3obob3ob7ob3o2b4o
2b2ob2ob4ob2o2b2obo2b2o5bobob7ob2ob2o4b3ob6o3b6o2b4o2b2o2b3o2bob2ob3ob
obobo2b5obo2bob2o7b6o2bob4o2bo6b6ob50o$51o3b2o2bo2b4ob2ob2ob2ob2o3bobo
2bo3bo2b5ob3obo3b9o2b2ob2ob4o3bob2o2bob3ob2o2b3obo3b3o2b5ob5o2b3obob3o
bob6ob3obobob2ob2o4bob3obo3b2obobobobobo2bob3ob2o2b2ob51o$52obo2b5obob
2obob2obob2ob2obob2o2b2ob3o3b4ob2ob4obob7o2bo4b3o8bo2b7ob3obo2b4o2bob
3ob2o2b2o4b2ob2ob3o2b7o3b2obobo2bob3ob4obob3obo3b2obo2bobobob3ob2ob52o
$53ob3o2b8ob2o2b2ob3ob7o2bo2b4o2b2obob2obobo2b4ob9ob4obo3b4o3b4ob4o2bo
2b5ob11o4b4ob2obobo5b2o2b2o2bo2bo3b3obo2bobob2ob2ob2obo2b6ob2obo2b53o$
54o5b5ob3o2bob2ob2o2b4obobo2bob2o2b2ob3o3bo2bob8o3b2obob3obob2o2bobo2b
2o4bo2b2ob12ob2o2bo2b2ob6obo2b3obob2o3bob9o4b2obob9ob3obob3obo2bo2b54o
$55o3b3o2b3obo3b2obob2o2b4ob2obob2obo2b3o2bo2b3o2b3o2b4ob5ob4obo3b3obo
3b3o4bo4b2ob9obob3obob5obobo2bobo3b4o5bob5o2b2ob2o5b3obob2o2b2ob2o3bob
56o$56ob2o3b2ob3o5bob2o2b2ob2obobo2bo5b8ob2ob4obob2o2b2ob5ob3ob5ob3o3b
4o2b6obob3ob4obo3b2ob2o2b2ob5o2b5o2b2obob4ob3ob3o2bo3bob5ob2o2bob2o2b
2ob56o$57o2b2o2b2obob2ob2ob2o2b3ob6ob7ob5obob3obob2obob2obob7obo2bob4o
bobob2o4bo4b8ob5ob3ob3ob3obo3b2obob3obo2bo2b10ob2obob3ob2o3bob2ob3ob4o
b57o$58ob4ob2o2bob2ob3ob4o2b5ob3obob3ob5o2b4o4bo2bobo3b8o2bobo2bobobo
2bob2o2bobo2bo2b3o2b4ob2ob3obob3obob8o2bobo3b2ob4ob2o2b5ob2ob2o2b3ob2o
b3ob60o$64o3bob4o3b3ob2obob2obobo2b4obob2o2b2ob2o3b2ob5o2b3ob2o2b12ob
3ob2o2bobobo2bobo2b4ob2o3b2ob2o4b3obo2b2ob2obo2bobob4ob2obo2bo4bob3o2b
o3b4ob62o$62obobob3ob3o2b8ob2ob7ob2o2b2o2bobob2o2bo3bob4obob3ob3o5bobo
3bob2o3bobob2ob4ob7o2bob3o2b2ob3ob2ob3ob2o2b3ob2obobo3b5ob3ob5o2bo2bob
obob61o$61obo4b2obobobob3ob5o2bobob4o4b2obo2b2o3bo2b5obo3b2obo4b2o2b2o
b2obob2obo4b3ob3ob2obobobob5o2bob5o3bo2b2o5bo3b2obob3o3b3obo5bobobob2o
bob3ob61o$62o3b8ob2o2b5o2b2obo3b4o3bobob3o3b3o2bob2o2b4ob2obobob3obobo
b4ob2obob3obob6o3b2ob4ob2ob5o2b2obo2b4obo6bo3b4o3b2o2bob4o4b3ob2ob63o$
72ob4o2bo3b2obob4obobo6b5obo6b2ob3o2bob2o2b5obob4o2b2ob2ob3o2bob5ob4ob
2obob4ob3ob2obo2bob4o4bo2b3ob4o2bobo3bo2b3ob3ob3ob65o$64ob2o2b4o2bo2b
2obo3b3ob2ob2ob2obo2b2o2b2o5bob2ob2o2bob6o2bob2ob2obo6b2obo2b3obo2b2o
2bobo2b7ob2obob3obobo2b2ob3o2b7ob5ob2o3b7o4bo2bob63o$65o2b2o4bobobob2o
3b3ob8ob2ob2o2b2obob5ob4o2b2obo4b14obobobo2bobobob3o5b14ob2o2b7o3bo2b
3ob2o2b2obob3o3b2obob4obo2b67o$66o3bob2o2b2o2bobo2b3o3b4o2b4o2b2ob4o2b
o4b2o2b4o6b8ob2o2b3ob3ob3o2bob3o2b2obobo2b3obo10b2obo2bo2b4o2bo2b2o2b
4obo2bo4bo2bo3bo2b65o$67obob2o2bob3ob3ob2ob2o3b4ob3o2bo2bobobob2o2b2ob
3ob2o2bob3ob4o3b2obob2o3bob2obo2b3ob2ob4o3b4obobob4obob3ob2ob4o2b4o2bo
b2o5b5o2bobobo2b67o$68o3bo2bobo4bo2bob2obob2obob2o3b2obo2b3ob4o3b3ob3o
b2o2bo2bobobo2b2o4bob3ob3obobo2b3obob3o2bo2b3ob2o3b3ob2ob4obo5bob7o2bo
b4ob4o4b68o$70o2b2ob2ob5obob5obo2bo6b2ob2o3bo2b2obo2b3o3b2o2bo3bob2o2b
o4b5ob2obo2bob2o2bo3b5o3b2obobobobo2bob6ob4ob4obob10o3b3obobob68o$70ob
o5b3ob8ob3ob3ob5o2bob2ob6obobob3obo2bobobob2obob2o2bob2o2b2obobob4ob8o
3b5obobo2b2o6b2ob2obob2o2b2o2bobo3b2obo2b4o4b69o$74o2b6ob2o2b4o2b5o2b
3obobobo2bo2bob4ob3o2b2obob2obob2obob4obob3obobo3bob2ob3ob2o2b3o3bobo
2b4o2bo4bob6o2b2ob2o4bob3ob5obob70o$74ob2o2bob6obobob2obo4b3ob5ob4obob
4ob3o2bob2ob2obo3b4ob5ob4o2b3o2b2obob2obob3ob2ob7ob2obob5obob5obo2b4ob
3o3b2ob2ob71o$78ob2o6bo2b4o4b5obobob3ob2ob5obo3b6o5bo2b3o4b2o2b2ob3obo
2b3obo5bobob2o3b4ob3o2bo3b4ob2obobob3obob2ob2obobo4b72o$74obo5bo2b2obo
2b6ob2o2b3obo2b5o2bobob3o2b4ob3o5bob3o2b2o3bob2o2b4o2b4o2b2obobobo2bob
4o2b2ob6ob2o3b7o3bobo2b3o2bo2b73o$75o3b2o2b2ob7obo4bo2b2ob3ob2obob3o3b
5o2bob2obo2bob2o4b3ob2o2bo3bob3obob3o2bob3ob2o3b2o2b2ob2obo2bob4ob2obo
2b2o2b2ob6o2b2ob74o$76o2bob3o2b2obobob6obo2bo2bobo2bo2bo2b2ob2ob2o2b3o
b3ob2o4b4o2bobob3obob2ob5ob2o4b2o7b2o2b3ob3obo2bo10bo2bo2bobobo2bob75o
$77o2b2o2bo2b4o2bobobob2ob2obob2ob2ob2obob7obobo2bob3o2bobo5b2ob2ob4o
2b8ob2o3b2obo2bob2obo2b2obob3ob3ob2o2bob2obobo2b2obobo2b76o$78ob8obob
5ob2ob4o3bob2obobo2b2ob3obobob2ob2o3bo4b2ob3ob3o2b2ob4o2b2ob2ob2obobo
4b4o3bo2b3ob7o5b3o2b9ob78o$79ob3obo2b8obob2o2b2obob2o2b4o2b2o3b4obo2bo
2b6ob4o3b4o2b5obo2bobob2obo2bobob5o2bo2bob2ob2ob5ob5obo2bo2b2obob79o$
80obob2o3b3ob3ob2o3b3ob2ob2ob5o2b6o2bob4ob3o3b2o3b3o2bobobob4ob4obob2o
b2ob8o3b9ob3o3bob2obo2b2ob2o2b81o$81o6b6ob3o3b3o3bobobob5obob3o7b5ob3o
bo2b2o2b8o4b2ob4o3bobobob4o3b4ob3ob7o2bobo2b4obo2b83o$82o4bo2b2ob2o2b
2obobobobob3o2bob3ob9o4b3o3bobob2o3bob2o2b2o2b2obob3ob3o2bo2b3o2b6obo
4bo2b3o5bobo2b3o4b83o$83obo4bobo2bobob2obobob4o2bob2obobobo2bob2ob2obo
2b2o2b2obo3bob2ob6ob4obob2ob2ob3o2b4o4bo2b2o2bobobo2b2obo3bob6ob83o$
85o3b2ob5ob6o2bobob3o2bob2ob2o3b2ob5ob3o2b3obo2b2o5b2ob4o2bob2obo2b3o
4bo2bobo4bob2o2bo2b2ob5o2b4o2bob83o$85obo2bo4bob5ob2obob2ob3o2b2o2bob
2ob3o2b2ob5ob2o2bo3b5ob2ob2ob4obobob3o4b2o6b9o5b3ob3obob2o2bob84o$86o
2b2ob6ob5o2b2ob4o3bo2b3ob3obob2o2b2ob4o2bo3bobo3b2ob2o5b4obo3bob6o4b4o
2b2obobob2ob2obobob2obo2b85o$88obob3o3b2ob2obobob2o2b2o3b2ob3obobob3ob
4obobob2obo2b3o2bobobob12o2bo2bobo6bob3o2bo2bobobob2obob5ob86o$88obobo
3b7obob4ob2obob2ob2o2bobobobob8ob4obo4b3obobo2b4o2b3ob3ob4obo4bobob5ob
3o3bob2obob3ob87o$90o7b5ob4ob2ob3ob2o2bo3bob2o2bob3ob2obob2o3bob2o2bob
ob9ob3obob6o2b2ob2ob2ob2o2bobob2o3b2obobob88o$90o4b2obo2b9ob3ob2obo2b
2o3bobo2b2o2b2ob2obob2o2b2o2b2obob3obob6o2b3o2bo3bob2o3b4ob3o4bob2o2bo
bob89o$91obob5o2b4ob2ob6obo2b3obob4o2bobob3o2b2obob5ob2ob5obo2bobob9o
2bo2bob2obob8ob2ob2obo2b90o$93ob4ob2o3bobobo2b2obo2bobobob5o3bobo3b2o
2b3o3bob3ob4o2b3ob2ob3ob3obobo3bob4ob9obob5ob91o$94o2bob2o2b3ob2ob3o4b
ob2ob4ob5o2b3o2bo3b2ob3ob3o2bobob4ob5ob6o2bobobobob2ob2o3b2ob3o3bob92o
$95o4bobobob2o3b8ob3obo3bob2ob3ob4ob4o3bo3b6ob2ob4ob4obob4o2b9o2bob2o
3bo3b94o$95o3b3obob3ob2o4b3obob4o8b3obo2b5o2b12o2b2obob11o2bob2ob3o3b
2ob9ob94o$96o3bobob7o7b6obob2o2bob2ob4obob2obo2b2o3b5o2b2o2bob2o2b4o5b
3obob2ob2obo2b102o$97o3b2o3bo3b7ob3obo4b2o2b3ob5o2bob2o3bo2b2obo4b3obo
b2ob2ob5ob4obobob4o2b3obo3b96o$99obob3o2bob3o2b10obob6ob2o2bobo2bo2b3o
2b5ob4ob3obo3bobob2o2b3obo2b2ob4ob5ob97o$99ob2o3bob4o4bobob5obo2bob3ob
4obo2b2obob3o2b5ob3obo2bo5bobobo3b5ob2o2bo4b2o2b98o$100o2b3ob2obob4o2b
5ob3ob2obobobob7obobo2bobo2b3ob2obo2bo2bo4b6o3bob3ob3ob4ob100o$101obo
2b2ob5o3b2obo2b2ob3ob2o2bo2bobo2bob4o2b4obo3b5o4bo2b2o2b2ob4o6bo2b106o
$103ob2obo2bobo2b2o2bob4obobo2b3obo2b2obob10o2bob2ob2obob3o5bob5ob2ob
2ob3ob2o2b101o$103ob2o2bobob8obob7o3b7ob6o2b2o2bo2b5o7bo3bobob2ob2ob2o
bo4bobob102o$104ob4o3bo2bob2o2b2obo2b9o2bo2bob4o2bo3b2ob2ob4o6bo3b7ob
2obo3bo4b103o$107ob3o2b4obo4bob3ob6o2b2ob9ob3obob4o3bob5ob4o2b2o2b2obo
b3o3b104o$106obob4o2bobobob4ob4ob2o2b3ob4o2b4o2b7ob3o2b3obob2o2b8obobo
bo2b106o$107o3bo3b3ob4ob2obo4b3o3b2o3bo2b4obo2b3ob3obo2b4obobob4obo2bo
bob2ob108o$108obob2o5b4o2bo2b5o5b4o2b4o2b2ob2o4b3o2b3obob6ob2o2bob2ob
3ob107o$109o3b2ob2ob4ob11ob3ob3ob4ob8o2b4ob4ob10o2b7ob108o$115ob2o2bo
2bo2b3ob2o2bo2b3o2bo2bo3bob3o2b2ob2ob2ob3obo5b4o2b3ob111o$111obob2obo
4bo2b6obobob9ob2o2b2obo2b7obob3ob6o2b3obobob110o$112ob4obobo3b5obo2bob
ob2o2b3obo2b2o4b3o4bobo2bobobo2bo3bobobo3b111o$113ob2obo3b2obob2ob6ob
6o3bob3o3b2ob6o2b2ob2ob5obob3o2b113o$114obob3obob4o3b5obo2bob3o2b2o3b
3ob2ob3obo2bo2bob4o2b3o4b113o$118ob6ob4o2b2ob2o2b2o2b7obobob9obo3b2o2b
o2b2o2bob114o$117ob6ob6obo2bob6o2b4obo2bo2bob5o2b2o2bobob7ob115o$117ob
2ob2ob2ob2obo2bob3obobo2b5ob7o5bo3b2ob2obobob2o2b116o$118o2bob2ob2ob2o
b3ob3o2b3obob6ob2o2b3obob2ob2o3b2obobob118o$119obo3b5o3b3ob5ob2ob5obo
2bo5b3obo2b2obob2obob119o$121o2b6ob2obob2ob3ob2o3bo2b2o2bo2bobobobo5b
127o$121o2b5o3bobo7bo2bob3ob2ob4ob2ob3ob4o2bo3b121o$122o3bo4bobob2o2bo
b7ob2o2b3o2b2ob5o2bo2bo3b122o$123obob4ob2o3b6o2b4ob2o2bo2bo2b2o3b2o7b
123o$124ob3ob2o2b2obo2bob5ob6o2bob4ob4o2bo3b124o$125ob4ob3ob4ob3o2b5ob
o2b3o2b2obo4bo2b126o$129ob2ob3ob3ob3ob5o4b3o2b3o2bo4b127o$127obob2o4b
5obob5o2b3o3b3obob3o3b127o$128obobobob3ob6o2bobobo3b2ob2ob3o2bob128o$
129o2bo4bob3o2bobob2o2b3o6bob3o2b129o$130ob5o2b3o2b3ob3o4b4ob5o2b130o$
131ob2o3bobob2ob11ob3o3b134o$132o2b2o3bo2bo2b2o2b3o2b2obo2b136o$133o2b
ob3obobobob2obob4o2bob136o$134obobo2b3o2b2ob4obo2bo2b137o$135ob2obobob
7o4bo2b139o$139o2b2ob2ob3o2bo2bob139o$137ob2o4bo3bob5ob140o$138o2bo2bo
3bob2obo2b141o$296o$141o2b8ob144o$296o$296o$296o$296o$296o$296o$296o$
296o$296o$296o!

-- and again Golly agrees every bit of the way (via isotropic-rule-gen).

[dvgrn]

The B0 + S8 rules look okay so far also:

Code: Select all

x = 64, y = 64, rule = B02ci3anyecr4yikrqtjzec5yji6nkec7e8_S2an3njyeqr4aynwkze5krcejna6ikca8
64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$
64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$32ob31o$33ob30o$31o3b
30o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$
64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o$64o!

runs the same in Golly (via isotropic-rule-gen.py again) as

Code: Select all

x = 3, y = 3, rule = B02ci3anyecr4yikrqtjzec5yji6nkec7e8_S2an3njyeqr4aynwkze5krcejna6ikca8
bo$2bo$3o!

runs in Molly. Here they are after 10 ticks, from Golly and from Molly:

Code: Select all

x = 63, y = 23, rule = B02ci3anyecr4yikrqtjzec5yji6nkec7e8/S2an3njyeqr4aynwkze5krcejna6ikca8
obobob3obobob3obobobo17bobobob3obobob3obobobo$2o3bo2bobobobob2o3bo18b
2o3bo2bobobobob2o3bo$bo2b2o2bob3ob4o2b2o19bo2b2o2bob3ob4o2b2o$2obo2b2o
3bo3b2ob4o18b2obo2b2o3bo3b2ob4o$2b3obob3o4b2o3b2o20b3obob3o4b2o3b2o$2o
b5o2bo4b2o3bo19b2ob5o2bo4b2o3bo$b3o3b2o7bo4bo19b3o3b2o7bo4bo$2obob5o2b
o2b2o2bo2bo17b2obob5o2bo2b2o2bo2bo$3o3b3o3b3ob2obo2bo17b3o3b3o3b3ob2ob
o2bo$3o7b6o5bo18b3o7b6o5bo$2b2o3b2ob2o2b3o3bo21b2o3b2ob2o2b3o3bo$2ob6o
b5o25b2ob6ob5o$5bo4bo2bobobo27bo4bo2bobobo$2ob2o3bo2bo2b2ob4o19b2ob2o
3bo2bo2b2ob4o$2b2o3b3ob2ob2o2bo23b2o3b3ob2ob2o2bo$2obobob6ob4ob2obo17b
2obobob6ob4ob2obo$2obobob2ob2o2bo3bob3o17b2obobob2ob2o2bo3bob3o$2o2b2o
4b2obo2bo23b2o2b2o4b2obo2bo$2b4o4b2o2bobo3bo21b4o4b2o2bobo3bo$3ob8obob
o24b3ob8obobo$4b3ob3o2b2obo2b3o22b3ob3o2b2obo2b3o$2obob5obob2ob6o18b2o
bob5obob2ob6o$2bobo2bo2bobo2bo2bobo21bobo2bo2bobo2bo2bobo!

Notice that this is not the same as what you get when you run the un-reversed glider in Golly.

The difference is in the first tick, when Golly turns all cells ON using the S0.../B...8 rule, and then keeps using that same rule.

Molly is basically assuming that at T=0, the pattern is already a rule-reversed pattern -- i.e., that the OFF cells are the interesting part, so the inverted+reversed rule should be applied immediately. This appears to be what Golly does also, for non-totalistic rules -- for example, try setting the rule to "AntiLife".

Seems to me that Golly would have to apply a different rule for the first tick, to produce ON cells to match the OFF cells that would ordinarily (using the isotropic-rule-gen.py rule table) be generated during the Big-Bang universal inversion at T=1.

I'm not quite sure what that different rule would be -- the simple bit-inversion of the original rule, I think, without the [8-n] reversal. But given Golly's current behavior with the "AntiLife" rule, maybe we shouldn't do that, anyway...?

[rowett]

Code: Select all

x = 3, y = 3, rule = B02ci3anyecr4yikrqtjzec5yji6nkec7e8_S2an3njyeqr4aynwkze5krcejna6ikca8
bo$2bo$3o!

runs in Molly. Here they are after 10 ticks, from Golly and from Molly:

Code: Select all

x = 63, y = 23, rule = B02ci3anyecr4yikrqtjzec5yji6nkec7e8/S2an3njyeqr4aynwkze5krcejna6ikca8
obobob3obobob3obobobo17bobobob3obobob3obobobo$2o3bo2bobobobob2o3bo18b
2o3bo2bobobobob2o3bo$bo2b2o2bob3ob4o2b2o19bo2b2o2bob3ob4o2b2o$2obo2b2o
3bo3b2ob4o18b2obo2b2o3bo3b2ob4o$2b3obob3o4b2o3b2o20b3obob3o4b2o3b2o$2o
b5o2bo4b2o3bo19b2ob5o2bo4b2o3bo$b3o3b2o7bo4bo19b3o3b2o7bo4bo$2obob5o2b
o2b2o2bo2bo17b2obob5o2bo2b2o2bo2bo$3o3b3o3b3ob2obo2bo17b3o3b3o3b3ob2ob
o2bo$3o7b6o5bo18b3o7b6o5bo$2b2o3b2ob2o2b3o3bo21b2o3b2ob2o2b3o3bo$2ob6o
b5o25b2ob6ob5o$5bo4bo2bobobo27bo4bo2bobobo$2ob2o3bo2bo2b2ob4o19b2ob2o
3bo2bo2b2ob4o$2b2o3b3ob2ob2o2bo23b2o3b3ob2ob2o2bo$2obobob6ob4ob2obo17b
2obobob6ob4ob2obo$2obobob2ob2o2bo3bob3o17b2obobob2ob2o2bo3bob3o$2o2b2o
4b2obo2bo23b2o2b2o4b2obo2bo$2b4o4b2o2bobo3bo21b4o4b2o2bobo3bo$3ob8obob
o24b3ob8obobo$4b3ob3o2b2obo2b3o22b3ob3o2b2obo2b3o$2obob5obob2ob6o18b2o
bob5obob2ob6o$2bobo2bo2bobo2bo2bobo21bobo2bo2bobo2bo2bobo!

When I run the glider pattern in Molly I get the inverse of the result in your Molly vs Golly comparison:

Code: Select all

x = 23, y = 23, rule = B02ci3-ijkq4-anw5ijy6-ai7e8/S2an3-acik4aeknwyz5-iqy6-en8
bobobo3bobobo3bobobo$2b3ob2obobobobo2b3obo$ob2o2b2obo3bo4b2o2bo$2bob2o
2b3ob3o2bo4bo$2o3bobo3b4o2b3o2bo$2bo5b2ob4o2b3ob2o$o3b3o2b7ob4obo$2bob
o5b2ob2o2b2ob2o$3b3o3b3o3bo2bob2o$3b7o6b5obo$2o2b3o2bo2b2o3b3ob2o$2bo
6bo5b8o$5ob4ob2obobob5o$2bo2b3ob2ob2o2bo4b2o$2o2b3o3bo2bo2b2ob4o$2bobo
bo6bo4bo2bo$2bobobo2bo2b2ob3obo$2b2o2b4o2bob2ob6o$2o4b4o2b2obob3ob2o$
3bo8bobob7o$4o3bo3b2o2bob2o3bo$2bobo5bobo2bo6bo$2obob2ob2obob2ob2obob
2o!

[dvgrn]

When I run the glider pattern in Molly I get the inverse of the result in your Molly vs Golly comparison...

Right -- sorry, that was an artifact of the bitmap-copy method of getting the pattern out of Molly. Running the inverted-field glider pattern in Golly gives the inverse of running the plain glider pattern in Molly. But since Golly is showing the "true" infinite-ON-cells results of the rule, where Molly is showing the "simulated" finite-ON-cells results, that actually makes sense.

Similarly, running the inverted-field glider pattern in Molly gives the inverse of running the plain glider pattern in Golly -- but it's a different T=10 pattern:

Code: Select all

x = 23, y = 23, rule = B3/S23
bobobo3bobobo3bobobo$2b3ob2obobobobo2b3obo$ob2o2b2obobob3o3b2o$bob3o3b
2ob2o2b3ob3o$2o2b2o3bobobo4b2ob2o$b3o4bob3o3bob2o$o2bo4b3obobobo2b4o$b
o2bo3b6ob2ob2o$6bo9b2o3bo$2bo2bo4b3obob5obo$2o5b2o3b2o2b6o$3bobobob2ob
ob2o2b5o$7o2b2obo4b6o$4b3o3bob2o2b3ob2o$4obo2bobo2bo2b4o2bo$5b2obobo4b
5obo$b2o2bo5bo4bo2b2o$b2o3bobobo2b4obob3o$o2b2ob5o3b2ob3o$bob2o2b2o4b
2o3b5o$5o2bo3bo3bo2b5o$b4o2bob2ob2obo2b4o$ob3obobob3obobob3obo!

I'm still not absolutely clear on whether it makes sense to run a different rule for the first tick of S0.../B...8 patterns, to simulate the effects of the Big-Bang Universal Inversion. That is to say, which of the two possible T=10 patterns do we really want to end up with?

Evidence from the AntiLife experiment suggests that maybe it should not be the above pattern, but the one from my previous post, where the Big Bang Universal Inversion never happened. That has the additional advantage of not having to figure out a different rule to run at T=1...!

[rowett]

Evidence from the AntiLife experiment suggests that maybe it should not be the above pattern, but the one from my previous post, where the Big Bang Universal Inversion never happened. That has the additional advantage of not having to figure out a different rule to run at T=1...!

Is this only an issue with the B0/S8 case? Either way I'd be tempted to be consistent with the totalistic B0 handling (i.e. there was no Big Bang!).

[dvgrn]

Is this only an issue with the B0/S8 case? Either way I'd be tempted to be consistent with the totalistic B0 handling (i.e. there was no Big Bang!).

Sounds good to me. In that case, Molly seems to be working perfectly. Maybe someone else can try some tests also, if there are any likely edge cases I haven't thought of.

Yes, the B0-no-S8 cases have a Big Bang every tick -- thus the necessity for constant rule switching. For B0.../S...8 there's just the one anomalous conversion to all-ON. After that you can simulate the finite part of the pattern by inverting all the cells and running the "opposite of the rule" -- survival if the cell would have died (if all cells were inverted), and death if it would have survived (if all cells were inverted).

If anyone decides that they want to use Golly to simulate a Big Bang in a B0.../S...8 universe, it would be fairly easy to write a script that would change the current isotropic rule to its "bit-reversed rule", run for one tick, and then switch back to the original rule.

That would work for B0/S8 totalistic rules, too, of course, and we could see what a glider "really" does in AntiLife. (When you draw a glider and switch to AntiLife, Golly currently just simulates an anti-glider.)

-- Sorry for the continued re-explanations. It seems like a good idea to write all this stuff down while I still think I understand it, because it will probably all be a mystery to me again in a few weeks...!

[rowett]

Sounds good to me. In that case, Molly seems to be working perfectly. Maybe someone else can try some tests also, if there are any likely edge cases I haven't thought of.

Perfect, in which case I'll port my [GM]olly changes to LifeViewer.

-- Sorry for the continued re-explanations. It seems like a good idea to write all this stuff down while I still think I understand it, because it will probably all be a mystery to me again in a few weeks...!

Don't blame you. There are an increasingly large number of instances where I look at some old LifeViewer code and can't remember the excellent reason why it was implemented the way it was...

[muzik]

Excuse my ignorance, but what is Molly?

[dvgrn]

Excuse my ignorance, but what is Molly?

Try the link from this message. An early draft of an online version of Golly, basically.

[Gamedziner]

An easy way to deal with B0/S8 rules is to invert them then play them with an inverted theme, although this is a bit of a cheat.

Example:
Glider in Life (Using Theme 0)

Code: Select all

x = 3, y = 3, rule = B3/S23
bo$2bo$3o!
#C [[ THEME 0 ]]

Anti-Glider in AntiLife (Technically a Glider in Life, but shown in Theme 6)

Code: Select all

x = 3, y = 3, rule = B3/S23
bo$2bo$3o!
#C [[ THEME 6 ]]

[mniemiec]

I am glad to see that Golly 2.8 includes support for non-totalistic rule strings, but I'm a bit confused about the convention that is used. It appears to be based on Alan Hensel's notation (http://www.ibiblio.org/lifepatterns/neighbors.html), but there are some differences. In most cases, the changed rule names are fairly benign, and reduce the number of letters that must be used, and there is no ambiguity between the two notations. However, there are two rules (4r and 4n) that have valid but different meanings under the two systems, so if one sees such a rule string, it is not clear which one is meant. I'm curious why this change was made.

[Sphenocorona]

The notation used is a later one also created by Alan Hensel, which as you noted is more efficient: http://www.ibiblio.org/lifepatterns/neighbors2.html

[mniemiec]

The notation used is a later one also created by Alan Hensel, which as you noted is more efficient: http://www.ibiblio.org/lifepatterns/neighbors2.html

Thanks! I wasn't aware of newer version. Since that seems to be the new official notation, I'll upgrade all my references to it accordingly.

[_zM]

This is very interesting, to say the least. Resizing does not fix it.

[_zM]

Due to the attachment, I cannot edit this into the original post

And then this happened. What?

(envelope.py seems to have caused this)

[_zM]

Even on lower zooms, the colours blend flawlessly.

edit: multiple layers were the problem, yet I still wonder how they became transparent.

It's past midnight here after all.

[dvgrn]

Even on lower zooms, the colours blend flawlessly.

edit: multiple layers were the problem, yet I still wonder how they became transparent.

The envelope.py script changes the default layer option -- which is "not stacked and not tiled" -- to the stacked option.

There's a button on the Layers bar that does the same thing. Mostly no one ever uses it, because it's somewhat confusing unless your layers are very closely related. -- And maybe even more confusing if they _are_ closely related, except in special cases like envelope.py.

Anyway, envelope.py uses stacked layers to get its special LifeHistory-like effect using just a stack of two-state rules. It more or less assumes that that you're starting with a single layer, but doesn't actually enforce that. Probably it should at least give some kind of warning.

Anyone want to supply a quick patch? We'll need one for envelope.lua as well.

[Andrew]

Anyone want to supply a quick patch? We'll need one for envelope.lua as well.

Simplest solution would be to turn off layer stacking when the script exits by adding this command at the very end of both envelope.py and envelope.lua:

Code: Select all

g.setoption("stacklayers", 0)

[drc]

You should probably set a limit on the amount of characters in a rule string, because...:

Golly-exe-has-stopped-working.png (122.16 KiB) Viewed 381 times

[rowett]

You should probably set a limit on the amount of characters in a rule string

Thanks for reporting. This will be in the next build.

[rowett]

Running this on 64-bit Ubuntu, I'm experiencing major slowdowns while zooming in/out as opposed to 2.7. Additionally, holding down spacebar for a speed between 0.25s and unit step also just freezes.

Thanks for reporting. The slowdown issue while zooming in/out should be improved in the next build.

I have been unable to reproduce the spacebar freeze. Please could you provide more details?

[LegionMammal978]

I have been unable to reproduce the spacebar freeze. Please could you provide more details?

It's less of a freeze than general choppiness. Also, I've noticed that occasionally in normal usage for larger patterns, it has trouble keeping up with the cell count and just displays ? for several steps.