## Taming B37/S23

For discussion of other cellular automata.
Apple Bottom
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### Taming B37/S23

I was thinking about close variants of Conway Life recently, with added birth conditions. B34/S23 is explosive in nature, but B35/S23 (unnamed?), B36/S23 (HighLife) and B38/S23 (Pedestrian Life), where cells need more and more neighbors to be born, are not.

So far, that's not surprising. What is maybe surprising is that B37/S23 is explosive even though B36/S23 and B38/S23 aren't. What's even more surprising is that adding more birth conditions causes the rule to become stable. In particular, B357/S23 is stable. (A note on terminology: for the purpose of this post, "stable" means "eventually stable"; patterns may well show activity for a considerable number of generations, but will not generally grow without bound.)

So I wondered, given that we now have all the machinery to efficiently deal with non-totalistic rules (native support in Golly, Aidan's hacked version of apgsearch, and server-side support in Catagolue), what specific B5 subconditions are actually needed to tame B37/S23?

The subconditions that apply to B5 are a, c, e, i, j, k, n, q, r and y. Of these, e, j, n, q and r all immediately yield stable rules: B35e7/S23, B35j7/S23, B35n7/S23, B35q7/S23 and B35r7/S23.

What about a, c, i, k and y? They're not enough to stabilize the rule on their own, but I tried all possible combinations, with the following results:

Two subconditions:
• B5ac - explodes
• B5ai - explodes
• B5ak - explodes
• B5ay - looks stable, but explodes.
• B5ci - explodes
• B5ck - explodes
• B5cy - looks stable, but explodes.
• B5ik - explodes
• B5iy - stable
• B5ky - explodes, interesting patterns.
Three-letter combinations:
• B5aci - explodes
• B5ack - explodes
• B5acy - explodes
• B5aik - explodes
• B5aiy - looks stable, but explodes.
• B5aky - explodes
• B5cik - explodes
• B5ciy - explodes
• B5cky - explodes
• B5iky - looks stable, but explodes.
Four-letter combinations:
• B5acik - explodes
• B5aciy - explodes
• B5aiky - explodes
• B5acky - explodes
• B5ciky - explodes
Five-letter combination:
• B5aciky - explodes
I found it quite remarkable that precisely one combination (iy) turned out to yield a stable rule, B35iy7/S23.

And while B35ky7/S23 is explosive and does not lend itself to being soup-searched, it's got an interesting very common puffer:

Code: Select all

x = 16, y = 9, rule = B35ky7/S23
b2o$o2bo$ob2o6bo$bo8bo$b2o2bo3bo3b3o$b2o3b2o7bo$3bo9bobo$6b4o3b2o$8bo!

This one is so common, in fact, that the chaos arising from soups will often grow dendrite-like structures that will hit each other and interact; the backwards-travelling gliders for their part also trigger further reactions, yielding a quadratic-growth chaotic spacefiller, as in e.g. the following random soup:

Code: Select all

x = 20, y = 20, rule = B35ky7/S23
4obob4o5b4o$2ob4ob3o2b5obo$o3bo2b2o2bob3ob2o$2bo2bo2b2o2b3ob3o$ob2obob
6o2b4o$o6b2obo3b4o$3ob5ob2o4bo2bo$ob2obo2bo2b4o2bo$3ob3o9bo2bo$b3o2b4o bob2o2b2o$3bob2ob2ob2obo2b2o$2b2ob2ob3ob8o$3bo2b2o2bo3bo$4b2ob5o2bo3b 2o$2o2b2o4bob4o$obob2o2bo2b2o5b2o$4o2b2o3bobo2b3o$3bo2bob2ob2o2b3o$ob
2o3b2o2b2ob4o$bo4bo2b3obobo!  If you speak, your speech must be better than your silence would have been. — Arabian proverb Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_ Proud member of the Pattern Raiders! A for awesome Posts: 1996 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: Taming B37/S23 Another option is to remove one of the B7 transitions. It turns out that B37e/S23 is stable (although quite long-lived) while B37c/S23 is explosive: Code: Select all x = 4, y = 3, rule = B37e/S23 2bo$b3o$2obo! Code: Select all x = 3, y = 3, rule = B37c/S23 bo$3o$o! x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce BlinkerSpawn Posts: 1953 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: Taming B37/S23 B36k7/S23 is somewhat stable and has a very natural 5c/17 block puffer: Code: Select all x = 4, y = 5, rule = B36k7/S23 2bo$3bo$obo$3bo$2bo!  LifeWiki: Like Wikipedia but with more spaceships. [citation needed] drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Taming B37/S23 B35iy78/S23 is, well: Code: Select all x = 3, y = 3, rule = B35iy78/S23 3o$2bo$2bo!  \100\97\110\105 Apple Bottom Posts: 1030 Joined: July 27th, 2015, 2:06 pm Contact: ### Re: Taming B37/S23 A for awesome wrote:Another option is to remove one of the B7 transitions. It turns out that B37e/S23 is stable (although quite long-lived) while B37c/S23 is explosive: Nice. B37e/S23 has already been searched on Catagolue, as B37-c/S23. Quite a few interesting patterns there. Code: Select all x = 11, y = 14, rule = B37e/S23 3b3o5b$3bobo5b$2bo2bo5b$bo3bob2o2b$3o2bob2o2b$o5bo4b$3bo2bo4b$2bo3bo4b$2bo3bo4b$2bo8b$bo7bob$8bobo$8bobo$9bob!

BlinkerSpawn wrote:B36k7/S23 is somewhat stable and has a very natural 5c/17 block puffer:
Another rule to do some searching on, then! (Bit faster, too, ~10 soups/sec.) Funny how that one's stable even though both B37/S23 and B367/S23 are explosive.
If you speak, your speech must be better than your silence would have been. — Arabian proverb

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AbhpzTa
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### Re: Taming B37/S23

B34e7/S23:

Code: Select all

x = 4, y = 8, rule = B34e7/S23
bo$obo$obo$bo2$3o$o2bo$2obo!
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).

_zM
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### Re: Taming B37/S23

B34n7/S23 is also stable. apgsearching.

EDIT: c/17

Code: Select all

x = 10, y = 5, rule = B34n7/S23
8b2o$b2o4b2o$o2bo2bo2bo$b2o4b2o$8b2o!

Creator of multiple rules that may or may not be what you'd expect

Apple Bottom
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### Re: Taming B37/S23

Small puffer laying pairs of blinkers and barges in B36n7/S23:

Code: Select all

x = 11, y = 5, rule = B36n7/S23
bo7bo$4o3b4o$o3bobo3bo$bo2bobo2bo$b3o3b3o!

EDIT: pond pair-laying puffer in B34e7/S23:

Code: Select all

x = 13, y = 5, rule = B34e7/S23
b2o7b2o$2obo5bob2o$o2bo5bo2bo$3o7b3o$b2o7b2o!

If you speak, your speech must be better than your silence would have been. — Arabian proverb

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drc
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### Re: Taming B37/S23

I think the real question here is why B23/S23 explodes, B34/S23 explodes, but B33/S23 is completely stable???

Edit: I japed you all.
Last edited by drc on January 24th, 2017, 5:49 pm, edited 1 time in total.
\100\97\110\105

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### Re: Taming B37/S23

drc wrote:I think the real question here is why B23/S23 explodes, B34/S23 explodes, but B33/S23 is completely stable???
Well, B2 and B4 happen very often in those respective rules.
If you want to explore that question further, see which B4 transition makes Life explode the least.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Apple Bottom
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### Re: Taming B37/S23

drc wrote:I think the real question here is why B23/S23 explodes, B34/S23 explodes, but B33/S23 is completely stable???
Very pressing question indeed.

BTW, it turns out that (as best as I can tell so far) B34t7/S23 and B34z7/S23 are both stable, but also very slow to search thanks to very common infinite growth patterns. The latter runs at ~1-2 soups/sec, the former is well below 1 soup/sec. I'll leave both running overnight.

B34z7/S23 also has a very common period-20 ship:

Code: Select all

x = 20, y = 10, rule = B34z7/S23
b2o17b$b2o17b$20b$11bo8b$2b3o5b2o8b$bo2b2o3bo2bo4b2ob$o3bo5b2o6b2o$bo2b o6b2o4b2ob$2b4o7b2o2bo2b$3b3o7b2o5b!  EDIT: unfortunately B34t7/S23 triggers certain problems in apgsearch/Golly. After seeing it consume up to ~27 GB of RAM, I eventually got the following error: Code: Select all File "<string>", line 1, in <module> File "apgsearch-2016-2-06-v0.54+0.21i-update.py", line 12850, in <module> apg_main() File "apgsearch-2016-2-06-v0.54+0.21i-update.py", line 12763, in apg_main meandelay = soup.stabilise_soups_parallel(rootstring, scount + initpos, sqrtspp, symmstring) File "apgsearch-2016-2-06-v0.54+0.21i-update.py", line 12134, in stabilise_soups_parallel return self.stabilise_soups_parallel_orig(gsize, souplist, pos) File "apgsearch-2016-2-06-v0.54+0.21i-update.py", line 12229, in stabilise_soups_parallel_orig self.teenager(gsize, gspacing, ashes, stepsize, 18, pos) File "apgsearch-2016-2-06-v0.54+0.21i-update.py", line 12081, in teenager ceillist = g.join(g.getcells(g.getrect()), [0]) MemoryError  That said, here's a partial log showing results after 181 soups (the search did not get much further than this in the end): Code: Select all @VERSION v0.54+0.21i @MD5 a8c38ea05c206ef77eb46e3df291aeff @ROOT vFmDHhRVFsVe @RULE B34t7S23 @SYMMETRY C1 @NUM_SOUPS 181 @NUM_OBJECTS 469834 @CENSUS TABLE xp2_7 328798 xs4_33 131534 xs6_696 3881 xs4_252 1849 xs5_253 1069 xq4_153 1003 xs6_356 490 xs7_2596 454 xs8_6996 301 xs12_g8o653z11 144 yl30_1_36_d90bad5a24997f17e5e9851e49e89dc2 123 xs6_25a4 95 xp2_7e 24 xs8_69ic 14 xs7_25ac 14 z_LINEAR 13 xp2_318c 9 xs8_25ak8 5 xs7_178c 3 xs14_g88m952z121 2 z_QUADRATIC 2 xs10_4al96 2 xs20_3lkkl3z32w23 1 xs10_178kk8 1 yl60_1_138_3e1620c10530bdf483a1ef093e0d10b8 1 yl120_1_100_c873f786121c6a231a9ecc69136819a6 1 xs11_69lic 1 @TOP 100 51 600 135 420 12 300 154 300 166 300 55 300 98 300 3 240 141 240 58 240 87 240 145 190 4 180 146 180 176 180 42 180 177 180 124 180 1 120 2 120 10 120 151 120 162 120 164 120 68 120 71 120 75 120 92 120 97 120 105 120 13 61 179 60 9 60 14 60 17 60 147 60 149 60 23 60 28 60 30 60 160 60 37 60 167 60 168 60 156 60 48 60 56 60 61 60 64 60 139 60 70 60 74 60 76 60 79 60 82 60 83 60 142 60 88 60 90 60 91 60 95 60 96 60 99 60 104 60 113 60 114 60 170 60 47 7 94 4 @SAMPLE_SOUPIDS xp2_7 74 74 74 74 74 74 74 74 79 74 xs4_33 74 74 79 79 74 74 74 79 79 74 xs6_696 58 58 58 58 58 58 58 58 51 51 xs4_252 75 75 75 75 75 74 74 75 75 75 xs5_253 75 75 75 75 79 72 72 79 74 74 xs6_356 74 80 79 79 79 79 75 68 58 58 xs7_2596 75 75 75 75 75 80 75 75 75 70 xs8_6996 75 79 75 75 70 68 58 58 58 58 xs12_g8o653z11 51 51 51 51 51 51 51 51 51 51 yl30_1_36_d90bad5a24997f17e5e9851e49e89dc2 74 79 75 76 75 71 68 64 68 71 xs6_25a4 71 58 50 12 10 2 1 87 87 87 xp2_7e 58 58 58 58 55 51 12 12 12 3 xs8_69ic 51 51 47 12 3 91 127 135 176 176 xs7_25ac 58 61 51 51 14 3 3 87 97 93 z_LINEAR 70 51 12 12 10 9 2 3 146 135 xp2_318c 58 58 42 34 90 98 105 146 135 xs8_25ak8 78 51 87 154 166 xs7_178c 58 51 51 xs14_g88m952z121 177 177 z_QUADRATIC 58 141 xs10_4al96 47 145 xs20_3lkkl3z32w23 145 xs10_178kk8 13 yl60_1_138_3e1620c10530bdf483a1ef093e0d10b8 12 yl120_1_100_c873f786121c6a231a9ecc69136819a6 135 xs11_69lic 94  If you speak, your speech must be better than your silence would have been. — Arabian proverb Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_ Proud member of the Pattern Raiders! Saka Posts: 3199 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X Contact: ### Re: Taming B37/S23 What about B34e7/S23? Code: Select all x = 17, y = 10, rule = B3/S23 b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Apple Bottom
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### Re: Taming B37/S23

Saka wrote:What about B34e7/S23?
Can be searched; I'm getting ~10 soups/second on that one.

B34z7/S23 ran into memory issues eventually as well, but I was able to submit a few hauls overnight. Here's the most common period-40 puffer (two blocks, one beehive, one glider):

Code: Select all

x = 13, y = 7, rule = B34z7/S23
6bo$6bo2b2o$5bobo3bo$bo4bobo2b2o$obo3bo3b2o$obo5b3o$bo!

Another period-40 puffer (four boats, four blinkers):

Code: Select all

x = 3, y = 15, rule = B34z7/S23
b2o$2o$b2o$2bo8$2bo$b2o$2o$b2o!  Another (two traffic lights): Code: Select all x = 3, y = 13, rule = B34z7/S23 2o$b2o$2o$o6$o$2o$b2o$2o!

There's many more; they're all variants of each other as far as I can tell, differing in how far apart the engine components are and how it interacts with the (pre-existing) ash.

Higher-period and/or asymmetric variants also exist, and of course they're all based on the xq20 mentioned further up in this thread.

BONUS: a pretty xp74 in B36ai7/S23:

Code: Select all

x = 13, y = 7, rule = B36ai7/S23
2b3o3b3o2b$bo2bo3bo2bob$o3bo3bo3bo$o11bo$o3bo3bo3bo$bo2bo3bo2bob$2b3o3b
3o2b!

If you speak, your speech must be better than your silence would have been. — Arabian proverb

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_zM
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Joined: June 26th, 2016, 3:07 pm

### Re: Taming B37/S23

Adding survival conditions is also an option. For example, B37/S234j is stable. However, the only interesting pattern so far that doesn't appear in Life is this p16 oscillator:

Code: Select all

x = 8, y = 8, rule = B37/S234j
5bo$4b2o$4bob2o$5b2o$b2o$2obo$2b2o$2bo!  Creator of multiple rules that may or may not be what you'd expect Apple Bottom Posts: 1030 Joined: July 27th, 2015, 2:06 pm Contact: ### Re: Taming B37/S23 _zM wrote:Adding survival conditions is also an option. For example, B37/S234j is stable. Good idea. Here's some preliminary results on adding individual subconditions in the S5 to S8 range: • B37/S238 - explodes • B37/S237 - explodes • B37/S237c - explodes • B37/S237e - explodes • B37/S236 - explodes • B37/S236a - explodes • B37/S236c - explodes • B37/S236e - explodes • B37/S236i - explodes • B37/S236k - explodes • B37/S236n - explodes • B37/S235 - explodes • B37/S235a - explosive • B37/S235c - explosive • B37/S235e - explosive • B37/S235k - explosive • B37/S235i - explosive • B37/S235j - explosive • B37/S235n - explosive • B37/S235q - explosive • B37/S235r - explosive • B37/S235y - stable I'm soup-searching B37/S235y now. So far the search has hit two (distinct) objects not in Conway Life, a period-28 oscillator and a period-10 spaceship. Code: Select all x = 6, y = 5, rule = B37/S235y bo2bob$bo3bo$o2b3o$bo3bo$bo2bob!  Code: Select all x = 11, y = 3, rule = B37/S235y o2bo3bo2bo$b3o3b3ob$b3o3b3ob!  If you speak, your speech must be better than your silence would have been. — Arabian proverb Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_ Proud member of the Pattern Raiders! drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Taming B37/S23 Various B37/S235y ships from c/2, 2c/5, c/3, c/4 (including a partial antstretcher at c/4): Code: Select all x = 266, y = 499, rule = B37/S235y 6bo12bo6bo10bo13bo12bo7bo11b2o14b2o13bo5bo9bo9bo11bo15bo12bo7bo11bo3bo 47bo6bo$5b3o10bobo4bobo8bobo11bobo10bobo5bobo6b2obo2bob2o6b2obo2bob2o
7b4o3b4o5b3o9b3o8bobo14bo12bo7bo11bo3bo47bo6bo$3b2obob2o7b2ob2o2b2ob2o 6bo3bo9bo3bo8bo3bo3bo3bo5b2o6b2o6b2o6b2o6b2o3bobo3b2o4bo2bob2ob2obo2bo 6bo2bo2bo11bobo10bobo5bobo9bobobobo45bobo4bobo$2bo2bobo2bo6b2o2bo2bo2b
2o7bobo11bobo9bo3b2ob2o3bo5bobo4bobo6bobo4bobo5bo3bobobobo3bo2bo4bobob
obo4bo4b2obobob2o$bo3bobo3bo6b2ob4ob2o8b3o11b3o9b3ob2ob2ob3o7b2o2b2o 10b2o2b2o11bo2bo2bo7bob3obobob3obo5bo2bobo2bo10bobo10bobo5bobo9bobobob o$bo3bobo3bo5bo3bo2bo3bo32bo2b2obobob2o2bo5b2ob2ob2o8b2ob2ob2o9bo7bo
25bo9bo22b2o7b2o7bo3bobo3bo44bo6bo$2obobobobob2o3b2obo6bob2o5b5o9b5o6b obo2bo5bo2bobo6bo2bo12bo2bo10b2obo3bob2o5b3o9b3o8b3o12bobobo12b2ob2o9b ob2obobob2obo42b3ob2ob3o$obob2ob2obobo6b2o4b2o7bobobobo7bobobobo7b3o7b
3o6bo6bo9bo4bo9b4o3b4o25bo7bo11bo14b2ob2o14bobo47b3ob2ob3o$2bob5obo6b 2o8b2o7bobo11bobo7bo2bo9bo2bo4bo6bo5b3ob2o2b2ob3o7b3ob3o29bo3bo10bobob obo10b2o3b2o7bo2b2o5b2o2bo41bobo4bobo$2bo7bo10b4o11bobo11bobo8b3obo5bo
b3o17bo5bo2bo5bo4b3o2bo2b3o27bo3bo10b2o3b2o11b2ob2o8bobob3ob3obobo43bo
4bo$3bob3obo10b6o9bo3bo9bo3bo9b3o5b3o7b8o5bo2b3o2b3o2bo5bo9bo27b2ob2o 8bo9bo6b2ob2ob2ob2o4b3o2b3ob3o2b3o41b2o4b2o$6bo12bo6bo53b2o6b2o8bob2ob
o46bo5bo10b5o7b3o3bobo3b3o6bo7bo46bo4bo$6bo12bobo2bobo7bobobobo7bobobo bo8b3o5b3o22b2o6b2o10b5o44bo7bo11bobo8bo3bob2ob2obo3bo41bo6bo$19bobo2b
obo8b2ob2o8bobobobo7b2ob2o3b2ob2o40b2obob2o30b3o10bo7bo5b2o4bobo4b2o3b
o5bobo5bo39b4o6b4o$49b2ob2o13bobo43b2o7b2o25b3o3b3o7b2o2bo2b2o10bo3bo 10bobobobobobo43bo8bo$35bo3bo7bo2bobo2bo7bobobobobobo40bo7bo41bo9bo5bo
11bo7b2obobob2o42bobo3b2o3bobo$34bo5bo5bob2obob2obo5b2o3bobo3b2o38bo9b o28b3o14bo9bobobo5bobobo6bo2bobo2bo42bobo3b2o3bobo$34bobobobo5bo4bo4bo
6bo3bobo3bo40bo7bo28b5o6b2obo2bobo2bob2o3b2ob2o3b2ob2o6b2ob2ob2ob2o42b
2o2bo2bo2b2o$34bo5bo4b2o2bo3bo2b2o6b2obobob2o77bo5bo6bo2bobobobo2bo5bo 3bobo3bo7b2o7b2o41bo12bo$37bo13bo13bobobobo77bobo3bobo5bo2bobobobo2bo
7b2o3b2o7bo13bo38b5o6b5o$36b3o6b3obo3bob3o7bobobobo77b2o5b2o6bo3bobo3b o5b2o9b2o3bo2bo2bo3bo2bo2bo39bo10bo$36b3o6bo11bo7bobobobo76b2o7b2o7bob
obobo7bo11bo4b2o3b2ob2o3b2o41b2o6b2o$36b3o8b2o2bo2b2o6b2obobobobob2o 90b2obobob2o8bo7bo12bobo49bo4bo$46b3o5b3o5b2obobobobob2o73bo9bo8bo3bo
9b2o7b2o11bobo47b2o2b2o2b2o$33b3o3b3o4bo4bo4bo5bobo2bobo2bobo78bo26b2o 9b2o8bobobobo48bo2bo$33b2obobob2o8bobo8b2o4bobo4b2o72b2ob2ob2ob2o6b2o
5b2o6b3ob2ob2ob3o7b2o5b2o48b2o$33b2o5b2o5bobo3bobo5b3o2bo3bo2b3o73bo2b obo2bo6bo2bo3bo2bo10bobo11b2ob2ob2ob2o47b2o$33bo7bo4b2obo3bob2o7b2o5b
2o76b2obobob2o5bo2bo5bo2bo4b2ob2o3b2ob2o7bo7bo$34bobobobo20b2ob2o5b2ob 2o73bo2bobo2bo5b2o9b2o6b2o5b2o8b2o7b2o46bo2bo$49bo3bo9b3o5b3o74b2o7b2o
5b2o7b2o4bo13bo4b2o9b2o45bo2bo$49bobobo94b3o5b3o5bobo5bobo7bo7bo8bob2o 3b2obo47b2o$148b2o7b2o4b2obo5bob2o4bobo7bobo5bob2o5b2obo46b2o$64bo7bo 89bo4bo3bo4bo5bo7bo8bo9bo$62b2obo5bob2o72bo11bo7bo3bo10bo2bobo2bo8bob
2o3b2obo46bo2bo$61b2o2bo5bo2b2o73b3o3b3o4bobo3bobo3bobo5bo2bobo2bo6b3o b2o3b2ob3o44bo2bo$61b2o3bo3bo3b2o73bo2bobo2bo24bo7bo6b3obo5bob3o45b2o$63b4o3b4o76bob3obo6b2obo5bob2o5bo2bo3bo2bo5bobo9bobo45b2o$63bo2bo3bo2b
o75bo7bo8b2o3b2o8b3o5b3o7bo9bo$147bo2bo5bo2bo6b2o3b2o8bo9bo6b3o7b3o45b o2bo$64b2o5b2o74bobo7bobo5b2o5b2o26bo7bo47bo2bo$65bobobobo93bobo3bobo 6b2o9b2o4bobo9bobo45b2o$65bobobobo93bob2ob2obo23bo2bobo3bobo2bo45b2o$65bo5bo93bob2ob2obo6b3o7b3o5bob2obobob2obo$66bo3bo95bo5bo27b2obobob2o
47bo2bo$165bo2bobo2bo8bo7bo10b2o3b2o48bo2bo$167bo3bo11bo5bo11bo5bo49b
2o$164bo9bo8bobobobo11bo5bo49b2o$163b2o9b2o23b2o2bobo2b2o$165bo7bo8bo 2bobo2bo7bob3o3b3obo45bo2bo$165b2o5b2o8bobo3bobo6bo3bo5bo3bo44bo2bo$166b2o3b2o8b2o7b2o5bo3b2o3b2o3bo45b2o$166bo5bo30bobo51b2o$181bo9bo7b2o b2ob2ob2o$165bo2b3o2bo6b2o9b2o7bob2ob2obo47bo2bo$165b3o3b3o6b2o9b2o7bo 2bobo2bo47bo2bo$164b2o7b2o5bo11bo7bo2bobo2bo48b2o$182b2o5b2o7bo2bobobo bo2bo46b2o$163bo11bo4bo2bo5bo2bo4bobobobobobobobo$164bo9bo5bo11bo8bobo bobo48bo2bo$164bo3b3o3bo5bobo7bobo4b2o2bobobobo2b2o44bo2bo$167bo3bo10b o7bo9b2obobob2o48b2o$166b2o3b2o8b2o7b2o8b2obobob2o48b2o$163bobo7bobo6b o2bobo2bo12bobo$163b2o9b2o6bo2bobo2bo8b2o2bobo2b2o46bo2bo$162bo5b3o5bo 3bob2o5b2obo4b2obo2bobo2bob2o44bo2bo$164b2o7b2o4bobo9bobo3b2ob2o5b2ob
2o45b2o$197b2obob2ob2obob2o45b2o$163b2o9b2o5bo9bo6bobo7bobo$166bo5bo8b o9bo5b2obob2ob2obob2o44bo2bo$164bo2bo3bo2bo6bo9bo8bob2ob2obo47bo2bo$164bobo5bobo5b2o9b2o4bo2bo7bo2bo45b2o$167b2ob2o8b2o9b2o7b2o5b2o48b2o$181bob3ob3obo7bob3ob3obo$167bo3bo11b3ob3o66bo2bo$167bo3bo11bobobobo12b 2ob2o49bo2bo$165b3o3b3o8b2obobob2o12bobo51b2o$165b2o5b2o7bobobobobobo 8b2o5b2o48b2o$166bo5bo8bo3bobo3bo7b4o3b4o$168b3o9b3o2bobo2b3o63bo2bo$
168b3o13bo3bo8bo2b2o5b2o2bo44bo2bo$169bo27b2o2bo5bo2b2o45b2o$164b3ob3o
b3o9b2ob2o7bobo11bobo44b2o$167bo3bo8b6ob6o4b3obo5bob3o$163bo2bob3obo2b
o3bo2b3o3b3o2bo4b3o7b3o45bo2bo$163b3o3bo3b3o25bo5bo48bo2bo$165bo7bo23b
o3bo5bo3bo45b2o$165b2o5b2o7b2o7b2o5bo4bo3bo4bo45b2o$165bo7bo7bobo5bobo
6bob2o5b2obo$197b3o9b3o44bo2bo$165b2ob3ob2o8b3o3b3o65bo2bo$163b2ob2o3b 2ob2o7b2o3b2o67b2o$166bob3obo24bo2bo7bo2bo45b2o$165bo2b3o2bo9bo5bo8bob o7bobo$164bob2o3b2obo26bo5bo48bo2bo$168bobo10b2obo3bob2o64bo2bo$167b2o
b2o11bo5bo8bo11bo46b2o$165b2obobob2o6bo2bo5bo2bo4b2obob2ob2obob2o45b2o$165bo2bobo2bo6b3o7b3o9b2ob2o$167b2ob2o10bo7bo8b2o2bobo2b2o46bo2bo$
166b3ob3o29bo3bo49bo2bo$163b3o7b3o6b2o5b2o11bo3bo50b2o$163bob2o5b2obo
26bo3bo50b2o$182b3o3b3o6bo2bobo3bobo2bo$196b2ob2o2bobo2b2ob2o43bo2bo$199b2o7b2o46bo2bo$199b2o7b2o47b2o$199b3o5b3o47b2o$201bo5bo$201bo5bo48b o2bo$197bobo9bobo44bo2bo$197b3obo5bob3o45b2o$197bo2bo7bo2bo45b2o$199b 2o7b2o$197b3o9b3o44bo2bo$198b2o9b2o45bo2bo$257b2o$200bo7bo48b2o$198b3o
bo3bob3o$199b3obobob3o46bo2bo$199b2ob2ob2ob2o46bo2bo$199b2o2bobo2b2o 47b2o$203bobo51b2o$200bo7bo$201bobobobo48bo2bo$203bobo50bo2bo$202b2ob
2o50b2o$257b2o$200b2o5b2o$199b4o3b4o46bo2bo$199bob2o3b2obo46bo2bo$198b obo7bobo46b2o$198b3o7b3o46b2o$197b2o2bo5bo2b2o$199bo9bo46bo2bo$200b3o 3b3o47bo2bo$199bo9bo47b2o$197bob2o7b2obo45b2o$197bob2o7b2obo$197bo2bo 7bo2bo44bo2bo$199bo9bo46bo2bo$198bo3b2ob2o3bo46b2o$201bobobobo49b2o$200b2obobob2o$256bo2bo$199b2o7b2o46bo2bo$257b2o$199bo9bo47b2o$197b3o9b
3o$197b2ob2o5b2ob2o44bo2bo$199bobo5bobo46bo2bo$199bo3bobo3bo47b2o$203b
obo51b2o$201bobobobo$201bo5bo48bo2bo$202b2ob2o49bo2bo$203bobo51b2o$202bo3bo50b2o$200b2o5b2o$200b2o5b2o47bo2bo$198bo2bo5bo2bo45bo2bo$197bo 2bo7bo2bo45b2o$196b2o13b2o44b2o$199bo9bo$196b2o13b2o43bo2bo$197b2o11b 2o44bo2bo$196b2o13b2o44b2o$199b2obo3bob2o47b2o$199b2ob2ob2ob2o$199bo2b o3bo2bo46bo2bo$256bo2bo$200b3o3b3o48b2o$200bo2bobo2bo48b2o$199bo2b2ob 2o2bo$201bo5bo48bo2bo$200bo7bo47bo2bo$257b2o$199b2o7b2o47b2o$199b4o3b
4o$196b5ob2ob2ob5o43bo2bo$203bobo50bo2bo$202b2ob2o50b2o$196b2o2bo2bobo
2bo2b2o44b2o$198bobo2bobo2bobo$198b2obobobobob2o45bo2bo$198b2obobobobo b2o45bo2bo$199bo3bobo3bo47b2o$199b2o2bobo2b2o47b2o$198bo4bobo4bo$256bo 2bo$200bobo3bobo47bo2bo$202bo3bo50b2o$199bo3bobo3bo47b2o$201b2o3b2o$
198bo3bo3bo3bo45bo2bo$197b2o3bo3bo3b2o44bo2bo$197b2o3bo3bo3b2o45b2o$197b5o5b5o45b2o$201bo5bo$201b2o3b2o48bo2bo$200bo2bobo2bo47bo2bo$200bo 2bobo2bo48b2o$200b2obobob2o48b2o$203bobo$199bobobobobobo46bo2bo$198bo 2bobobobo2bo45bo2bo$197bo3bobobobo3bo45b2o$197bo5bobo5bo45b2o$201bobob
obo$199bobobobobobo46bo2bo$198b2o2bo3bo2b2o45bo2bo$198b3o7b3o46b2o$
201bo5bo49b2o$198b2o2bo3bo2b2o$197b2o3bo3bo3b2o44bo2bo$197b2o4bobo4b2o 44bo2bo$198b5o3b5o46b2o$197b5o5b5o45b2o$197bo3b2o3b2o3bo$197bo13bo44bo 2bo$256bo2bo$197bob4o3b4obo45b2o$198bo11bo46b2o$202b2ob2o$201bobobobo
48bo2bo$200b2obobob2o47bo2bo$199bobobobobobo47b2o$199b2obo3bob2o47b2o$
200bo7bo$197bo4b2ob2o4bo44bo2bo$197bobob3ob3obobo44bo2bo$197bobo2b2ob 2o2bobo45b2o$197b2o11b2o45b2o$198bo11bo$199bo9bo46bo2bo$198b3o7b3o45bo 2bo$199bobo5bobo47b2o$200b2o5b2o48b2o$199b3o5b3o$256bo2bo$197bobo9bobo
44bo2bo$196b2o13b2o44b2o$196b2obo9bob2o44b2o$197bo2bo7bo2bo$199b3o5b3o
46bo2bo$197bo3bo5bo3bo44bo2bo$198bo11bo46b2o$202b2ob2o50b2o$203bobo$200b2obobob2o47bo2bo$200bo2bobo2bo47bo2bo$198bo2bobobobo2bo46b2o$198b
3ob2ob2ob3o46b2o$198b4o5b4o$199b2ob2ob2ob2o46bo2bo$198b3ob2ob2ob3o45bo 2bo$198bobo7bobo46b2o$198b2o9b2o46b2o2$200bo7bo47bo2bo$199b2o7b2o46bo 2bo$199b2o7b2o47b2o$201bo5bo49b2o$202b2ob2o$200bob2ob2obo47bo2bo$201b
2o3b2o48bo2bo$200bobo3bobo48b2o$200b2o5b2o48b2o$199bo9bo$199bo2bo3bo2b
o46bo2bo$198bo11bo45bo2bo$200b2o5b2o48b2o$257b2o$200b2o5b2o$201bo5bo 48bo2bo$256bo2bo$201b2o3b2o49b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b
2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256b o2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$
256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256b
o2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo
$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b 2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$
257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b
2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256b o2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$
256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256b
o2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo
$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b 2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$
257b2o2$256bo2bo$256bo2bo$257b2o$257b2o2$256bo2bo$256bo2bo$257b2o$257b
2o2$256bo2bo$255bo4bo$253bo2bo2bo2bo$252b2o8b2o$251b3ob6ob3o$251b2o3b
4o3b2o!

\100\97\110\105

Apple Bottom
Posts: 1030
Joined: July 27th, 2015, 2:06 pm
Contact:

### Re: Taming B37/S23

All rules matching B37/S234? (i.e. all rules consisting of B37/S23 plus a single S4 subcondition) are explosive except for B37/S234j (already mentioned).

B37/S234w has a very common ship-laying puffer:

Code: Select all

x = 5, y = 3, rule = B37/S234w
2ob2o$bobo$2bo!

On the flip-side, removing any single S3 subcondition always creates a stable rule (though B37/S23-y has very common puffers that make soup-searching that rule very slow). Some interesting patterns:

xq20 in B37/S23-a:

Code: Select all

x = 3, y = 4, rule = B37/S23-a
3o$o2b$obo$b2o!  xq6 and xp30 in B37/S23-e: Code: Select all x = 5, y = 5, rule = B37/S23-e bob2o$o2b2o$o4b$2bobo$2b3o!  Code: Select all x = 4, y = 4, rule = B37/S23-e b2ob$2obo$2b2o$2bob!

xq13 in B37/S23-i:

Code: Select all

x = 3, y = 5, rule = B37/S23-i
2bo$2ob$bob$b2o$2bo!

xq2 and xq4 in B37/S23-j:

Code: Select all

x = 7, y = 4, rule = B37/S23-j
2o3b2o$b5ob$2b3o2b$3bo3b!  Code: Select all x = 3, y = 5, rule = B37/S23-j 2bo$b2o$2ob$bob$2bo!  xq4 in B37/S23-n: Code: Select all x = 3, y = 5, rule = B37/S23-n b2o$obo$o2b$2ob$2bo!  xp14 in B37/S23-q: Code: Select all x = 3, y = 8, rule = B37/S23-q 2ob$b2o$3o$3o$3o$3o$b2o$2ob!

xq4 and xp37 in B37/S23-r:

Code: Select all

x = 5, y = 5, rule = B37/S23-r
2o3b$b2o2b$2b2ob$bob2o$4bo!


Code: Select all

x = 10, y = 5, rule = B37/S23-r
2o6b2o$2o6b2o$2o6b2o$2o6b2o$2o6b2o!

That xp37 is actually the pentadecathlon in disguise, BTW.

EDIT: finally, removing any single S2 subcondition also always creates a stable rule. These rules are less interesting, but B37/S2-i3 has both a well-known xq5 (the "T" ship), a common xp34 and a common xp172.

Code: Select all

x = 2, y = 3, rule = B37/S2-i3
bo$2o$bo!


Code: Select all

x = 5, y = 5, rule = B37/S2-i3
3o2b$b2o2b$3bob$bo2bo$b3ob!


Code: Select all

x = 7, y = 4, rule = B37/S2-i3
2o5b$2o2b2ob$5b2o$6bo!  Furthermore, B37/S2-n3 has a very common period-180 puffer, as well as a period-20 puffer: Code: Select all x = 21, y = 44, rule = B37/S2-n3 10b2o$2o7bob2o6b2o$2o6b2obo7b2o$9b2o17$4b2o10b2o$3bob2o8bob2o$2b2obo8b 2obo$3b2o10b2o17$10b2o$9bob2o$8b2obo$9b2o!

This also yields a twin puffer with replicator-like behavior:

Code: Select all

x = 5, y = 4, rule = B37/S2-n3
2b2o$bob2o$2obo$b2o!  The yl20 is this: Code: Select all x = 9, y = 3, rule = B37/S2-n3 ob2ob2obo$3o3b3o$bo5bo!  EDIT 2: searching B37/S2-n3 runs into memory problems again eventually, but here's a an xq64 that showed up in B37/S2-i3: Code: Select all x = 4, y = 10, rule = B37/S2-i3 b2ob$2o2b$b3o$3bo$4b$4b$4b$4b$2o2b$2o2b!

If you speak, your speech must be better than your silence would have been. — Arabian proverb

Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_

Proud member of the Pattern Raiders!

Hdjensofjfnen
Posts: 1487
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Taming B37/S23

You can also do this (removing B7c):

Code: Select all

x = 5, y = 3, rule = B37e/S23
bob2o$o3bo$b3o!

"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!