Thread for basic non-CGOL questions

[confocaloid]

Check Tutorials/Software, Tutorials/RLifeSrc (the latter should be included into the category Category:Search software).

Are there some search programs with simple setup? I tried to apgsearch but its setup is too complex for me.

Edit: Online or Windows 10

[b-engine]

Are there some search programs with simple setup? I tried to apgsearch but its setup is too complex for me.

Edit: Online or Windows 10

WinLifeSrc (for Windows, obviously) only require a download, and is easy to setup. However it could only search in outer-totalistic rules.
RLifeSrc is similar to WLS, but could also search in isotropic rules.

[get_Snacked]

in range-2 INT on the Moore neighbourhood of a square tiling, what is the closest non-explosive self-complementary rule to B3/S23 in terms of transitions (aka transition rules)?

[confocaloid]

in range-2 INT on the Moore neighbourhood of a square tiling, what is the closest non-explosive self-complementary rule to B3/S23 in terms of transitions (aka transition rules)?

I assume you mean two-state isotropic CA with range-2 Moore neighbourhood, and I assume you mean transition rules.

Before it would be possible to answer the question (including whether or not there is an unique answer), one would need to define a "yes/no" test on the set of all such cellular automata:

Code: Select all

def is_non_explosive(ca):
    # check that the input is supported at all, otherwise fail:
    assert ca.number_of_cellstates() == 2
    assert ca.is_isotropic()
    assert ca.is_on_square_tiling()
    nbhd = ca.neighbourhood()    # a set of (dx,dy) ordered pairs
    assert nbhd.is_subset_of(std_neighbourhoods.MooreR2)
    # seems legit, now do the _actual_ yes/no test:
    if ActuallyNonExplosive(ca):
        return True
    else:
        return False

If and when there is a clear definition of nonexplosive cellular automaton (at least for the specific CA type discussed here), the answer(s) could arrive in the form of "boring ruletable(s)".

Currently, it appears to be unknown and not very well-understood even whether or not Conway's Life itself is "ActuallyNonExplosive". See the link:
viewtopic.php?p=164201#p164201

---
As for the terminology remark, I suggest to read for example this page:
https://web.archive.org/web/20230928182 ... ary_03.htm "Part 3 Banks' Proof of Universality in 2-dimensional, 5-neighborhood Cellular Automata"
It distinguishes between a rule (a transition rule, such as B3 or D4 using the existing shorthand notation) and a transition (a state-to-state transition, determined by states of a single cell in two consecutive generations).
The same distinction can be found in other CA-related sources.
The distinction also matches intuitive understanding. A transition happens (or doesn't happen). A rule tells/prescribes when a certain transition happens, but the rule itself doesn't in any way "happen", instead, the rule is simply sitting there in the definition of some particular cellular automaton of interest.

[hth3]

Is there a rule in which loafers are common or semi-common?

[confocaloid]

Is there a rule in which loafers are common or semi-common?

Multistate CA should be possible to engineer, in roughly the same way how people made "1-cell Sir Robin gun" and other similar patterns.
Multistate isotropic CA where soups made out of state-0 and state-1 cells often produce loafers is also probably possible.
Two-state isotropic CA with some higher-range neighbourhood and commonly-occurring loafers might be possible to calculate/engineer in some way.
Two-state isotropic CA with Moore neighbourhood, well, I can't really tell how plausible this is, or whether there is a way to calculate/engineer it instead of it being a lucky discovery.

[WhiteHawk]

Is there a CC reflector that can be used in B38/S238 to complete this p56 gun partial. I have hit a block with my personal attempts to rectify the streams.

Code: Select all

x = 232, y = 178, rule = B38/S238
65b3o4bo9bo$65bo6b3o5b3o$66bo8bo3bo$74b2o3b2o$85bo$83b3o$82bo$82b2o4$
69b2o$68bobo$68bo$67b2o19b2o$77b3o8b2o$77bo2bo$76bo2b2o$76b2o11b2o$87b
ob2o$80bo6bo$72b2o7b2o4bo$61b2o10bo6b2o5bo2bo$61bobo6b3o15b2o$61bo8bo
8$76b2o3bo12b2o$74bo6bo12bobo54b2o$73bo7bo14bo4b2o48b2o$73bo5b2o11b4o
b2o2bo2bo32bo$73b2o17bo2bobobobob2o32b3o$75b2o18bobobobo38bo9bob2o$64b
4o28b2obobo37b2o9bobo$59b2o7bo31bo50bo$59b2o2b2o3bo75bo6b2o$63b2o2bo18b
2o55bobo5b2o$87bo8bo46bo2bo4b2o$87bobo5b3o46b2o13b2o$66b2o20b2o4b5o59b
obo$63b2o2bo15b2o8b2o3b2o57b3o14bo$64bobo16bobo6b3o3b3o56b2o13b3o$64b
ob2o17bo7b2o3b2o60b2o9bo$63b2o3bo16b2o7b5o60b3o9b2o$65bob2o26b3o40b2o
$61b4o3bo4b3o20b3o38bobo9bobo15bo$60bo5b2o5bo2bo21b2o39bo10b2o7b2o6bo
$58bo2b2obobo5bo3bo21bo51bo8b2o4b3o$58b2obo4bo6bo2b2o21b3o$61bobobob2o
6bo25bo$61bobobobo5b2o$59b2ob2obobo4b3o10b2o25bo$60bo2b3o2b2o2b3o11b2o
25b2o34b2o13bo$60bo5bobo16bo26b2o35bobo10b2o$59b2ob5obo82bo11b2o$60bo
bo4bo83b2o$60bo3b3o$61b2obo84b4o21b3o$66b3o23b2o30b2o23bo2bo21bo$59b7o
2bo19b2o2b2o2b2o25bobo24bo14b2obo6bo$59bo2bo2bo22b2o2bo2bobo27bo21b3o
15b2ob3o$82bo11b3o50bo23bo$81b2o11b2o24bo44b2ob3o$80bo2bo36b2o44bobo$
80bobo6b2o28bo2bo6b2o21b2o2b3o7bobo$72b2o6bo2bo5bo2b2o26bobo5bo2bo24b
3o8bo$71bobo6bo2bo6bobo27b2o6bo27b2o$71bo9bobo5b2obo35bo26b2o$70b2o8b
3o5bo3b2o23b2o9bob2o23bo$88b2obo26bo11b2o$88bo3b4o19b3o$89b2o5bo18bo72b
3o$90bobob2o2bo30b2o57bo$90bo4bob2o30b2o25b2o31bo$88b2obobobo48b2o9bo
bo4b2o$63b2o24bobobobo49bo11bo4b2o$64bo24bobob2ob2o47bobo14b2o$64bobo
15b2o3b2o2b3o2bo49b2o14bo$65b2o15b2o4bobo5bo52b2o10bobo$88bob5ob2o51b
2o10bob2o$89bo4bobo54b3o$78bo11b3o3bo51b2o2bo$77b3o12bob2o37bo2bo2bo8b
2ob3o8b2o$76b2o2bo7b3o42b7o2bo6b2o11b2o$67b2o11b2o6bo2b7o42b3o7bo2b2o
$67b2o8b3ob2o8bo2bo2bo37b2obo12b3o48b3o$78bo2b2o51bo3b3o11bo49bo$77b3o
54bobo4bo61bo$66b2obo10b2o51b2ob5obo$67bobo10b2o52bo5bobo4b2o15b2o$68b
o14b2o49bo2b3o2b2o3b2o15bobo$67b2o14bobo47b2ob2obobo24bo$56b2o9b2o4bo
11bo49bobobobo24b2o$56bo2bo7b2o4bobo9b2o48bobobob2o80bo2b2o$42bo30b2o
25b2o30b2obo4bo81bo3b2o2b2o$42b3o11bo2bo40b2o30bo2b2obobo81bo7b2o$45b
o9bo2bo56bo18bo5b2o81b4o$44b2o9bobo55b3o19b4o3bo$56bo42b2o11bo26bob2o
$49bo25bo23b2obo9b2o23b2o3bo5b3o8b2o55b3o$48bobo5b2o16b2o26bo35bob2o5b
obo9bo56bo$48bo2bo4b2o15b2o27bo6b2o27bobo6bo2bo6bobo57bo$49b2o12bo8b3o
24bo2bo5bobo26b2o2bo5bo2bo6b2o63b2o$62bobo7b3o2b2o21b2o6bo2bo28b2o6bo
bo70bo2bo$62bobo44b2o36bo2bo69b2ob2o$60b3ob2o44bo24b2o11b2o72bo$59bo23b
o50b3o11bo77b2o$60b3ob2o15b3o21bo27bobo2bo2b2o22bo2bo2bo54bobo$43bo11b
o6bob2o14bo24bobo25b2o2b2o2b2o19bo2b7o56bo$43b2o11bo21bo2bo23b2o30b2o
23b3o63b2o$42bobo9b3o21b4o84bob2o40bo$164b3o3bo39b2o$78b2o83bo4bobo38b
obo$66b2o11bo82bob5ob2o$67b2o10bobo35b2o26bo16bobo5bo$66bo13b2o34b2o25b
2o11b3o2b2o2b3o2bo$118bo25b2o10b3o4bobob2ob2o$156b2o5bobobobo$129bo25b
o6b2obobobo$129b3o21b2o2bo6bo4bob2o$63b3o4b2o8bo51bo21bo3bo5bobob2o2b
o$63bo6b2o7b2o10bo39b2o21bo2bo5b2o5bo$29bo33bo15bobo9bobo38b3o20b3o4b
o3b4o$29b2o60b2o40b3o26b2obo$28bobo27b2o9b3o60b5o7b2o16bo3b2o$59bo9b2o
60b2o3b2o7bo17b2obo$56b3o13b2o56b3o3b3o6bobo16bobo$56bo14b3o57b2o3b2o
8b2o15bo2b2o$70bobo59b5o4b2o20b2o$70b2o13b2o46b3o5bobo$78b2o4bo2bo46b
o8bo$78b2o5bobo55b2o18bo2b2o$78b2o6bo75bo3b2o2b2o$79bo50bo31bo7b2o$78b
obo9b2o37bobob2o28b4o$77b2obo9bo38bobobobo18b2o$15bo75b3o32b2obobobob
o2bo17b2o$15b2o76bo32bo2bo2b2ob4o11b2o5bo$14bobo61b2o48b2o4bo14bo7bo$
78b2o54bobo12bo6bo$135b2o12bo3b2o8$160bo8bo$141b2o15b3o6bobo$bo138bo2b
o5b2o6bo10b2o$b2o140bo4b2o7b2o$obo140bo6bo$140b2obo$140b2o11b2o$150b2o
2bo$150bo2bo$141b2o8b3o$141b2o19b2o$162bo$160bobo$160b2o4$147b2o$148b
o$145b3o$145bo$150b2o3b2o$151bo3bo8bo$148b3o5b3o6bo$148bo9bo4b3o!

[confocaloid]

^^ In the event that you already have an overunity reaction that appears to be solvable except you need a colour-changing glider reflector to route some output streams back to the input streams, it should be possible to do without a colour-changing reflector, by putting two instances of the overunity reaction and connecting them to each other using colour-preserving reflectors.

[WhiteHawk]

Is there a CC reflector that can be used in B38/S238 to complete this p56 gun partial. I have hit a block with my personal attempts to rectify the streams.

Code: Select all

x = 232, y = 178, rule = B38/S238
65b3o4bo9bo$65bo6b3o5b3o$66bo8bo3bo$74b2o3b2o$85bo$83b3o$82bo$82b2o4$
69b2o$68bobo$68bo$67b2o19b2o$77b3o8b2o$77bo2bo$76bo2b2o$76b2o11b2o$87b
ob2o$80bo6bo$72b2o7b2o4bo$61b2o10bo6b2o5bo2bo$61bobo6b3o15b2o$61bo8bo
8$76b2o3bo12b2o$74bo6bo12bobo54b2o$73bo7bo14bo4b2o48b2o$73bo5b2o11b4o
b2o2bo2bo32bo$73b2o17bo2bobobobob2o32b3o$75b2o18bobobobo38bo9bob2o$64b
4o28b2obobo37b2o9bobo$59b2o7bo31bo50bo$59b2o2b2o3bo75bo6b2o$63b2o2bo18b
2o55bobo5b2o$87bo8bo46bo2bo4b2o$87bobo5b3o46b2o13b2o$66b2o20b2o4b5o59b
obo$63b2o2bo15b2o8b2o3b2o57b3o14bo$64bobo16bobo6b3o3b3o56b2o13b3o$64b
ob2o17bo7b2o3b2o60b2o9bo$63b2o3bo16b2o7b5o60b3o9b2o$65bob2o26b3o40b2o
$61b4o3bo4b3o20b3o38bobo9bobo15bo$60bo5b2o5bo2bo21b2o39bo10b2o7b2o6bo
$58bo2b2obobo5bo3bo21bo51bo8b2o4b3o$58b2obo4bo6bo2b2o21b3o$61bobobob2o
6bo25bo$61bobobobo5b2o$59b2ob2obobo4b3o10b2o25bo$60bo2b3o2b2o2b3o11b2o
25b2o34b2o13bo$60bo5bobo16bo26b2o35bobo10b2o$59b2ob5obo82bo11b2o$60bo
bo4bo83b2o$60bo3b3o$61b2obo84b4o21b3o$66b3o23b2o30b2o23bo2bo21bo$59b7o
2bo19b2o2b2o2b2o25bobo24bo14b2obo6bo$59bo2bo2bo22b2o2bo2bobo27bo21b3o
15b2ob3o$82bo11b3o50bo23bo$81b2o11b2o24bo44b2ob3o$80bo2bo36b2o44bobo$
80bobo6b2o28bo2bo6b2o21b2o2b3o7bobo$72b2o6bo2bo5bo2b2o26bobo5bo2bo24b
3o8bo$71bobo6bo2bo6bobo27b2o6bo27b2o$71bo9bobo5b2obo35bo26b2o$70b2o8b
3o5bo3b2o23b2o9bob2o23bo$88b2obo26bo11b2o$88bo3b4o19b3o$89b2o5bo18bo72b
3o$90bobob2o2bo30b2o57bo$90bo4bob2o30b2o25b2o31bo$88b2obobobo48b2o9bo
bo4b2o$63b2o24bobobobo49bo11bo4b2o$64bo24bobob2ob2o47bobo14b2o$64bobo
15b2o3b2o2b3o2bo49b2o14bo$65b2o15b2o4bobo5bo52b2o10bobo$88bob5ob2o51b
2o10bob2o$89bo4bobo54b3o$78bo11b3o3bo51b2o2bo$77b3o12bob2o37bo2bo2bo8b
2ob3o8b2o$76b2o2bo7b3o42b7o2bo6b2o11b2o$67b2o11b2o6bo2b7o42b3o7bo2b2o
$67b2o8b3ob2o8bo2bo2bo37b2obo12b3o48b3o$78bo2b2o51bo3b3o11bo49bo$77b3o
54bobo4bo61bo$66b2obo10b2o51b2ob5obo$67bobo10b2o52bo5bobo4b2o15b2o$68b
o14b2o49bo2b3o2b2o3b2o15bobo$67b2o14bobo47b2ob2obobo24bo$56b2o9b2o4bo
11bo49bobobobo24b2o$56bo2bo7b2o4bobo9b2o48bobobob2o80bo2b2o$42bo30b2o
25b2o30b2obo4bo81bo3b2o2b2o$42b3o11bo2bo40b2o30bo2b2obobo81bo7b2o$45b
o9bo2bo56bo18bo5b2o81b4o$44b2o9bobo55b3o19b4o3bo$56bo42b2o11bo26bob2o
$49bo25bo23b2obo9b2o23b2o3bo5b3o8b2o55b3o$48bobo5b2o16b2o26bo35bob2o5b
obo9bo56bo$48bo2bo4b2o15b2o27bo6b2o27bobo6bo2bo6bobo57bo$49b2o12bo8b3o
24bo2bo5bobo26b2o2bo5bo2bo6b2o63b2o$62bobo7b3o2b2o21b2o6bo2bo28b2o6bo
bo70bo2bo$62bobo44b2o36bo2bo69b2ob2o$60b3ob2o44bo24b2o11b2o72bo$59bo23b
o50b3o11bo77b2o$60b3ob2o15b3o21bo27bobo2bo2b2o22bo2bo2bo54bobo$43bo11b
o6bob2o14bo24bobo25b2o2b2o2b2o19bo2b7o56bo$43b2o11bo21bo2bo23b2o30b2o
23b3o63b2o$42bobo9b3o21b4o84bob2o40bo$164b3o3bo39b2o$78b2o83bo4bobo38b
obo$66b2o11bo82bob5ob2o$67b2o10bobo35b2o26bo16bobo5bo$66bo13b2o34b2o25b
2o11b3o2b2o2b3o2bo$118bo25b2o10b3o4bobob2ob2o$156b2o5bobobobo$129bo25b
o6b2obobobo$129b3o21b2o2bo6bo4bob2o$63b3o4b2o8bo51bo21bo3bo5bobob2o2b
o$63bo6b2o7b2o10bo39b2o21bo2bo5b2o5bo$29bo33bo15bobo9bobo38b3o20b3o4b
o3b4o$29b2o60b2o40b3o26b2obo$28bobo27b2o9b3o60b5o7b2o16bo3b2o$59bo9b2o
60b2o3b2o7bo17b2obo$56b3o13b2o56b3o3b3o6bobo16bobo$56bo14b3o57b2o3b2o
8b2o15bo2b2o$70bobo59b5o4b2o20b2o$70b2o13b2o46b3o5bobo$78b2o4bo2bo46b
o8bo$78b2o5bobo55b2o18bo2b2o$78b2o6bo75bo3b2o2b2o$79bo50bo31bo7b2o$78b
obo9b2o37bobob2o28b4o$77b2obo9bo38bobobobo18b2o$15bo75b3o32b2obobobob
o2bo17b2o$15b2o76bo32bo2bo2b2ob4o11b2o5bo$14bobo61b2o48b2o4bo14bo7bo$
78b2o54bobo12bo6bo$135b2o12bo3b2o8$160bo8bo$141b2o15b3o6bobo$bo138bo2b
o5b2o6bo10b2o$b2o140bo4b2o7b2o$obo140bo6bo$140b2obo$140b2o11b2o$150b2o
2bo$150bo2bo$141b2o8b3o$141b2o19b2o$162bo$160bobo$160b2o4$147b2o$148b
o$145b3o$145bo$150b2o3b2o$151bo3bo8bo$148b3o5b3o6bo$148bo9bo4b3o!

EDIT:

^^ In the event that you already have an overunity reaction that appears to be solvable except you need a colour-changing glider reflector to route some output streams back to the input streams, it should be possible to do without a colour-changing reflector, by putting two instances of the overunity reaction and connecting them to each other using colour-preserving reflectors.

I guess that's what I have now, except I am still struggling to match lane spacing and timing.

[confocaloid]

Code: Select all

x = 474, y = 257, rule = B38/S238
37b3o$37bo$38bo12$51b3o$51bo$52bo6$33b2o$33bobo$33bo4$65b3o4bo9bo$65bo
6b3o5b3o$66bo8bo3bo$74b2o3b2o$85bo$83b3o$82bo$82b2o$47b2o$47bobo$47bo$
69b2o$68bobo$68bo$67b2o19b2o$77b3o8b2o$77bo2bo$76bo2b2o$76b2o11b2o$87b
ob2o$80bo6bo$72b2o7b2o4bo$61b2o10bo6b2o5bo2bo$61bobo6b3o15b2o$61bo8bo
8$76b2o3bo12b2o$74bo6bo12bobo54b2o$73bo7bo14bo4b2o48b2o$73bo5b2o11b4ob
2o2bo2bo32bo$73b2o17bo2bobobobob2o32b3o$75b2o18bobobobo38bo9bob2o$64b
4o28b2obobo37b2o9bobo$59b2o7bo31bo50bo$59b2o2b2o3bo75bo6b2o$63b2o2bo
18b2o55bobo5b2o$87bo8bo46bo2bo4b2o$87bobo5b3o46b2o13b2o$66b2o20b2o4b5o
59bobo$63b2o2bo15b2o8b2o3b2o57b3o14bo$64bobo16bobo6b3o3b3o56b2o13b3o$
64bob2o17bo7b2o3b2o60b2o9bo$63b2o3bo16b2o7b5o60b3o9b2o$65bob2o26b3o40b
2o$61b4o3bo4b3o20b3o38bobo9bobo15bo$60bo5b2o5bo2bo21b2o39bo10b2o7b2o6b
o$58bo2b2obobo5bo3bo21bo51bo8b2o4b3o$58b2obo4bo6bo2b2o21b3o$61bobobob
2o6bo25bo$61bobobobo5b2o$59b2ob2obobo4b3o10b2o25bo$60bo2b3o2b2o2b3o11b
2o25b2o34b2o13bo$60bo5bobo16bo26b2o35bobo10b2o171b3o$59b2ob5obo82bo11b
2o172bo$60bobo4bo83b2o183bo$60bo3b3o$61b2obo84b4o21b3o$66b3o23b2o30b2o
23bo2bo21bo$59b7o2bo19b2o2b2o2b2o25bobo24bo14b2obo6bo$59bo2bo2bo22b2o
2bo2bobo27bo21b3o15b2ob3o$82bo11b3o50bo23bo$81b2o11b2o24bo44b2ob3o$80b
o2bo36b2o44bobo$80bobo6b2o28bo2bo6b2o21b2o2b3o7bobo$72b2o6bo2bo5bo2b2o
26bobo5bo2bo24b3o8bo140b2o2bo33bo$71bobo6bo2bo6bobo27b2o6bo27b2o146b2o
2b2o3bo32bobo$71bo9bobo5b2obo35bo26b2o147b2o7bo7b3o22b2o$70b2o8b3o5bo
3b2o23b2o9bob2o23bo153b4o10bo$88b2obo26bo11b2o190bo$88bo3b4o19b3o$89b
2o5bo18bo72b3o$90bobob2o2bo30b2o57bo124bo$90bo4bob2o30b2o25b2o31bo122b
obo$88b2obobobo48b2o9bobo4b2o147bo2bo$63b2o24bobobobo49bo11bo4b2o148b
2o$64bo24bobob2ob2o47bobo14b2o$64bobo15b2o3b2o2b3o2bo49b2o14bo$65b2o
15b2o4bobo5bo52b2o10bobo144b2o11bo$88bob5ob2o51b2o10bob2o142bobo10b2o
10bo$89bo4bobo54b3o153bo12bobo9bobo$78bo11b3o3bo51b2o2bo153b2o24b2o$
77b3o12bob2o37bo2bo2bo8b2ob3o8b2o$76b2o2bo7b3o42b7o2bo6b2o11b2o$67b2o
11b2o6bo2b7o42b3o7bo2b2o$67b2o8b3ob2o8bo2bo2bo37b2obo12b3o48b3o$78bo2b
2o51bo3b3o11bo49bo$77b3o54bobo4bo61bo122b2o$66b2obo10b2o51b2ob5obo176b
2o4bo2bo$67bobo10b2o52bo5bobo4b2o15b2o153b2o5bobo$68bo14b2o49bo2b3o2b
2o3b2o15bobo152b2o6bo$67b2o14bobo47b2ob2obobo24bo153bo$56b2o9b2o4bo11b
o49bobobobo24b2o151bobo9b2o$56bo2bo7b2o4bobo9b2o48bobobob2o175b2obo9bo
$42bo30b2o25b2o30b2obo4bo191b3o$42b3o11bo2bo40b2o30bo2b2obobo193bo50b
3o$45bo9bo2bo56bo18bo5b2o177b2o66bo$44b2o9bobo55b3o19b4o3bo176b2o65bo$
56bo42b2o11bo26bob2o$49bo25bo23b2obo9b2o23b2o3bo5b3o8b2o55b3o$48bobo5b
2o16b2o26bo35bob2o5bobo9bo56bo$48bo2bo4b2o15b2o27bo6b2o27bobo6bo2bo6bo
bo57bo$49b2o12bo8b3o24bo2bo5bobo26b2o2bo5bo2bo6b2o$62bobo7b3o2b2o21b2o
6bo2bo28b2o6bobo$62bobo44b2o36bo2bo$60b3ob2o44bo24b2o11b2o$59bo23bo50b
3o11bo$60b3ob2o15b3o21bo27bobo2bo2b2o22bo2bo2bo$43bo11bo6bob2o14bo24bo
bo25b2o2b2o2b2o19bo2b7o$43b2o11bo21bo2bo23b2o30b2o23b3o206b3o$42bobo9b
3o21b4o84bob2o203bo$164b3o3bo201bo$78b2o83bo4bobo185b2o$66b2o11bo82bob
5ob2o58b3o124bo$67b2o10bobo35b2o26bo16bobo5bo59bo124bo$66bo13b2o34b2o
25b2o11b3o2b2o2b3o2bo60bo123b5o14b2o$118bo25b2o10b3o4bobob2ob2o188bo
13bo$156b2o5bobobobo187b3o12bobo$129bo25bo6b2obobobo186bo15b2o$129b3o
21b2o2bo6bo4bob2o183b4o$63b3o4b2o8bo51bo21bo3bo5bobob2o2bo181b2o3bo3b
2o$63bo6b2o7b2o10bo39b2o21bo2bo5b2o5bo182bo2b3o4b2o$29bo33bo15bobo9bob
o38b3o20b3o4bo3b4o183b2obo12b3o$29b2o60b2o40b3o26b2obo190bo12bo$28bobo
27b2o9b3o60b5o7b2o16bo3b2o188b2o12bo40bo$59bo9b2o60b2o3b2o7bo17b2obo
243bo$56b3o13b2o56b3o3b3o6bobo16bobo243b3o$56bo14b3o57b2o3b2o8b2o15bo
2b2o76b3o117b2o$70bobo59b5o4b2o20b2o79bo120bo$70b2o13b2o46b3o5bobo101b
o116b3o$78b2o4bo2bo46bo8bo218bo6bo$78b2o5bobo55b2o18bo2b2o199b3o$78b2o
6bo75bo3b2o2b2o194bo$79bo50bo31bo7b2o194b2o$78bobo9b2o37bobob2o28b4o
223bo$77b2obo9bo38bobobobo18b2o234b3o$15bo75b3o32b2obobobobo2bo17b2o
225b3o7bo$15b2o76bo32bo2bo2b2ob4o11b2o5bo225bo8b2o$14bobo61b2o48b2o4bo
14bo7bo226bo12bo$78b2o54bobo12bo6bo239bo$135b2o12bo3b2o241b3o6b2o$258b
3o145bo$258bo147bobo$259bo147b2o$274b2o126b2o$274bo120b2o5bobo$276bo
118b2o7bo$256b2o14b5o127b2o$160bo8bo87bo13bo$141b2o15b3o6bobo87bobo12b
3o116bo$bo138bo2bo5b2o6bo10b2o88b2o15bo114bobob2o$b2o140bo4b2o7b2o113b
4o114bobobobo$obo140bo6bo116b2o3bo3b2o109b2obobobobo2bo$140b2obo123b2o
4b3o2bo108bo2bo2b2ob4o$140b2o11b2o105b3o12bob2o110b2o4bo$150b2o2bo107b
o12bo119bobo$150bo2bo107bo12b2o120b2o49b3o$141b2o8b3o295bo$141b2o19b2o
284bo$162bo103b2o$160bobo103bo$160b2o105b3o$183bo78bo6bo$181bobo78b3o$
182b2o81bo$147b2o115b2o$148bo$145b3o$145bo100b3o$150b2o3b2o91bo$151bo
3bo8bo82bo185b3o$148b3o5b3o6bo269bo$148bo9bo4b3o268bo$418b2o$419bo$
417bo$197bo219b5o14b2o$195bobo224bo13bo$196b2o221b3o12bobo$418bo15b2o$
418b4o$416b2o3bo3b2o$232b3o180bo2b3o4b2o$234bo180b2obo12b3o$178bo54bo
184bo12bo$179bo238b2o12bo38bobo$177b3o291b2o$472bo$426b2o$427bo$211bo
212b3o$209bobo212bo6bo$210b2o217b3o$428bo$428b2o2$218b3o$220bo224b3o$
192bo26bo225bo$193bo252bo10bobo$191b3o263b2o$206bo251bo$204b3o$203bo$
203b2o20bo$223bobo$197b2o25b2o226b2o$190b2o8b3o242b2o4bo2bo$190bo4bo4b
o2b2obo238bo2bo3bobo$188bobo7bo4b5o245bo$188b2o8bo2b4ob2o237bo2bo$193b
o3b2o5b2o238bo2bo9b2o$192bob2o3b2ob2o240bobo10bo$192bo6bobobo241bo12b
3o$191b2o267bo$200b3o242b2o$201b2o2bo239b2o$201b2obobo$200bobobobo$
197bo2bobobobob2o$197b4ob2o2bo2bo$201bo4b2o$199bobo$199b2o!

I solved one of remaining connections (using a pair of Snarks). On the right are shown three different composite 180-degree reflectors. In a p56 context, one of three connections can work where the other two will not work (56 is a multiple of 8, and 8 ticks is the smallest change when doing a trombone-slide adjustment). You can try combining reflectors in various ways to better understand the possibilities.

[WhiteHawk]

Code: Select all

I solved one of remaining connections (using a pair of Snarks). On the right are shown three different composite 180-degree reflectors. In a p56 context, one of three connections can work where the other two will not work (56 is a multiple of 8, and 8 ticks is the smallest change when doing a trombone-slide adjustment). You can try combining reflectors in various ways to better understand the possibilities.

Got it! The problem i had before was trying bumpers instead of snarks.

Code: Select all

x = 271, y = 224, rule = B38/S238
78b2o$77bobo$71b2o4bo$69bo2bo2b2ob4o$69b2obobobobo2bo$72bobobobo$72bo
bob2o$73bo2b2o$76b3o$86b2o$75bobobo6bo$75b2ob2o3b2obo$73b2o5b2o3bo$71b
2ob4o2bo$71b5o4bo$72bob2o2bo4bo$76b3o$80b2o2$74b2o$75bo$72b3o$72bo$85b
3o4bo9bo$85bo6b3o5b3o$59bo26bo8bo3bo$58bo35b2o3b2o$58b3o44bo$103b3o$102b
o$102b2o$67b2o$67bobo$67bo$89b2o$88bobo$88bo$87b2o19b2o$97b3o8b2o$45b
o51bo2bo$44bo51bo2b2o$44b3o49b2o11b2o$107bob2o$100bo6bo$92b2o7b2o4bo$
93bo6b2o5bo2bo$90b3o15b2o$90bo6$31bo51b2o$30bo53bo$30b3o51bobo9b2o3bo
12b2o$85b2o7bo6bo12bobo54b2o$93bo7bo14bo4b2o48b2o$13b2o78bo5b2o11b4ob
2o2bo2bo32bo$13bo79b2o17bo2bobobobob2o32b3o$14b3o78b2o18bobobobo38bo9b
ob2o$9bo6bo99b2obobo37b2o9bobo$9b3o75b2o31bo50bo$12bo73bobo75bo6b2o$11b
2o72b3o18b2o55bobo5b2o$85b2o20bo8bo46bo2bo4b2o$88b2o17bobo5b3o46b2o13b
2o$3b2o12bo69b3o18b2o4b5o59bobo$3bo12bo86b2o8b2o3b2o57b3o14bo$2obo12b
3o84bobo6b3o3b3o56b2o13b3o$o2b3o4b2o75b2o16bo7b2o3b2o60b2o9bo$b2o3bo3b
2o75b2o16b2o7b5o60b3o9b2o$3b4o108b3o40b2o$3bo15b2o72b3o20b3o38bobo9bo
bo15bo$4b3o12bobo71bo2bo21b2o39bo10b2o7b2o6bo$7bo13bo70bo3bo21bo51bo8b
2o4b3o$2b5o14b2o70bo2b2o21b3o$2bo92bo25bo$4bo88b2o$3b2o87b3o10b2o25bo
$19bo72b3o11b2o25b2o34b2o13bo$20bo84bo26b2o35bobo10b2o$18b3o150bo11b2o
$171b2o2$169b4o21b3o$112b2o30b2o23bo2bo21bo$108b2o2b2o2b2o25bobo24bo14b
2obo6bo$108b2o2bo2bobo27bo21b3o15b2ob3o$102bo11b3o50bo23bo$101b2o11b2o
24bo44b2ob3o$100bo2bo36b2o44bobo$100bobo6b2o28bo2bo6b2o21b2o2b3o7bobo
$92b2o6bo2bo5bo2b2o26bobo5bo2bo24b3o8bo$33bo57bobo6bo2bo6bobo27b2o6bo
27b2o$34bo56bo9bobo5b2obo35bo26b2o$32b3o55b2o8b3o5bo3b2o23b2o9bob2o23b
o$108b2obo26bo11b2o$108bo3b4o19b3o$109b2o5bo18bo72b3o$110bobob2o2bo30b
2o57bo$110bo4bob2o30b2o25b2o31bo$108b2obobobo48b2o9bobo4b2o$83b2o24bo
bobobo49bo11bo4b2o$84bo24bobob2ob2o47bobo14b2o$84bobo15b2o3b2o2b3o2bo
49b2o14bo$85b2o15b2o4bobo5bo52b2o10bobo$108bob5ob2o51b2o10bob2o$47bo61b
o4bobo54b3o$48bo49bo11b3o3bo51b2o2bo$46b3o48b3o12bob2o37bo2bo2bo8b2ob
3o8b2o$96b2o2bo7b3o42b7o2bo6b2o11b2o$87b2o11b2o6bo2b7o42b3o7bo2b2o$87b
2o8b3ob2o8bo2bo2bo37b2obo12b3o48b3o$98bo2b2o51bo3b3o11bo49bo$97b3o54b
obo4bo61bo$86b2obo10b2o51b2ob5obo$87bobo10b2o52bo5bobo4b2o15b2o$88bo14b
2o49bo2b3o2b2o3b2o15bobo$87b2o14bobo47b2ob2obobo24bo$87b2o4bo11bo49bo
bobobo24b2o$87b2o4bobo9b2o48bobobob2o$61bo31b2o25b2o30b2obo4bo$62bo57b
2o30bo2b2obobo$60b3o72bo18bo5b2o$133b3o19b4o3bo$119b2o11bo26bob2o$95b
o23b2obo9b2o23b2o3bo5b3o8b2o55b3o$94b2o26bo35bob2o5bobo9bo56bo$93b2o27b
o6b2o27bobo6bo2bo6bobo57bo$83bo8b3o24bo2bo5bobo26b2o2bo5bo2bo6b2o$82b
obo7b3o2b2o21b2o6bo2bo28b2o6bobo$82bobo44b2o36bo2bo$80b3ob2o44bo24b2o
11b2o$79bo23bo50b3o11bo$80b3ob2o15b3o21bo27bobo2bo2b2o22bo2bo2bo$75bo
6bob2o14bo24bobo25b2o2b2o2b2o19bo2b7o$76bo21bo2bo23b2o30b2o23b3o$74b3o
21b4o84bob2o$184b3o3bo$98b2o83bo4bobo$86b2o11bo82bob5ob2o58b3o$87b2o10b
obo35b2o26bo16bobo5bo59bo$86bo13b2o34b2o25b2o11b3o2b2o2b3o2bo60bo$138b
o25b2o10b3o4bobob2ob2o74b2o$176b2o5bobobobo76bo$149bo25bo6b2obobobo78b
o$149b3o21b2o2bo6bo4bob2o55b2o14b5o$83b3o4b2o8bo51bo21bo3bo5bobob2o2b
o56bo13bo$83bo6b2o7b2o10bo39b2o21bo2bo5b2o5bo58bobo12b3o$83bo15bobo9b
obo38b3o20b3o4bo3b4o60b2o15bo$111b2o40b3o26b2obo78b4o$78b2o9b3o60b5o7b
2o16bo3b2o71b2o3bo3b2o$79bo9b2o60b2o3b2o7bo17b2obo72b2o4b3o2bo$76b3o13b
2o56b3o3b3o6bobo16bobo65b3o12bob2o$76bo14b3o57b2o3b2o8b2o15bo2b2o66bo
12bo$90bobo59b5o4b2o20b2o68bo12b2o$90b2o13b2o46b3o5bobo$98b2o4bo2bo46b
o8bo$98b2o5bobo55b2o18bo2b2o70b2o$98b2o6bo75bo3b2o2b2o66bo$99bo50bo31b
o7b2o67b3o$98bobo9b2o37bobob2o28b4o67bo6bo$97b2obo9bo38bobobobo18b2o78b
3o$111b3o32b2obobobobo2bo17b2o79bo$113bo32bo2bo2b2ob4o11b2o5bo78b2o$98b
2o48b2o4bo14bo7bo$98b2o54bobo12bo6bo$155b2o12bo3b2o63b3o$240bo$239bo6$
180bo8bo$161b2o15b3o6bobo$160bo2bo5b2o6bo10b2o$163bo4b2o7b2o$163bo6bo
$160b2obo$160b2o11b2o49b3o$170b2o2bo51bo$170bo2bo51bo$161b2o8b3o$161b
2o19b2o$182bo$180bobo$180b2o$203bo$201bobo$202b2o$167b2o$168bo$165b3o
$165bo44b3o$170b2o3b2o35bo$171bo3bo8bo26bo$168b3o5b3o6bo$168bo9bo4b3o
$198bo$196b3o$195bo$195b2o20bo$215bobo$189b2o25b2o$192b3o$187bo4bo2b2o
bo$190bo4b5o$190bo2b4ob2o$185bo3b2o5b2o$184bob2o3b2ob2o$184bo6bobobo$
183b2o$192b3o$193b2o2bo$193b2obobo$192bobobobo32bo$189bo2bobobobob2o27b
obo$189b4ob2o2bo2bo28b2o$193bo4b2o$191bobo$191b2o!

[pifricted]

Is there any range-2 HROT weighted neighborhood rule which patterns made of 2x2 blocks could escape their bounding diamond, and singular cells would show up a completely different behavior (i.e. no trivial equivalents of Moore neighbourhood)?

Example:

Code: Select all

x = 24, y = 8, rule = /
2o$2o11bo4b4o$2b2o9b2o3b4o$2b2o6b6o4b4o$2b4o7b2o5b4o$2b4o7bo8b2o$6b2o
14b2o$6b2o!

This rule isn't equal to an moore rules, but it is range-3:

Code: Select all

x = 6, y = 6, rule = R3,C2,S4-5,B4-5,N@aa02a8154055
4o$4o$2o2b2o$2o2b2o$2b2o$2b2o!

[b-engine]

This rule isn't equal to an moore rules, but it is range-3:

I don't want the singular cells with spacings to emulate the exact rule.

Code: Select all

x = 5, y = 5, rule = R3,C2,S4-5,B4-5,N@aa02a8154055
obo2$o3bo2$2bo!

[pifricted]

I don't want the singular cells with spacings to emulate the exact rule.

Code: Select all

x = 5, y = 5, rule = R3,C2,S4-5,B4-5,N@aa02a8154055
obo2$o3bo2$2bo!

ok...

We must use R3 HROT to emulate "4x4" rule:

Code: Select all

x = 46, y = 10, rule = LifeHistory
FBFBFBFB2F2.10F2.10F2.2FBFBFBFBF$B2A2C2ACBF2.F8BF2.F8BF2.FBC2A2C2AB$F
2A2C2ACBF2.B2C2A2CABF2.FBA2C2A2CB2.FBC2A2C2AF$B2C2D2CABF2.F2A2C2ACBF2.
FBC2A2C2AF2.FBA2C2D2CB$F2CDE2CABF2.B2A2C2ACBF2.FBC2A2C2AB2.FBA2CED2CF
$B2A2C2ACBF2.F2CDE2CABF2.FBA2CED2CF2.FBC2A2C2AB$F2A2C2ACBF2.B2C2D2CAB
F2.FBA2C2D2CB2.FBC2A2C2AF$B2C2A2CABF2.F2A2C2ACBF2.FBC2A2C2AF2.FBA2C2A
2CB$F8BF2.B2A2C2ACBF2.FBC2A2C2AB2.F8BF$10F2.FBFBFBFB2F2.2FBFBFBFBF2.10F
!

(I will edit the post then)

[islptng]

A nice rule! Here's a P36 and a P8 I found in a soup:

Code: Select all

x = 45, y = 14, rule = R3,C2,S4-5,B4-5,N@aa02a8154055
2b6o31b4o$2b6o31b4o$2o6b2o29b4o$2o6b2o29b4o$2o6b2o29b4o$2o6b2o29b4o$2o
2b4o29b2o4b2o$2o2b4o29b2o4b2o$2b2o35b4o$2b2o35b4o$39b4o$39b4o$39b4o$39b
4o!

I prefer this equivalent when running soups:

Code: Select all

x = 1, y = 1, rule = R3,C0,S,B4-5,N@105155AA8A08
! [[ RANDOMIZE ]]

[b-engine]

Is there any range-2 HROT weighted neighborhood rule which patterns made of 2x2 blocks could escape their bounding diamond, and singular cells would show up a completely different behavior (i.e. no trivial equivalents of Moore neighbourhood)?

What I had asked for???

The emulated 2x2 rule isn't quite explosive, but would cause stripes and dots replicators to fill the world if a minor mistake is made:

Code: Select all

x = 6, y = 4, rule = B1c2a/S3a|B2c3ci4i5a/S5i6a7c:T120
4o$4o$4b2o$4b2o!

[confocaloid]

Is there a rule in which loafers are common or semi-common?

Here is a 14-bit parent of a phase of the loafer. However, it doesn't evolve into the loafer (the loafer doesn't exist in this CA):

Code: Select all

#C [[ GRID THEME Caterer SHOWGENSTATS ]]
x = 9, y = 8, rule = R1,C0,S0-3,7,10-11,15,B3,6,NW151505151
o2bo2bo$2bo5bo$5bobo$6bo$bo$b2o$3bo$2o!

Here is a 18-bit loafer predecessor, in a two-state isotropic cellular automaton where the loafer does exist:

Code: Select all

#C [[ GRID THEME Caterer SHOWGENSTATS  ]]
x = 9, y = 8, rule = R3,C0,S10-19,30-39,50-59,75-79,135-144,155-164,175-184,200-204,260-269,276,280-284,286-289,300-309,325-329,385-394,405-414,425-434,450-454,510-519,530-539,550-559,575-579,635-644,655-664,675-684,700-704,760-769,780-789,800-809,825-829,885-894,905-914,925-934,950-954,1010-1019,1030-1039,1050-1059,1075-1079,1135-1144,1155-1164,1175-1184,1200-1204,1260-1269,1280-1289,1300-1309,1325-1329,1385-1394,1405-1414,1425-1434,1450-1454,1510-1519,1530-1539,1550-1559,1575-1579,1635-1644,1655-1664,1675-1684,1700-1704,1760-1769,1780-1789,1800-1809,1825-1829,1885-1894,1905-1914,1925-1934,1950-1954,2010-2019,2030-2039,2050-2059,2075-2079,2135-2144,2155-2164,2175-2184,2200-2204,2260-2269,2280-2289,2300-2309,2325-2329,2385-2394,2405-2414,2425-2434,2450-2454,2510-2519,2530-2539,2550-2559,2575-2579,2635-2644,2655-2664,2675-2684,2700-2704,2760-2769,2780-2789,2800-2809,2825-2829,2885-2894,2905-2914,2925-2934,2950-2954,3010-3019,3030-3039,3050-3059,3075-3079,B15-19,35-39,55-59,75-79,140-144,160-161,163-164,180-184,200-204,265-269,285-289,305-309,325-329,385,390-394,410-414,430-434,450-454,515-519,535-539,555-559,575-579,640-644,660-664,680-684,700-704,765-769,785-789,805-809,825-829,890-894,910-914,930-934,950-954,1015-1019,1035-1039,1055-1059,1075-1079,1140-1144,1160-1164,1180-1184,1200-1204,1265-1269,1285-1289,1305-1309,1325-1329,1390-1394,1410-1414,1430-1434,1450-1454,1515-1519,1535-1539,1555-1559,1575-1579,1640-1644,1660-1664,1680-1684,1700-1704,1765-1769,1785-1789,1805-1809,1825-1829,1890-1894,1910-1914,1930-1934,1950-1954,2015-2019,2035-2039,2055-2059,2075-2079,2140-2144,2160-2164,2180-2184,2200-2204,2265-2269,2285-2289,2305-2309,2325-2329,2390-2394,2410-2414,2430-2434,2450-2454,2515-2519,2535-2539,2555-2559,2575-2579,2640-2644,2660-2664,2680-2684,2700-2704,2765-2769,2785-2789,2805-2809,2825-2829,2890-2894,2910-2914,2930-2934,2950-2954,3015-3019,3035-3039,3055-3059,3075-3079,NW007D7D7D7D7D007D7D0001007D7D7D00051905007D7D01190019017D7D00051905007D7D7D0001007D7D007D7D7D7D7D00
bo2bo3bo$b2o4b2o$4bob3o2$bo$obobo$3bo$bobo!

Questions:

• Can anyone find a lower-population predecessor of some phase of the loafer? The above example gives an upper bound of 14 alive cells.
• Can anyone find a lower-population predecessor of the loafer, in some two-state isotropic cellular automaton where the loafer exists? The above example gives an upper bound of 18 alive cells.

[hth3]

Is there a way to stabilize this agar in the specified rule or some close non-explosive relative of it?

Code: Select all

x = 145, y = 146, rule = B38/S23-c78
145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o$145o
$145o$145o$145o$145o$145o$145o!

[confocaloid]

Is there a way to stabilize this agar [...]

Code: Select all

x = 145, y = 146, rule = B38/S23-c78

If I understand correctly, then by "this agar" you mean the infinite universe completely filled with alive cells, all of which are surviving because of the S8 survival condition?

I don't know what are your restrictions on what a "close relative" can be.

Redefine using a fully-symmetric weighted neighbourhood

An interesting property of B38/S23-c78 is that the rules of this CA can be rewritten in terms of

• the current state of a cell (0 through 1),
• the number of currently-alive orthogonal neighbours of the cell (0 through 4),
• the number of currently-alive diagonal neighbours of the cell (0 through 4).

In other words, this cellular automaton can be equivalently defined using a fully-symmetric weighted neighbourhood:

Code: Select all

#C Weighted neighbourhood:
#C 1 5 1
#C 5 - 5
#C 1 5 1
x = 3, y = 3, rule = R1,C0,S2,6-7,10-11,15,19,23-24,B3,7,11,15,24,NW151505151
2o$b2o$bo!

This means it's possible to extend the neighbourhood, to include some additional information about the current condition of a cell.

Extend the neighbourhood

For example, it's possible to use the following weighted neighbourhood (note that the weights of neighbours are given in hexadecimal, '19' means 25, '7D' means 125):

Code: Select all

NW00000101010000000001010100000101197D19010101017D007D01010101197D1901010000010101000000000101010000
-- -- 01 01 01 -- --
-- -- 01 01 01 -- --
01 01 19 7D 19 01 01
01 01 7D -- 7D 01 01
01 01 19 7D 19 01 01
-- -- 01 01 01 -- --
-- -- 01 01 01 -- --

I think the following is an equivalent definition of the same cellular automaton, only using the above weighted neighbourhood:

Code: Select all

x = 73, y = 43, rule = R3,C0,S50-74,150-199,250-299,375-399,475-499,575-624,B75-99,175-199,275-299,375-399,600-624,NW00000101010000000001010100000101197D19010101017D007D01010101197D1901010000010101000000000101010000
2o$b2o$bo15$47b2ob2ob2ob2ob2ob2ob2ob2ob2o$47b2ob2ob2ob2ob2ob2ob2ob2ob
2o2$47b2ob20ob2o$47b2ob20ob2o$50b20o$47b2ob20ob2o$47b2ob20ob2o$50b20o$
47b2ob20ob2o$47b2ob20ob2o$50b20o$47b2ob20ob2o$47b2ob20ob2o$50b20o$47b
2ob20ob2o$47b2ob20ob2o$50b20o$47b2ob20ob2o$47b2ob20ob2o$50b20o$47b2ob
20ob2o$47b2ob20ob2o2$47b2ob2ob2ob2ob2ob2ob2ob2ob2o$47b2ob2ob2ob2ob2ob
2ob2ob2ob2o!

Tweak the rules of the cellular automaton

At this point, to make the shown patch of the agar into a still-life, it suffices to add survival conditions S441 and S443, which have the following meanings in this case:

• S441 is the following survival condition (note that 441 = 1 * 16 + 25 * 2 + 125 * 3):
  "The cell is currently alive, it has precisely 3 alive orthogonal neighbours, it has precisely 2 alive diagonal neighbours, and it has precisely 16 alive higher-range neighbours"
• S443 is the following survival condition (note that 443 = 1 * 18 + 25 * 2 + 125 * 3):
  "The cell is currently alive, it has precisely 3 alive orthogonal neighbours, it has precisely 2 alive diagonal neighbours, and it has precisely 18 alive higher-range neighbours"

Here is the resulting two-state isotropic cellular automaton:

Code: Select all

#C [[ GRID THEME MCell ]]
x = 73, y = 43, rule = R3,C0,S50-74,150-199,250-299,375-399,441,443,475-499,575-624,B75-99,175-199,275-299,375-399,600-624,NW00000101010000000001010100000101197D19010101017D007D01010101197D1901010000010101000000000101010000
2o$b2o$bo15$47b2ob2ob2ob2ob2ob2ob2ob2ob2o$47b2ob2ob2ob2ob2ob2ob2ob2ob
2o2$47b2ob20ob2o$47b2ob20ob2o$50b20o$47b2ob20ob2o$47b2ob20ob2o$50b20o$
47b2ob20ob2o$47b2ob20ob2o$50b20o$47b2ob20ob2o$47b2ob20ob2o$50b20o$47b
2ob20ob2o$47b2ob20ob2o$50b20o$47b2ob20ob2o$47b2ob20ob2o$50b20o$47b2ob
20ob2o$47b2ob20ob2o2$47b2ob2ob2ob2ob2ob2ob2ob2ob2o$47b2ob2ob2ob2ob2ob
2ob2ob2ob2o!

[WhiteHawk]

How likely is it that Day and Night is omniperiodic?

EDIT: Bad phrasing of question. Different question: how close is D&N to omniperiodicity?

[confocaloid]

(for the first question:) 50/50, either it is, or it isn't.

(for second question:) "how close" isn't a clear question that can be answered. You didn't tell how to measure closeness.

However, the first step might be to look for which periods there are known oscillators. The wiki page gives examples of nontrivial oscillators of periods up to 16

Code: Select all

x = 176, y = 12, rule = B3678/S34678
o28b2o9b2o55bo77bo$2o5b4o7bo8b4o9b2o10bobo20b2o5b2o11bob3o9bo2bo9bobo
7b2o9b3o28b2o$bo6b2o7b3o7b6o6b5o7b6o6b5o6b3o5b3o10b5o9b3obo9bo8b2o10b
2o28b2o$8b2o8bo10b4o7b4o7b6o7b3o7b2o7b2o6b2o2b4o10b5o8bo11bo9bo3bo7b2o
b2o4b2o$8b2o18bob2o9bo9bo2b2o23bo11b9o8b5o8b2ob2o9b2o11b2o6b4o3b4o$7b
4o19b2o22b3o21b3o11b4o2b2o7b5o12bo10b2o11b2o7b9o$53b3o9bo11b5o10b2o12b
5o12bo32b4o3b4o$63b2o13b3o25bob3o11bobo31b2o4b2ob2o$65bo13bo27bo2bo$
63bo10b2o7b2o$64b2o8b3o5b3o$63bo11b2o5b2o!

At least periods 18, 19, 20, 23, 24, 36 are also covered by known nontrivial oscillators:

Code: Select all

x = 69, y = 126, rule = B3678/S34678
bo2b3o20b2o$2o2bobo16bob6o$bo2b3o15bob7o$bo2bobo15b10o$3ob3o16b9o$21b
10o$24b7o$23b7o$22bobob3obo$22b2o2bob2o$26bo10$bo2b3o14bo15bo$2o2bobo
13b3o13b3o$bo2b3o14bo7bo7bo$bo4bo19b7o$3ob3o20b5o$25b9o$23bob9obo$23b
13o$23b13o$22b15o$23b13o$23b13o$23bob9obo$25b9o$27b5o$26b7o$21bo7bo7bo
$20b3o13b3o$21bo15bo12$3ob3o$2bobobo14b3o2b3o$3obobo15b2o2b2o$o3bobo$
3ob3o16bo2bo$23b4o15$3ob3o16b3ob2ob3o19b3ob2o2b2ob3o$2bo3bo15bob8obo
17bob5o2b5obo$3ob3o15b12o17b16o$o5bo16b10o19b14o$3ob3o16b10o19b14o$22b
12o17b16o$20b16o13b20o$21b14o15b18o$20b6ob2ob6o13b20o$20b4o8b4o13b9o2b
9o$20b4o8b4o13b9o2b9o$20b6ob2ob6o13b20o$21b14o15b18o$20b16o13b20o$22b
12o17b16o$23b10o19b14o$23b10o19b14o$22b12o17b16o$22bob8obo17bob5o2b5ob
o$23b3ob2ob3o19b3ob2o2b2ob3o10$42b2obo$3obobo16bo18bob3o$2bobobo14b4o
17b6o$3ob3o13b2o2bo14b9o$o5bo14bo2b2o13bob9o$3o3bo14b4o15b11o$22bo16b
13o$40b11o$41b9obo$43b9o$43b6o$44b3obo$45bob2o9$3ob3o$2bobo16bo$3ob3o
15b2o$2bobobo15bob2o$3ob3o16b3o$23b2o!

How likely is it that Day and Night is omniperiodic?

EDIT: Bad phrasing of question. Different question: how close is D&N to omniperiodicity?

[wildmyron]

Is there a way to stabilize this agar in the specified rule or some close non-explosive relative of it?

Code: Select all

x = 145, y = 146, rule = B38/S23-c78
<snip solid filled rectangular area>

I tried a few searches in LLS and I'm confident it's not possible to stabilise the solid agar in the rule you specified - presumably because there aren't any survival conditions with 4,5, or 6 live neighbours to support live cells on the boundary. This is the closest I could find in the range 2 INT rulespace on the Moore neighbourhood (an explosive rule):

Code: Select all

x = 18, y = 16, rule = B3-q8/S23-c4a78
2o14b2o$o2b2o8b2o2bo$2b2o10b2o$5b2ob2ob2o$4b10o$4b10o$5b8o$4b10o$4b10o
$5b8o$4b10o$4b10o$5b2ob2ob2o$2b2o10b2o$o2b2o8b2o2bo$2o14b2o!

It's possible to easily make that non-explosive by removing birth conditions, but I suspect you'd consider that uninteresting. Here's the same stabilised agar in a nearby rule which isn't explosive but probably still interesting.

Code: Select all

x = 18, y = 16, rule = B3-q8/S23-ac4a78
2o14b2o$o2b2o8b2o2bo$2b2o10b2o$5b2ob2ob2o$4b10o$4b10o$5b8o$4b10o$4b10o
$5b8o$4b10o$4b10o$5b2ob2ob2o$2b2o10b2o$o2b2o8b2o2bo$2o14b2o!

In terms of rule closeness - confocaloid's range 2 rule could be considered closer within the space of range 2 rules on the Moore neighbourhood. However, the step from range 1 rules to range 2 rules might be a bigger step in closeness relative to a changes in a small subset of birth and survival conditions - depending on personal point of view / definition of closeness.

I acknowledge there's some imprecise use of terminology in previous paragraph, hopefully the meaning is clear.

[LittleLWSS]

Title. Golly currently don't accept isotropic Hexagonal rule.

[confocaloid]

Title. Golly currently don't accept isotropic Hexagonal rule.

This is a basic question, it doesn't need its own thread. Please don't make a new thread for every question.

I suggest to read the linked thread: viewtopic.php?p=193449#p193449

[...]
Paul Callahan's notation: Paul Callahan came up with a notation for six neighbor hexagonal neighborhoods. If you haven't already, be sure to read his article here:
http://www.radicaleye.com/lifepage/hexrule.txt and download this zip file: http://ruletablerepository.googlecode.c ... oS2m34.zip
As Callahan points out, his notation only covers the case of two neighbors. A good project would be to extend his notation to cover three and four neighbors (five and six neighbors don't need a notation, as there is only one configuration for each, in isotropic rules.)
[...]

The current rulestring notation for isotropic cellular automata with the honeycomb neighbourhood is a result of contributions by several people. This forum post is an attempt to give a summary.

According to Paul Callahan's 1997 write-up (which is also available as a forum thread with viewable patterns), the original notation only allowed to distinguish between different configurations of precisely two live neighbours, and the mnemonic "ortho/meta/para" for the three possibilities was suggested by Rich Schroeppel and Achim Flammenkamp.

In March 2014, "EricG" on these forums posted an extension of the notation, allowing to distinguish between different configurations of three or four live neighbours, while still using only three letters "o", "m", "p".
In September 2017, the same way of extending the notation was posted by "_zM", likely independently.


echnotation.png

[...] Taking symmetries
into account, there are three ways each of getting 2, 3, and 4 neighbors,
for a total of 13 different neighborhoods. I tried a lot of variations, but
the one I settled on only distinguishes between different ways of getting two
neighbors. For these, one can use the organic chemists' naming convention
for benzene-ring disubstitutions: ortho, meta, and para. Rich Schroeppel and
Achim Flammenkamp suggested this, and it may be a useful mnemonic for some
people. It has the disadvantage that there is no standard extension to
subsets of 3 or 4 neighbors. Fortunately, we don't need this for the rule
used here. So let's call these neighborhoods 2o, 2m, and 2p
as follows:

Code: Select all

       O O            O .            O .
 2o:  . x .     2m:  . x O     2p:  . x .
       . .            . .            . O

Extending the birth/survival convention used above, the rule is B2o/S2m34.

That is, we always have survival but not birth on 3 or 4 neighbors. On
two neighbors we have birth but not survival if the neighbors are adjacent (2o),
and survival but not birth if there is one empty neighbor cell in between (2m).
If they are opposite each other (2p), there is no birth or survival (which
is also the case for 0, 1, 5, or 6 neighbors).
[...]

[WhiteHawk]

EDIT: Pedestrian Life synth based on vilc's synthesis completion costing 29 gliders (probably reducible).

Code: Select all

x = 426, y = 31, rule = B38/S23
271bo$269b2o$270b2o2$bo12bo316bo$2bo10bo315b2o$3o10b3o131bo120bobo2bo
bo54b2o$146bo4bobo72b2o41b2o2b2o51b2o34b2o51b2o$53b2o38b2o38b2o11b3o2b
2o30b2o41bobo40bo4bo50bo2bo33bobo50bobo$18b2o33bobo2b2o33bobo37bobo16b
o30bobo42bo34b2o49b2o10b2o36bo4b2o46bo4b2o$2o16bobo34bo3bo35bo39bo49b
o38b4ob2o3b2o27bobo48bobo43b4ob2o2bo2bo40b4ob2o2bo2bo$b2o15bo32b4ob3o
3b2o27b4ob2o33b4ob2o43b4ob2o36bo2bobobobobo29bo50bo4b2o37bo2bobobobob
2o40bo2bobobobob2o$o50bo2bobo5bobo26bo2bobo34bo2bobobo6b2o34bo2bobobo
b2o35bobobobo27b4ob2o3b2o39b4ob2o2bo2bo38bobobobo46bobobobo$6b2o4b2o40b
obo5bo31bobo37bobobo5b2o38bobobobo37b2obobo27bo2bobobobobo39bo2bobobo
bob2o39b2obobo47b2obobo$7b2o2b2o42bo39bo3bo4b2o29b2ob2o6bo38b2obobo41b
o31bobobobo44bobobobo46bo52bo$6bo6bo85b2o2b2o84bo5bo69b2obobo45b2obob
o$98bobo4bo89bobo71bo50bo$148b2o45b2o83b2o81b2o51b2o$147b2o131bobo80b
2o51b2o$149bo75b2o37b2o5b3o6bo34b2o$192b3o3b3o23bobo37b2o7bo41b2o$194b
o3bo27bo45bo139bo$193bo5bo31b2o170b2o5bobo$231bobo130bo39b2o5b2o2b2o$
231bo130bobo38bo12b2o$363b2o50bo$419b2o$419bo$365b2o53b3o$366b2o54bo$
365bo!

Is there a way to potentially reduce the 29g Snark synthesis in Pedestrian Life using soups like this one? Remaining steps would only cost 18g.

Code: Select all

x = 16, y = 16, rule = B38/S23
b2o3b3o5b2o$2bob3o2bo2bo2bo$3b2o3bob2o2bo$5o3b3o2bobo$2b5ob3obob2o$4b
o4bo2bob2o$bo2b2o5bobo$o3b4obob5o$bo4bo2bobo2b2o$9bo2b2o$b4ob2ob2obob
o$ob2o2bo3b3o$2obo2bobob3o2bo$6b2obobob3o$obobo3bob2o2b2o$o2bob2o2bob
o3bo!

Bad seed

Code: Select all

x = 27, y = 15, rule = B38/S23
20bo$19bo2bo$22b2o$22b2obo$24b3o$25b2o$22b4o$2b2o16b2o2bo$2b2o17b3o$o
5bo15bo$2o4bo$2obo2bo$bo3bo$2b3o$3bo!

EDIT: This soup is better

Code: Select all

x = 16, y = 16, rule = B38/S23
3ob3o4bob2o$3b4o5b3o$bo5b2ob2o3bo$3o2b2o2bob2o2bo$2b2ob3o3bo2b2o$2obo
2b2o6b2o$o2b3ob4o2b3o$5b2o2bobobobo$4bobo$obobo3bobo3b2o$bo3bob4o4bo$
bob3ob2ob2obo$3bo5bo$4b2o2bob2o2bo$2ob3obo2b2obobo$bo2b4obobo2bo!

Isolated seed.

Code: Select all

x = 28, y = 15, rule = B38/S23
2bo$obo$b2o18b2o3b2o$20bo2bo2b2o$20bobo$12b2o7bo$12b2o$11bo$13b3o$12b
o2bo$12b2obo4bo$11bo8bo$11bo3bo2bo$10bo$11bob2o!

EDIT 2:

Different seed from different soup (Blinker is clean-up from soup)

Code: Select all

x = 22, y = 24, rule = B38/S23
2b3o3$14bo$15b2o$14b2o$20b2o$b2o17b2o$o2bo$o2bo$b2o4$7b3o$7bo$7b3o2$17b
o$16bobo$16bobo$17bo$5b2o$5b2o!

EDIT 3:
Similar to second soup, very simple seed

Code: Select all

x = 32, y = 31, rule = B38/S23
bo3bo3b4ob4ob4o3bo3bo$5ob2o2bo10bo2b2ob5o$5bob2o2bobo4bobo2b2obo$2obo
3bo2bobobo2bobobo2bo3bob2o$b9o2bob4obo2b9o$2obo2b2obobobob2obobobob2o
2bob2o$2b3obob2o3b2o2b2o3b2obob3o$o3b2obobo2bob4obo2bobob2o3bo$o4bo2b
2o3b6o3b2o2bo4bo$2bo2b2o2bo3b6o3bo2b2o2bo$3o2bo3b2obob4obob2o3bo2b3o$
3bo3bo3b10o3bo3bo$4obobob3o3b2o3b3obobob4o$b2obobo2bobo3b2o3bobo2bobo
b2o$bo2b2obob2o2b6o2b2obob2o2bo$3bo3bo2bo10bo2bo3bo$bo2b2obob2o2b6o2b
2obob2o2bo$b2obobo2bobo3b2o3bobo2bobob2o$4obobob3o3b2o3b3obobob4o$3bo
3bo3b10o3bo3bo$3o2bo3b2obob4obob2o3bo2b3o$2bo2b2o2bo3b6o3bo2b2o2bo$o4b
o2b2o3b6o3b2o2bo4bo$o3b2obobo2bob4obo2bobob2o3bo$2b3obob2o3b2o2b2o3b2o
bob3o$2obo2b2obobobob2obobobob2o2bob2o$b9o2bob4obo2b9o$2obo3bo2bobobo
2bobobo2bo3bob2o$5bob2o2bobo4bobo2b2obo$5ob2o2bo10bo2b2ob5o$bo3bo3b4o
b4ob4o3bo3bo!

Code: Select all

x = 16, y = 13, rule = B38/S23
9b2o3b2o$8bo2bo2b2o$8bobo$9bo2$2bo2b3o$bobob2o$o4bo2bo$6b3o2bo$7bo$7b
2ob2o$9bo$7b2o!

EDIT 4:
One more bad seed

Code: Select all

x = 27, y = 26, rule = B38/S23
21b2o$21b2o7$22b3o$22bobo$22bo2bo$23bobo$15b2o6b3o$9bo4bo2bo$8bobo4b2o
$8b2o5$b2o$o2bo3b2o$b2o4b2o2$25b2o$25b2o!