UPMF: a case study in combinatorial mice theory

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confocaloid
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UPMF: a case study in combinatorial mice theory

Post by confocaloid »

Here is a small pattern collection in UPMF. With the exception of the p12 orthogonal c/4 spaceship and the c/4d p4 glider, all other spaceships (p2 orthogonal c/2, p3 orthogonal c/3, p4 orthogonal c/4, p5 orthogonal c/5, p5 orthogonal 2c/5) were found using qfind. The three oscillators are p5, p8, p12.

Code: Select all

#C [[ GRID THEME MCell ]]
x = 223, y = 81, rule = B35-enr7e/S234ce8
134b3o5b3o$133bo2bo5bo2bo$136b3ob3o$138bobo$133bo4bobo4bo$134bo2bo3bo
2bo9$3b3o4b3o8b3o3b3o13bo12bo11bo27b3o12b3o17b3o8bo8bo19bo21b2o3b2o12b
o4bo$2bo3bo2bo3bo6bo3bobo3bo11bobo10bobo9bobo11b3o12b3o12b3o18bo8b3o6b
3o17bobo19bob2ob2obo10b3o2b3o$2bobobo2bobobo6bobobobobobo10bo3bo8bo3bo
7bo3bo10b3o12bobo12bobo27b2obo4bob2o16bobobo17bob2o3b2obo8b10o$42b2obo
8bob2o22bo3bo8b2ob3ob2o6b2ob3ob2o26bo6bo18b5o16bo2bo5bo2bo5b2o3b4o3b2o
$3bob2o2b2obo8bob2ob2obo15b2o6b2o9b4ob4o6bo5bo7bo7bo6bo7bo14b3o35b5o
16bo2bo5bo2bo5b2o3bo2bo3b2o$3bob2o2b2obo8bob2ob2obo16b2o4b2o9b2o3bo3b
2o4b2o5b2o6bo7bo6bo7bo26bo6bo19bobo18bobo5bobo7b2ob2o2b2ob2o$2b2obob2o
bob2o6b2o2bobo2b2o13bob3o2b3obo7b2o7b2o7b3o9b2o2bo2b2o6b2o2bo2b2o12bo
5bo7bobo2bobo19bobo19b3o3b3o9b4o2b4o$bo12bo9bobo17bo2bo4bo2bo8b3obob3o
5b2ob3ob2o7bobobobo8bobobobo13bob3obo7bob4obo15bob2obob2obo15b3o3b3o9b
ob6obo$b2obo6bob2o5bo3bobo3bo14bo8bo10bo2bo2bo6bobo3bobo7bo5bo8bo5bo
12bo2b3o2bo6bo2b2o2bo14bo2b2obob2o2bo13bobo5bobo7bo3bo2bo3bo$b3o8b3o7b
obobobo15b2o2bo2bo2b2o9b2o3b2o23b5o10b5o27b2obo2bob2o13bo2bo5bo2bo14b
2o5b2o9b2ob4ob2o$2o12b2o29bobo4bobo11b5o7bo7bo55bobo4bobo17bo3bo18b3o
3b3o9b3ob2ob3o$45b2o6b2o11bobobo9bo3bo10bo3bo10bo3bo26b3o6b3o16b2ob2o
34b3ob2o2b2ob3o$45bo8bo27bo11bo5bo8bo5bo25b3o2b2o2b3o13bo2b2ob2o2bo14b
o2bo3bo2bo5bo2bob2o2b2obo2bo$43b2o10b2o10bobo11bobo10b3ob3o8b3ob3o30b
2o18bobo5bobo14bo9bo5bo4bo4bo4bo$42b2o2b2o4b2o2b2o22bobobo10b5o10b5o
27bobo4bobo12b2o3bo3bo3b2o13bo7bo$44bo3bo2bo3bo25b3o11bo3bo10bo3bo27bo
bo4bobo12b2o4bobo4b2o12bobo5bobo9bobo2bobo$44b2o2bo2bo2b2o24b2ob2o55b
2o2b2o2b2o2b2o11b6ob6o15b3ob3o9bo10bo$42b2o4b4o4b2o37bobobo10bobobo25b
2o10b2o12b2o7b2o15bo2bobo2bo9bo2bo2bo2bo$41b2o2bo3b2o3bo2b2o22bobo13bo
14bo28b2o8b2o14bo7bo18b2ob2o14b4o$45bo8bo27bo14bo14bo28b2o2bo2bo2b2o
39b3o3b3o10bo2b2o2bo$3b3o4b3o8b3o3b3o11b2o14b2o36bo3bo10bo3bo29b2o2b2o
17b2obobob2o16b3o3b3o13b2o$2bo3bo2bo3bo6bo3bobo3bo10bobo12bobo21bobobo
10b5o10b5o31b2o18b3obobob3o34bo2b2o2bo$2bobobo2bobobo6bobobobobobo13bo
10bo26bo59bo2b4o2bo13b2o9b2o34b6o$41bo3bo8bo3bo20bo2bo2bo9b2ob2o10b2ob
2o26b2o3b2o3b2o12b2o9b2o$3bob2o2b2obo8bob2ob2obo13bobo8bobo21bobo3bobo
7bobobobo8bobobobo25b2o8b2o$3bob2o2b2obo8bob2ob2obo14bo10bo21bo4bo4bo
5bo7bo6bo7bo23b2obo6bob2o$2b2obob2obob2o6b2o2bobo2b2o13b2o8b2o22b2obob
ob2o5bo3bobo3bo4bo3bobo3bo25bo2b2o2bo$bo3bo4bo3bo9bobo65bobo5bobo4bobo
5bobo25b3o2b3o$b2ob3o2b3ob2o5bo3bobo3bo62bo7bo6bo7bo26bobo2bobo$b3ob2o
2b2ob3o8b2ob2o64b2o7b2o4b2o7b2o25bobo2bobo$2o12b2o7b2ob2o$107b2o7b2o
28b2o$107bobo5bobo24b2o2b2o2b2o$110bo3bo27b2o6b2o$107bo3bobo3bo26bo4bo
$109bobobobo25b2o8b2o$110bo3bo25bo12bo$110b2ob2o25b2o10b2o16$39b2o$18b
o2bo16b4o$39b2o16bo$16bo6bo33bo$17b6o15bo2bo15bo20bo$14bo2bo4bo2bo8bo
2bo4bo2bo11bo21bo$17bo4bo10b3o3b2o3b3o8b2o20b3o$17bo4bo10b3o3b2o3b3o
10bo$14bo2bo4bo2bo8bo2bo4bo2bo11bo$17b6o15bo2bo15bo$16bo6bo33bo$39b2o$
18bo2bo16b4o$39b2o!
UPMF stands for "undergrounded pseudomice force" which is my name for this two-state isotropic cellular automaton with range-1 Moore neighbourhood. The definition of UPMF (B35-enr7e/S234ce8) can be golfed from the definition of PseudoLife (B357/S238) as follows:
  • remove the birth conditions B5e, B5n, B5r ("undergrounded"),
  • in the birth conditions, leave only the subcondition B7e instead of the full B7 ("pseudomice"),
  • add the survival conditions S4c, S4e ("force").
I'm unsure how interesting or noteworthy this specific cellular automaton is in particular, but evidently there are people in the local community interested in combinatorial mice theory (CMT) in general, so I figured out it might be a good idea to make a dedicated discussion thread for the topic. Feel free to share your insights in CMT

Linking previous discussion
tommyaweosme wrote: February 17th, 2025, 10:44 pmmice theory
unname4798 wrote: February 18th, 2025, 7:37 ammice theory
LuveelVoom wrote: February 18th, 2025, 12:45 pmmice theory
confocaloid wrote: February 18th, 2025, 8:51 pmmice theory
islptng wrote: February 19th, 2025, 1:37 ammice theory
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
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tommyaweosme
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Joined: January 15th, 2024, 9:37 am

Re: UPMF: a case study in combinatorial mice theory

Post by tommyaweosme »

and to think this all started with a funni thingy i made

anyway, some more mice theory for you:

antilife b0123478/s01234678
life b3/s23
anti b012478/s014678

snowlife b3/s1237
life b3/s23
snow b/s127

snow with mice b7/s127

ironlife b36/s238
life b3/s23
iron b6/s8

ironsnow with mice b67/s1278

lowflockdeath b368/s128
flock b3/s12
low death b68/s8
lowdeath b368/s238
life b3/s23
lowlifedeath b368/s23
therefore " " when used without syntax reasoning is removal of life

ironsnowlife with mice b367/s12378

"without death" has two meanings

here is its second:
life without death b3/s012345678
life b3/s23
without death b/s0145678

2x2 2 b3678/s1258
2x2 b36/s125
2 b678/s8


this post has culminated into...
ironsnowlife with mice 2 b3678/s12378
here's the gosper glider gun

Code: Select all

#R life
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o!
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confocaloid
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Joined: February 8th, 2022, 3:15 pm
Location: learn to protect yourself against stray gliders and sparks and self-destruct mechanisms

Re: UPMF: a case study in combinatorial mice theory

Post by confocaloid »

Currently apgsearching UPMF, here are some more objects. A spaceship (p17 diagonal c/17) and oscillators (p12, p22, p76):

Code: Select all

x = 93, y = 17, rule = B35-enr7e/S234ce8
79bo7bo$79bo7bo$76bo2b2o5b2o2bo$74bo3b2o7b2o3bo$b2o50bo4bo15bo3b2o7b2o
3bo$o27bo5bo18b2o2b2o$o2bo23b3o3b3o18bo2bo18b2o11b2o$o3bo23bo5bo$4bo$
2b2obo22bo5bo19bo2bo$5bo21b3o3b3o17b2o2b2o17b2o11b2o$28bo5bo18bo4bo$
74bo3b2o7b2o3bo$74bo3b2o7b2o3bo$76bo2b2o5b2o2bo$79bo7bo$79bo7bo!
There are some visible sparks, a rake or a gun might be possible?

edit: here is a p32760 "blockchain" pulse oscillator:

Code: Select all

x = 103, y = 4, rule = B35-enr7e/S234ce8
100bobo$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3obobo$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
obo$100bobo!
Here is an updated pattern collection with more objects from b35-enr7es234ce8:

Code: Select all

x = 300, y = 261, rule = B35-enr7e/S234ce8
196b3o5b3o$195bo2bo5bo2bo$198b3ob3o$200bobo$195bo4bobo4bo86bo$196bo2bo
3bo2bo87bob2o$295bo$295bo3bo$296bo2bo$299bo$297b2o4$65b3o4b3o8b3o3b3o
13bo12bo11bo27b3o12b3o17b3o8bo8bo19bo21b2o3b2o12bo4bo$64bo3bo2bo3bo6bo
3bobo3bo11bobo10bobo9bobo11b3o12b3o12b3o18bo8b3o6b3o17bobo19bob2ob2obo
10b3o2b3o$64bobobo2bobobo6bobobobobobo10bo3bo8bo3bo7bo3bo10b3o12bobo
12bobo27b2obo4bob2o16bobobo17bob2o3b2obo8b10o$104b2obo8bob2o22bo3bo8b
2ob3ob2o6b2ob3ob2o26bo6bo18b5o16bo2bo5bo2bo5b2o3b4o3b2o$65bob2o2b2obo
8bob2ob2obo15b2o6b2o9b4ob4o6bo5bo7bo7bo6bo7bo14b3o35b5o16bo2bo5bo2bo5b
2o3bo2bo3b2o14bo$65bob2o2b2obo8bob2ob2obo16b2o4b2o9b2o3bo3b2o4b2o5b2o
6bo7bo6bo7bo26bo6bo19bobo18bobo5bobo7b2ob2o2b2ob2o16bo$64b2obob2obob2o
6b2o2bobo2b2o13bob3o2b3obo7b2o7b2o7b3o9b2o2bo2b2o6b2o2bo2b2o12bo5bo7bo
bo2bobo19bobo19b3o3b3o9b4o2b4o15b3o$63bo12bo9bobo17bo2bo4bo2bo8b3obob
3o5b2ob3ob2o7bobobobo8bobobobo13bob3obo7bob4obo15bob2obob2obo15b3o3b3o
9bob6obo$63b2obo6bob2o5bo3bobo3bo14bo8bo10bo2bo2bo6bobo3bobo7bo5bo8bo
5bo12bo2b3o2bo6bo2b2o2bo14bo2b2obob2o2bo13bobo5bobo7bo3bo2bo3bo$63b3o
8b3o7bobobobo15b2o2bo2bo2b2o9b2o3b2o23b5o10b5o27b2obo2bob2o13bo2bo5bo
2bo14b2o5b2o9b2ob4ob2o$62b2o12b2o29bobo4bobo11b5o7bo7bo55bobo4bobo17bo
3bo18b3o3b3o9b3ob2ob3o$107b2o6b2o11bobobo9bo3bo10bo3bo10bo3bo26b3o6b3o
16b2ob2o34b3ob2o2b2ob3o$107bo8bo27bo11bo5bo8bo5bo25b3o2b2o2b3o13bo2b2o
b2o2bo14bo2bo3bo2bo5bo2bob2o2b2obo2bo$105b2o10b2o10bobo11bobo10b3ob3o
8b3ob3o30b2o18bobo5bobo14bo9bo5bo4bo4bo4bo$104b2o2b2o4b2o2b2o22bobobo
10b5o10b5o27bobo4bobo12b2o3bo3bo3b2o13bo7bo$106bo3bo2bo3bo25b3o11bo3bo
10bo3bo27bobo4bobo12b2o4bobo4b2o12bobo5bobo9bobo2bobo$106b2o2bo2bo2b2o
24b2ob2o55b2o2b2o2b2o2b2o11b6ob6o15b3ob3o9bo10bo$104b2o4b4o4b2o37bobob
o10bobobo25b2o10b2o12b2o7b2o15bo2bobo2bo9bo2bo2bo2bo$103b2o2bo3b2o3bo
2b2o22bobo13bo14bo28b2o8b2o14bo7bo18b2ob2o14b4o$107bo8bo27bo14bo14bo
28b2o2bo2bo2b2o39b3o3b3o10bo2b2o2bo$65b3o4b3o8b3o3b3o11b2o14b2o36bo3bo
10bo3bo29b2o2b2o17b2obobob2o16b3o3b3o13b2o$64bo3bo2bo3bo6bo3bobo3bo10b
obo12bobo21bobobo10b5o10b5o31b2o18b3obobob3o34bo2b2o2bo$64bobobo2bobob
o6bobobobobobo13bo10bo26bo59bo2b4o2bo13b2o9b2o34b6o$103bo3bo8bo3bo20bo
2bo2bo9b2ob2o10b2ob2o26b2o3b2o3b2o12b2o9b2o$65bob2o2b2obo8bob2ob2obo
13bobo8bobo21bobo3bobo7bobobobo8bobobobo25b2o8b2o$65bob2o2b2obo8bob2ob
2obo14bo10bo21bo4bo4bo5bo7bo6bo7bo23b2obo6bob2o$64b2obob2obob2o6b2o2bo
bo2b2o13b2o8b2o22b2obobob2o5bo3bobo3bo4bo3bobo3bo25bo2b2o2bo$63bo3bo4b
o3bo9bobo65bobo5bobo4bobo5bobo25b3o2b3o$63b2ob3o2b3ob2o5bo3bobo3bo62bo
7bo6bo7bo26bobo2bobo$63b3ob2o2b2ob3o8b2ob2o64b2o7b2o4b2o7b2o25bobo2bob
o$62b2o12b2o7b2ob2o$169b2o7b2o28b2o$169bobo5bobo24b2o2b2o2b2o$172bo3bo
27b2o6b2o$169bo3bobo3bo26bo4bo$171bobobobo25b2o8b2o$172bo3bo25bo12bo$
172b2ob2o25b2o10b2o17$80bo2bo2$78bo6bo$45bobobo29b6o$76bo2bo4bo2bo$45b
o33bo4bo$4o75bo4bo$45bobobo26bo2bo4bo2bo$4o75b6o$49bo28bo6bo$b2o$b2o
42bobobo30bo2bo$b2o2$b2o$b2o2$b2o$b2o2$b2o$b2o2$b2o$b2o2$b2o$b2o2$b2o$
b2o2$b2o$b2o42bobobo2$b2o46bo$b2o67b2o2b3ob3o2b2o$49bo20b2o2bobobobo2b
2o$b2o71bobobobo$b2o46bo2$b2o46bo$b2o2$b2o$b2o2$b2o$b2o2$b2o$b2o2$b2o$
b2o2$b2o$b2o2$b2o$b2o2$b2o$b2o42bobobo26b2o$75b4o$b2o42bo3bo26b2o$b2o
89b7o7b8o$45bobobo25bo2bo12bob5obo5bob6obo$b2o68bo2bo4bo2bo9b2o3b2o7b
2o4b2o$b2o42bo3bo20b3o3b2o3b3o8bo5bo7bo6bo$70b3o3b2o3b3o10bobo11bo2bo$
b2o42bobobo21bo2bo4bo2bo$b2o72bo2bo2$b2o73b2o$b2o72b4o$76b2o$b2o$b2o2$
b2o$b2o2$b2o$b2o2$b2o$b2o$133b3o4b3o$b2o130bobo4bobo$b2o130b3o4b3o2$b
2o110b2o$b2o37bo4bobobo19bo11bo3bo12b2o13b2o13b3o14b3o12b2o18b2o$69bo
10b3ob3o11b2o28bobo14bobo12bobo16bobo$b2o35bobo8bo19bo11bo3bo42b3o14b
3o13b2o16b2o$b2o66bo27b4o9b8o48b3o4b3o$40bo4bobobo17b2o27b6o7b3o4b3o
47bobo4bobo$b2o66bo25bo2b2o2bo6b2o6b2o47b3o4b3o$b2o37bo4bo23bo11bo3bo
24b2o4b2o$69bo10b3ob3o41b3o14b3o$b2o35bobobo2bobobo19bo11bo3bo12b2o28b
obo14bobo$b2o95b2o28b3o14b3o$113b2o$b2o110b2o$b2o130b3o4b3o$133bobo4bo
bo$b2o130b3o4b3o$b2o15$40bo4bobobo20b2o17b2o$70bobo15bobo$38bobo8bo21b
2o15b2o$75b3o5b3o$40bo4bobobo25bobo5bobo$75b3o5b3o$40bo8bo2$38bobobo2b
obobo22$38bobobo2bobobo$72bo4bo$42bo6bo22b2o2b2o$73bo2bo$38bobobo2bobo
bo2$38bo6bo27bo2bo$72b2o2b2o$38bobobo2bobobo22bo4bo21$68bo11bo$38bobob
o2bobobo$70b3o3b3o$42bo2bo26bo3bo$70b3o3b3o$42bo2bobobo$70b3o3b3o$42bo
2bo3bo22bo3bo$70b3o3b3o$42bo2bobobo$68bo11bo!
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
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