User:Melwin22/Workspace: Difference between revisions

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yhhhhh this looks very weird but it fits on the page...
Plow World next
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{{Rule
{{Rule
|name            = Walled Cities
|name            = Plow World
|char            = Stable
|char            = Explosive
|b              = 45678
|b              = 378
|s              = 2345
|s              = 012345678
|reversal        = B01278/S5678
|ruleinteger    =
|ruleinteger    = 15608
|reversal        = B/S234678
}}
}}
'''Walled Cities''' is a [[Life-like cellular automaton]]. Its rulestring is B45678/S2345, which means that a cell is born when it has from 4 to 8 alive neighbours, and an alive cell survives when it has from 2 to 5 alive neighbours.
'''Plow World''' is a [[Life-like cellular automaton]] in which live [[cell]]s never die, and dead cells are born if they have 3, 7 or 8 life neighbours.


Rectangle-shaped soups tend to generate a rectangular stable wall, which surrounds a region of high activity.
==Patterns==
Because it is impossible for cells to die under this rule, patterns such as [[oscillator]]s and [[spaceship]]s cannot be constructed.


==Notable patterns==
Because the lowest birth condition in Walled Cities is B4, no pattern can escape its initial bounding box. There are no spaceships or infinitely growing objects.


===Still lives===
</references>
Non-existence of low birth conditions and existence of many low survival conditions allows for a large variety of still lives. There are at least 42 strict still lives with population up to 8; they are shown below, together with examples of bigger ones.
{{EmbedViewer
|rle = x = 152, y = 44, rule = B45678/S2345
2o$o3$2o5b2o5bo$2o4b2o5b3o3$8bo5bo$3o4b2o4b3o$2o4b2o6bo2$39b2o$8b2o4bo
3bo20bo$3o4b2o4b3o2b2o4b2o5b3o4bo$3o3b2o6b2o2b3o2b4o3b3o4b2o3$40b2o14b
o$9bo6bo23bo14b2o24bo23bo$4o4b2o5b3o21bo14bo15bo9b2o22b2o$3o4b2o7b3o
19bo14bo14b2ob2o4b3o22b2o$6b2o29b2o13b2o14bo3bo5bo22b2o3$41b2o5b2o7bo
5b2o17bo6b2o15bo20b2o5b2o$9b2o5bo24bo6bo7b2o5b2o6bo9b2o6bo7bo7b2o6b2o
6bo5bo6bo$4o4b2o5b3o6b3o4b4o5bo6bo7bo6bo7bob2o6bo7bo7b3o5bo7b2o6b3o3bo
6bo7bo7bo$4o3b2o7b3o4b5o2b4o5bo7bo6bo6bo6b2o3bo3b3o5b3o5b3o6b2o6b2o6b
2o5b2o5b2o4b3ob2o3b2ob2o$6b2o9bo20bo7bo6bo6b2o6bo9bo7bo7bo6b2o6b2o6b2o
6b2o4b2o6bo3bo2b2o3bo$37b2o6b2o5b2o3$2b2o7bo7b3o4b2o3b2o3bo16b2o11b4o
9b5o22bo$bo2bo5bobo5bo3bo3b2o3b2o2b3o14bo2bo10b4o7b2o5b2o19b2o$o4bo3bo
3bo3bo5bo4bobo5b2o6bo5b2o4b2o7bo4bo6bo7bo18b2o$o4bo2bo5bo2bo5bo5bo8bo
4b3o3bo8bo5bo6bo4bo9bo16bo$bo2bo4bo3bo3bo5bo4bobo8bo3b2o3bo10bo2b2o8b
2o2bo9bo15bo$2b2o6bobo5bo3bo3b2o3b2o7bobo5bo10bo2b2o8b2o2bo9bo13b2o$
11bo6b2ob2o3b2o3b2o8bo7bo8bo5bo6bo4bo9bo12b3o$50b2o4b2o7bo4bo5bo9bo7b
5o$52bo2bo10b4o7bo7bo7b5o$53b2o11b4o7b2o5b2o4b3o$79b5o5b3o!
|position = center}}


===Oscillators===
==External links==
Any pattern that doesn't stabilize eventually turns into an oscillator. For large regions this can take a while, but because the space inside any wall is finite, it has finite configurations and must eventually become periodic.
 
Walled Cities allows for the existence of oscillators with the smallest possible [[rotor]] (and lowest possible [[heat]]), which can be attached to different [[stator]]s:
 
{{EmbedViewer
|rle = x = 23, y = 8, rule = B45678/S2345
2o3b2o3b3o2b3o$obo2bobo2bobo2bobo$2o4b2o2b2o3b3o2$22bo$2b2o4b2o4b3o4b
2o$bobo3bobo3bobo4bobo$3o3b4o2b3o4b3o!
|position = center}}
 
Here are some small oscillators with periods from 2 to 39.<ref>{{LinkForumThread|p=220033|format = ref|title=Re: Miscellaneous Discoveries in Other Cellular Automata}}</ref>
 
{{EmbedViewer
|rle = x = 96, y = 38, rule = B45678/S2345
11bo10bo8b3o7b3o8b2o7b4o6b5o5b4o6b5o$10bobo8bobo6bo3bo5b2obo7bo2bo5b2o
b3o4bo3b2o4b2o2b2o4bo4bo$10b3o7bo3bo6bobo6b4o6bo3bo5b2o2bo5bob4o4bob4o
4bo4bo$21bobo8bo7b4o7bo2bo5b4o6b6o5b5o4b2o3bo$22bo18b2o9b2o17b5o6b3o6b
2o2bo$92b3o5$b4o6b5o4b4o6b6o6b3o6b4o8bo6b6o15b4o$o4bo4b2obobo4bo2b2o5b
o2b4o4b2o2bo4b6o6b3o5bob4o14bo2b3o$o2bobo4b2obobo4bobo2bo4bo2b3o4bo2bo
bo4bo2bobo5bo2b2o4b6o14b3ob2o$bo3bo4b6o4bob4o4b2o2bo5b4obo5b2o2bo4b2o
4bo4bo2bo15b6o$2bo2bo14b5o5b4o7b5o6b3o6b2o3bo5b2o17b4o$3b2o57bo2bo$63b
2o4$b5o14b4o$o3b2o14bo2b2o$4obo14bo2b3o$b4o15bo2b3o$2b2o17b4o6$4bo7b3o
57b3o6b3o$3b3o5bob3o55bo3bo4bo3bo$2bob2o4b3ob2o54bo5bo3bo4bo$bo3bo4b6o
54bobo3bo3b3o2bo$o4bo4b6o54bo2bo2bo3b5o$o4bo65bo3bo4b4o$bo2bo67b3o$2b
2o!
|position = center}}
 
A typical city usually fills in the entire area it can reach, that is, the intersection of its [[bounding box]] and its [[bounding diamond]].
 
{{EmbedViewer
|rle = x = 21, y = 23, rule = B45678/S2345
16b2o$16bo$16bo$15bo$15bo$o13bo$o13bo$6o7bo$6b6obo$12b2o$12bobo$12bob
o$11bo3bo$11bo4b2o$10bo7bo$10bo8b2o$9bo9b2o$9bo$8bo$7bo$7bo$5b2o$6bo!
|viewerconfig = #C [[ AUTOSTART GPS 6 LOOP 60 ]]
|position = center}}
 
This happens for majority of [[apgsearch]]-size soups, so simple objects in this rule are very difficult to find using apgsearch.
 
Periods of oscillators emerging from hollow rectangles are an extensively researched topic in Walled Cities.<ref>{{LinkForumThread|p=226491|format = ref|title=Re: Miscellaneous Discoveries in Other Cellular Automata}}</ref> A {{times|3|n}} rectangle always results in a p2 oscillator, with every cell inside flashing on in one phase and flashing off in the other phase. Otherwise, if a rectangle has sides {{times|m|n}}, it will produce an oscillator with period listed in the table:
 
{|class = "wikitable"
|-
! !!colspan="21"|m
|-
!n ||4 ||5 ||6 ||7 ||8 ||9 ||10 ||11 ||12 ||13 ||14 ||15 ||16 ||17 ||18 ||19 ||20 ||21 ||22 ||23
|-
|'''4''' ||2
|-
|'''5''' ||4 ||3
|-
|'''6''' ||2 ||2 ||5
|-
|'''7''' ||4 ||9 ||4 ||7
|-
|'''8''' ||4 ||7 ||14 ||7 ||7
|-
|'''9''' ||4 ||5 ||5 ||11 ||17 ||10
|-
|'''10''' ||6 ||8 ||14 ||28 ||11 ||10 ||17
|-
|'''11''' ||4 ||10 ||7 ||2 ||10 ||20 ||56 ||17
|-
|'''12''' ||4 ||11 ||19 ||40 ||50 ||41 ||24 ||3 ||48
|-
|'''13''' ||4 ||6 ||21 ||32 ||11 ||58 ||222 ||69 ||716 ||56
|-
|'''14''' ||10 ||26 ||18 ||51 ||18 ||118 ||384 ||31 ||176 ||504 ||31
|- style="writing-mode: vertical-rl"
|'''15''' ||4 ||22 ||46 ||2 ||48 ||169 ||219 ||748 ||2004 ||1041 ||453 ||58
|- style="writing-mode: vertical-rl"
|'''16''' ||4 ||66 ||46 ||54 ||69 ||176 ||85 ||461 ||2073 ||2412 ||2979 ||9811 ||57
|- style="writing-mode: vertical-rl"
|'''17''' ||4 ||54 ||32 ||185 ||88 ||46 ||468 ||262 ||220 ||4746 ||1612 ||11433 ||62146 ||518
|- style="writing-mode: vertical-rl"
|'''18''' ||14 ||64 ||28 ||4 ||199 ||47 ||373 ||164 ||2241 ||3158 ||24243 ||521 ||63817 ||54080 ||677
|- style="writing-mode: vertical-rl"
|'''19''' ||4 ||85 ||18 ||79 ||33 ||353 ||101 ||3127 ||2106 ||10938 ||4270 ||57784 ||117911 ||52951 ||385624 ||674
|- style="writing-mode: vertical-rl"
|'''20''' ||4 ||20 ||18 ||208 ||404 ||512 ||339 ||6784 ||14769 ||13819 ||2388 ||46276 ||218102 ||594883 ||346159 ||132674 ||5160
|- style="writing-mode: vertical-rl"
|'''21''' ||4 ||77 ||19 ||820 ||486 ||696 ||1518 ||6519 ||5875 ||8649 ||105386 ||41636 ||219190 ||380124 ||1601041 ||4675530 ||1513062 ||22118
|- style="writing-mode: vertical-rl"
|'''22''' ||18 ||71 ||41 ||1398 ||204 ||2611 ||4128 ||17329 ||14684 ||12556 ||177336 ||22508 ||446333 ||302811 ||2885033 ||1922818 ||6454838 ||53388029 ||21598
|- style="writing-mode: vertical-rl"
|'''23''' ||4 ||98 ||10 ||679 ||890 ||368 ||1261 ||16126 ||44115 ||152006 ||190534 ||238989 ||70813 ||419435 ||2247711 ||12795738 ||45071 ||? ||? ||?
|}


Periods of oscillators emerging from hollow squares (hypotenuse of the triangle above) are listed as sequence A178880 in OEIS.<ref>https://oeis.org/A178880</ref> Sequence starts with two 1's, for the {{times|1|1}} dot (which disappears, leaving unchanging void) and {{times|2|2}} block, a still life.
==See also==
*{{rl|Vote}}
*{{rl|Rings 'n' Slugs}}
==References==
<references/>
==External links==
*{{LinkCatagolueRule|b45678s2345}}


[[Category:Life-like cellular automata]]
[[Category:Life-like cellular automata]]
[[Category:Rules without death]]

Revision as of 19:32, 23 July 2026

Plow World
x=64, y = 64, rule = B378/S012345678 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated pseudorandom soup
Rulestring 012345678/378
B378/S012345678
Character Explosive
Black/white reversal B/S234678

Plow World is a Life-like cellular automaton in which live cells never die, and dead cells are born if they have 3, 7 or 8 life neighbours.

Patterns

Because it is impossible for cells to die under this rule, patterns such as oscillators and spaceships cannot be constructed.


</references>

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