User:Melwin22/Workspace

Walled Cities
x=64, y = 64, rule = B45678/S2345 ! #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	2345/45678 B45678/S2345
Character	Stable

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.

Rectangle-shaped soups tend to generate a rectangular stable wall, which surrounds a region of high activity.

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

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 40 strict still lives with population up to 8; they are shown below, together with examples of bigger ones.

x = 141, y = 44, rule = B45678/S2345 2o$o3$2o5b2o5bo$2o4b2o5b3o3$8bo5bo$3o4b2o4b3o$2o4b2o6bo2$35b2o$8b2o4bo 20bo$3o4b2o4b3o4b2o5b3o4bo$3o3b2o6b2o3b4o3b3o4b2o3$36b2o7bo$9bo4bo21bo 7b2o24bo23bo$4o4b2o3b3o19bo7bo15bo9b2o22b2o$3o4b2o5b3o17bo7bo14b2ob2o 4b3o22b2o$6b2o25b2o6b2o14bo3bo5bo22b2o3$37b2o7bo5b2o17bo6b2o15bo20b2o 5b2o$9b2o3bo22bo7b2o5b2o6bo9b2o6bo7bo7b2o6b2o6bo5bo6bo$4o4b2o3b3o4b3o 4b4o5bo7bo6bo7bob2o6bo7bo7b3o5bo7b2o6b3o3bo6bo7bo7bo$4o3b2o5b3o2b5o2b 4o5bo7bo6bo6b2o3bo3b3o5b3o5b3o6b2o6b2o6b2o5b2o5b2o4b3ob2o3b2ob2o$6b2o 7bo18bo7bo6b2o6bo9bo7bo7bo6b2o6b2o6b2o6b2o4b2o6bo3bo2b2o3bo$33b2o6b2o 3$2b2o7bo7b3o4b2o3b2o3bo16b2o11b4o9b5o22bo$bo2bo5bobo5bo3bo3b2o3b2o2b 3o14bo2bo10b4o7b2o5b2o19b2o$o4bo3bo3bo3bo5bo4bobo5b2o6bo5b2o4b2o7bo4bo 6bo7bo18b2o$o4bo2bo5bo2bo5bo5bo8bo4b3o3bo8bo5bo6bo4bo9bo16bo$bo2bo4bo 3bo3bo5bo4bobo8bo3b2o3bo10bo2b2o8b2o2bo9bo15bo$2b2o6bobo5bo3bo3b2o3b2o 7bobo5bo10bo2b2o8b2o2bo9bo13b2o$11bo6b2ob2o3b2o3b2o8bo7bo8bo5bo6bo4bo 9bo12b3o$50b2o4b2o7bo4bo5bo9bo7b5o$52bo2bo10b4o7bo7bo7b5o$53b2o11b4o7b 2o5b2o4b3o$79b5o5b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

Oscillators

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 stators:

x = 23, y = 8, rule = B45678/S2345 2o3b2o3b3o2b3o$obo2bobo2bobo2bobo$2o4b2o2b2o3b3o2$22bo$2b2o4b2o4b3o4b 2o$bobo3bobo3bobo4bobo$3o3b4o2b3o4b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

A typical city usually fills in the entire area it can reach, that is, the intersection of its bounding box and its bounding diamond.

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 6 LOOP 60 ]]

(click above to open LifeViewer)

Periods of oscillators emerging from hollow rectangles are an extensively researched topic in this rule. If a rectangle has sides m × n, it will produce an oscillator with period listed in the table:

	m
n	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
3	2
4	2	2
5	2	4	3
6	2	2	2	5
7	2	4	9	4	7
8	2	4	7	14	7	7
9	2	4	5	5	11	17	10
10	2	6	8	14	28	11	10	17
11	2	4	10	7	2	10	20	56	17
12	2	4	11	19	40	50	41	24	3	48
13	2	4	6	21	32	11	58	222	69	716	56
14	2	10	26	18	51	18	118	384	31	176	504	31
15	2	4	22	46	2	48	169	219	748	2004	1041	453	58
16	2	4	66	46	54	69	176	85	461	2073	2412	2979	9811	57
17	2	4	54	32	185	88	46	468	262	220	4746	1612	11433	62146	518
18	2	14	64	28	4	199	47	373	164	2241	3158	24243	521	63817	54080	677
19	2	4	85	18	79	33	353	101	3127	2106	10938	4270	57784	117911	52951	385624	674
20	2	4	20	18	208	404	512	339	6784	14769	13819	2388	46276	218102	594883	346159	132674	5160
21	2	4	77	19	820	486	696	1518	6519	5875	8649	105386	41636	219190	380124	1601041	4675530	1513062	22118
22	2	18	71	41	1398	204	2611	4128	17329	14684	12556	177336	22508	446333	302811	2885033	1922818	6454838	53388029	21598
23	2	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. Sequence starts with two 1's, for the 1 × 1 dot (which disappears, leaving unchanging void) and 2 × 2 block, a still life.

See also

• Vote
• Rings 'n' Slugs