User:Melwin22/Castles/random patterns

Diehards, methuselahs and other stuff.

Diehards

Not counting fuses, the longest-lasting object I found that leaves nothing behind is the pumpkin. It reaches a maximum population of 110 and dies after 596 generations. Almost any solid object with population above 100 turns into a proper castle, and exceptions like the pumpkin are very rare.

x = 6, y = 6, rule = B3678/S135678 3b2o$2b2o$6o$2o2b2o$6o$6o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

L	Name	BB	MCPS	I	F	L/I	F/I	F/L	L/MCPS
596	Pumpkin	6 × 6	26	26	0	22.9	0	0	22.9

Another pattern, based on the "pentaswirl" (see below for more details), almost matches the same lifespan with only 7 cells. More precisely, this one lives for 534 generations and reaches a maximum population of 101.

x = 10, y = 3, rule = B3678/S135678 5bo$o4bobobo$bo7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

Pentaselah

Five cells are enough to make something interesting happen. Five different 5-cell patterns fall into this evolutionary sequence, which becomes a large, symmetrical castle with no chambers. Here are all of them: the 2nd is a grandparent of the 1st, then there is a great-grandparent, great-great, and great-great-great.

x = 37, y = 5, rule = B3678/S135678 17bo6bo7bo$bo8bo5b2o7bo7bo$2obo4b2o9bo$11bo6bo7b3o5bobo$bo7bo25bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

The 3rd form is what I consider to be the "main" pentaselah. 4th and 5th are asymmetric and have larger bounding boxes, so they are less... uhhh... something. Whatever, here is the 3rd form by itself.

x = 4, y = 4, rule = B3678/S135678 2bo$2b2o$o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

L	Name	BB	MCPS	I	F	L/I	F/I	F/L	L/MCPS
6224	Pentaselah	4 × 4	6	5	48753	1244.8	9750.6	7.833	1037.3

F refers here to the population in generation 6224, when everything settles down into periodic oscillations. The largest population ever reached is 48779, and in its final form, pentaselah is technically an oscillator with period 7392, although this number is simply a multiple of periods of all wall defenders (32 for flag bearer, 11 for rubble, 7 for half-ballista, 3 for bird's nest).

Baby pentaselah

A similar pattern that also commonly appears in soups, also has a minimum population of 5 cells, and similarly to the pentaselah, in generation 1 it has more cells than the starting population, but a 3x3 bounding box.

x = 4, y = 4, rule = B3678/S135678 o$b2o$o$3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

As a methuselah it's not that impressive (thus the "baby" name, also referring monster and baby monster), but is still be useful due to its simplicity.

L	Name	BB	MCPS	I	F	L/I	F/I	F/L	L/MCPS
684	Baby pentaselah	4 × 4	6	5	1880	136.8	376	2.749	114

Pentaswirl

After pentaselah and baby pentaselah, the next longest-lasting sequence starting from 5 cells is this thing, which swirls for 65 generations and disappears.

x = 5, y = 3, rule = B3678/S135678 o$obobo$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

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All other patterns with at most 5 cells live for 24 generations or less, and leave behind only duoplets, dominoes, blocks, stable hexaplets, simple p2 and p4 oscillators.

Pentaselah + other objects

Combined with other patterns, pentaselah can react in various ways, which can be used to synthesize more complex objects. For example, a reaction with a single duoplet can create a p24 pulsating eye or a p42 butterfly.

x = 44, y = 60, rule = B3678/S135678 30b2o$12bo17b2o$13bo19bo$15bo16b2obo$14b2obo$33bo$15bo4$bo$2o$3bo34bo$ 2bo34b2o$23b2o15bo$21bo17bo$20b2obo$8bo$7bo13bo2bo14b2o$23bo5$37bo$19b o16b2o$bo16b2o4bo14bo$2o19bo3bo12bo$3bo16bo$2bo4bo$7bo$6bo12bo$20bo17b 2o$38b2o3$6bo$5b2o13bo$8bo10b2o14b2o$7bo14bo$21bo16bo3bo$37b2obobo2$ 20b2o16bo$5bo$4bo4$bo32bo$2o31b2o$3bo32bo$2bo16bo15bo$18b2obo$9bo13bo$ 8bo10bo2bo2$6bo$5bo36bo$43bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

More of such reactions are shown here.

Monstrosity

Castles are not an explosive rule, although sometimes it really looks like the chaotic growth doesn't end. One of the best examples of such growth is what I call the "monstrosity". I discovered it in 2019, and even though I later found bigger objects, I still have some sort of sentiment to this one.

Perturbing evolution of a pentaselah in just the right way results in a greatly extended lifespan (almost 85k) and greatly embiggened final pattern (over 2.5M). For more details, check the "summary" at the bottom of this page.

x = 10, y = 13, rule = B3678/S135678 9bo$9bo8$2bo$2b2o$o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

Monstrosity has a total of 927 wall defenders (see the census) and 59 chambers, ranging from anti-blocks (14 instances) and anti-ponds (7 instances) to the enormous central chamber, which has an area of over 107k cells. This chamber is over twice as big as the original pentaselah, but unfortunately there doesn't seem to be a way to fit it inside.

Evolution of the monstrosity takes so long that it's useful to write out some interesting phases.

Generation	Description
0	Smallest MCPS of 15, smallest population of 7 (equaled in generation 3), smallest bounding box of 10 × 13 (equaled in gen 1, 2, 4, 8, 9 and 10).
28	Population falls below the generation number, and stays below until generation 130.
118	Population reaches 100.
176	Only time when population is equal to the generation number.
179	Last time when population is smaller than generation number.
369	Pentaselah sequence hits the domino and stops being symmetrical.
705	Population reaches 1k.
726	Last generation in which there is an empty cell inside the original 10 × 13 bounding box.
1046	Final population of the baby pentaselah is reached. Monstrosity took 362 more generations than baby pentaselah to get here, but from this point, growth really starts speeding up.
2241	Population reaches 10k.
2897	First chamber forms.
5050	Final population of the unaltered pentaselah is reached, 1171 generations earlier than normal.
7365	Population reaches 100k. At this point the pattern grows in almost all directions and looks very similar to a typical blob in explosive rules.
12476	Third chamber forms, much bigger than previous two.
28741	Southern side of the pattern stabilizes.
30935	A giant chamber, ultimately second in terms of area, is formed.
31842	Population reaches 1M.
32974	A diagonal wickstretcher appears.
34363	Wickstretcher is destroyed.
≈37420	A different kind of a diagonal wickstretcher appears.
≈39230	Second wickstretcher is destroyed.
49544	Main chamber is closed off.
53307	Main chamber stabilizes. Growth now happens only on the northern side of the pattern.
60190	Population reaches 2M.
82193	North-east corner stabilizes.
84984	North-west corner stabilizes.

Other notable mentions

Everything listed here is parametrized in the "summary" section.

In 2026 I found these reactions, which beat the original monstrosity in most aspects.

x = 9, y = 10, rule = B3678/S135678 2o6$5bo$6b2o$5bo$8bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

x = 12, y = 13, rule = B3678/S135678 10b2o9$2bo$2b2o$o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

Two next objects were found by using ikpx2 and are present on Catagolue. One holds the current record for lifespan (155k+), while the other one has the largest overall period, if treated as a single trivial oscillator (510048 = 2^5 * 3^2 * 7 * 11 * 23), thanks to a large variety of wall defenders.

x = 8, y = 24, rule = B3678/S135678 4bo$bob3obo$2b5o$bob3obo$2bobobo2$2b2ob2o$3b3o$3b4o$3b3o$3b2o$6bo$4b2o 2$3bo$3bo$2bo$2bo$bo$3o2$2b2o$2bo$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

x = 13, y = 11, rule = B3678/S135678 5b3o$b2obobobob2o$2obob3obob2o$3obobobob3o$2bo2bobo2bo$b2o2bobo2b2o$bo 2b5o2bo$bo4bo4bo$3b2o3b2o$3obobobob3o$4o5b4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

Integer constructions

Most small integer constructions in Castles disappear quickly or turn into dominoes/duoplets/blocks/simple oscillators. Here are all the exceptions up to 300 and some more examples up to 3000:

Integer	Description
31	Creates the p24 pulsating eye.
39	Turns into gen 1 of a baby pentaselah after 12 generations.
103	Forms a miniature castle with two bird nests and one small archer.
205	Forms a miniature castle with two guards.
215	Creates a p12 oscillator.
252	Forms a castle with final population of 322k.
256	Forms a castle with final population of 206k.
266	Forms a castle with final population of 113k.
293	Forms a mid-sized castle with 9 wall defenders.
344	Creates a very rare 8-cell still life.
395	Forms the largest castle out of all sub-1000 integers (final population 2.153M) with tons of chambers.
452	A die hard that lasts 293 generations before disappearing.
712	Turns into gen 2 of a pentaselah at generation 34.
744	Forms a large castle, which emits a diagonal wickstretcher (smallest integer construction that exhibits infinite growth).
795	Forms a castle that also emits the same diagonal wickstretcher.
854	Turns into gen 4 of a pentaselah after 56 generations.
926	Forms a castle that emits two diagonal wickstretchers.
1029	A die hard that lasts 417 generations before disappearing.
1276	Forms the largest castle out of all sub-3000 integers (final population 2.323M).
1296	Creates a very rare 8-cell still life (different from the 344 integer).
1475	Creates a rare p2 oscillator.
1675	A die hard that lasts 471 generations before disappearing.
1954	Creates a rare p2 oscillator (different from the 1475 integer).
2286	Stabilizes into two dominoes and a microscopic castle with one guard and one flag. Very cute.
2662	On generation 1519, it becomes the smallest integer construction that emits an orthogonal wickstretcher (and the very first time I saw one emerge from asymmetric chaos). Sadly, the wickstretcher is destroyed on generation 1861.
2894	Creates a giant p2 oscillator – "the sun".
2907	Turns into gen 4 of a pentaselah after 155 generations.

Repunit numbers quickly disappear/stabilize for digits 0, 1, 2, 3, 5, 7 and 8; castle forming occurs only for 4, 6 and 9.

Lines

Even starting patterns as simple as a line of width 1 can exhibit interesting and unpredictable behavior. So far I checked lines up to 200 cells.

Length	Result
1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 17	Disappear. This is most likely a complete set.
2, 6, 14, 18, 20	Turn into a still life (in case of n=2, it already is a still life). Not sure if this is a complete set, but with increasing length, probability of another still life appearing decreases.
10, 16, 19, 21, 22...	Form typical for this rule oscillating patterns without any particularly interesting features. Most lines fall in this category; only first 5 examples are listed.
15	Turns into eight separated oscillators.
25	Creates a chamber with a rare p4 oscillator in the center.
27	Forms two p37 "cannon" oscillators.
55	Emits two orthogonal wickstretchers; first example of infinite growth.
102	Shortest line that evolves into a pattern larger than 100k (F ~= 256,400).
105	Almost triples the previous record (F ~= 690,500).
114	Forms two p19 oscillating chambers.
122	Grows absurdly large (see the summary below). Emits eight diagonal wickstretchers, which are destroyed after quite a long time, allowing the insane final population of over 11M.
130	Besides the main body, forms two large separate "islands", which is extremely unusual.
183	Grows beyond 1M and emits four diagonal wickstretchers; second example of infinite growth.
185	Not counting the infinitely-growing patterns, this gets the 2nd place in terms of final size (F ~= 1,330,500), out of 200 checked lines.

Summary

A comparison between the most notable methuselahs. Every time, F refers to the population in generation L, when the pattern stops evolving; the largest population ever reached can be up to few hundred cells higher. Some patterns were evolved for N ticks in order to get the minimal I; all parameters are calculated from that evolved pattern as the starting point.

L	Name	BB	MCPS	I	F	L/I	F/I	F/L	L/MCPS
84984	Monstrosity	10 × 13	15	7	2578423	12140.6	368346.1	30.34	5665.6
100803	"Other notable mention" #1	9 × 10	13	7	2777472	14400.4	396781.7	27.553	7754.1
142868	"Other notable mention" #2	12 × 13	16	7	2659574	20409.7	379939.1	18.616	8929.3
155538	"Other notable mention" #3, evolved for 4 ticks	8 × 20	49	46	2150333	3381.3	46746.4	13.825	3174.2
98526	"Other notable mention" #4, evolved for 24 ticks	15 × 10	63	60	3117761	1642.1	51962.7	31.644	1563.9
118949	395 integer, evolved for 2 ticks	11 × 7	31	29	2153950	4101.7	74274.1	18.108	3837.1
99163	1276 integer, evolved for 13 ticks	12 × 7	19	16	2323348	6197.7	145209.3	23.43	5219.1
97129	Line of 122 cells	122 × 1	122	122	11110958	796.1	91073.4	114.394	796.1