Rules with small adjustable spaceships

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nolovoto
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Re: Rules with small adjustable spaceships

Post by nolovoto » March 13th, 2020, 7:49 am

Would my adjustable wickstretcher rule belong in this thread?

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Saka
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Re: Rules with small adjustable spaceships

Post by Saka » May 10th, 2020, 12:54 am

WildMyron has found "Billiard table" adjustable spaceships based on the concept of a ship inside a box pushing the box, but instead, the ship pushes the box and gets reflected as a different ship which pulls the other end of the box.
c/(23+5N), N >= 0

Code: Select all

x = 16, y = 42, rule = B2ci3-ciqy4jnqrt5eqy6c8/S012eik3cejnr4ainrwz5ejry6ac8
8o$o6bo$o6bo$o2bo3bo$o2b2o2bo$o2bo3bo$o6bo$o6bo$8o3$11o$o9bo$o9bo$o5bo
3bo$o5b2o2bo$o5bo3bo$o9bo$o9bo$11o3$12o$o10bo$o10bo$o5bo4bo$o5b2o3bo$o
5bo4bo$o10bo$o10bo$12o3$16o$o14bo$o14bo$o5bo8bo$o5b2o7bo$o5bo8bo$o14bo
$o14bo$16o!
c/(19+5N), N >= 0

Code: Select all

x = 16, y = 42, rule = B2ci3aenry4inrtyz5k6ci8/S012ei3ejnry4ainqrz5ky6cik7e
8o$o6bo$o6bo$o2bo3bo$o2b2o2bo$o2bo3bo$o6bo$o6bo$8o3$11o$o9bo$o9bo$o5bo
3bo$o5b2o2bo$o5bo3bo$o9bo$o9bo$11o3$12o$o10bo$o10bo$o5bo4bo$o5b2o3bo$o
5bo4bo$o10bo$o10bo$12o3$16o$o14bo$o14bo$o5bo8bo$o5b2o7bo$o5bo8bo$o14bo
$o14bo$16o!
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muzik
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Re: Rules with small adjustable spaceships

Post by muzik » May 10th, 2020, 1:13 pm

Those are by far some of the nicest adjustable ships I've ever seen purely just to look at, even if it isnKt bringing any new speeds to the table.

Code: Select all

x = 278, y = 9, rule = B2ci3-ciqy4jnqrt5eqy6c8/S012eik3cejnr4ainrwz5ejry6ac8
278o$o276bo$o276bo$o5bo270bo$o5b2o269bo$o5bo270bo$o276bo$o276bo$278o!

Code: Select all

 x = 818, y = 9, rule = B2ci3-ciqy4jnqrt5eqy6c8/S012eik3cejnr4ainrwz5ejry6ac8
818o$o816bo$o816bo$o5bo810bo$o5b2o809bo$o5bo810bo$o816bo$o816bo$818o!

Code: Select all

 x = 1046, y = 9, rule = B2ci3-ciqy4jnqrt5eqy6c8/S012eik3cejnr4ainrwz5ejry6ac8 
1046o$o1044bo$o1044bo$o5bo1038bo$o5b2o1037bo$o5bo1038bo$o1044bo$o1044b
o$1046o!

Code: Select all

 x = 1481, y = 9, rule = B2ci3-ciqy4jnqrt5eqy6c8/S012eik3cejnr4ainrwz5ejry6ac8
1481o$o1479bo$o1479bo$o5bo1473bo$o5b2o1472bo$o5bo1473bo$o1479bo$o1479b
o$1481o!
The third c/5648 spaceship ever:

Code: Select all

 x = 1133, y = 9, rule = B2ci3-ciqy4jnqrt5eqy6c8/S012eik3cejnr4ainrwz5ejry6ac8
1133o$o1131bo$o1131bo$o5bo1125bo$o5b2o1124bo$o5bo1125bo$o1131bo$o1131b
o$1133o!
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yujh
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Re: Rules with small adjustable spaceships

Post by yujh » May 11th, 2020, 10:01 pm

77topaz wrote:
February 10th, 2019, 6:29 am
muzik wrote:A similar concept from drc posted a few years ago:

Code: Select all

x = 3, y = 3, rule = B346/S12/G3
.A$A.A$A.A!
[[ THEME Blues ]]
Here's another Generations ship which can be slowed by increasing the number of states:

Code: Select all

x = 7, y = 5, rule = 235678/3456/7
2.3A$.5A$AF.CDCA$.5A$2.3A!

Code: Select all

x = 7, y = 5, rule = 235678/3456/8
2.3A$.5A$AG.CDCA$.5A$2.3A!

Code: Select all

x = 7, y = 5, rule = 235678/3456/9
2.3A$.5A$AH.CDCA$.5A$2.3A!

Code: Select all

x = 7, y = 5, rule = 235678/3456/10
2.3A$.5A$AI.CDCA$.5A$2.3A!
...

Code: Select all

x = 7, y = 5, rule = 235678/3456/100
2.3A$.5A$AsC.CDCA$.5A$2.3A!
With six states, the ship still sort of works, but behaves somewhat differently:

Code: Select all

[code]x = 7, y = 5, rule = 235678/3456/6
2.3A$.5A$AE.CDCA$.5A$2.3A!

Code: Select all

x = 7, y = 5, rule = 235678/3456/6
2.3A$.5A$AE.CDCA$.5A$2.3A!
B34kz5e7c8/S23-a4ityz5k!!!

b2n3-q5y6cn7s23-k4c8

B3-kq6cn8/S2-i3-a4ciyz8

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yujh
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Re: Rules with small adjustable spaceships

Post by yujh » May 11th, 2020, 11:09 pm

Can anyone make this faster?(orthorgonal)

Code: Select all

x = 576, y = 105, rule = B3-cry4j5ci6c/S02ae3aijnr4r5ijny6ae
51b3o100bo88bo72bo56bo49bo37bo$o12bo12bo12bo13bo$52bo446bo35bo29bo$41b
o$29bo12bo$17bo12bo9b3o488b3o27b3o$5bo12bo9b3o129bo88bo72bo56bo49bo37b
o65bo29bo$6bo9b3o24bo117bo88bo72bo56bo49bo37bo63bo29bo$4b3o24bo127b3o
86b3o70b3o54b3o47b3o19bo15b3o$19bo429b2o40b3o12bo$7bo440bob2o41bo13bo
34b3o27b3o$449b2o41bo12b3o35b3o27b3o$543b2o28b2o$162bo2bo85bo2bo69bo2b
o53bo2bo46bo2bo34bo2bo53bo29bo$161bo88bo72bo56bo49bo37bo20bo19bo$161b
3o86b3o70b3o54b3o47b3o35b3o34bo$504bo33bo29bo$504b3o30bo29bo$537b3o27b
3o$456bo37bo36b3o27b3o$457bo37bo36b3o27b3o$455b3o35b3o36b2o28b2o3$396b
o62bo37bo$395b2o$394bob2o$395b2o8$402bo$403bo$401b3o3$330bo74bo$329b2o
$328bob2o$329b2o8$336bo$337bo$335b3o3$257bo81bo$256b2o$255bob2o$256b2o
8$263bo$264bo$262b3o3$168bo97bo$167b2o$166bob2o$167b2o8$174bo$175bo$
173b3o3$63bo113bo$62b2o$61bob2o$62b2o8$69bo$70bo$68b3o3$72bo!
Much faster compare to the original post
B34kz5e7c8/S23-a4ityz5k!!!

b2n3-q5y6cn7s23-k4c8

B3-kq6cn8/S2-i3-a4ciyz8

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wildmyron
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Re: Rules with small adjustable spaceships

Post by wildmyron » May 12th, 2020, 8:28 am

yujh wrote:
May 11th, 2020, 11:09 pm
Can anyone make this faster?(orthorgonal)

Code: Select all

<snip>
Much faster compare to the original post
I'm not sure what you mean, and I also don't know which post is the original post you are referring to. Could you please link to older posts when you refer to them in future?

As for faster adjustable ships - it depends. This specific reaction in this rule can go up to c/8, p24:

Code: Select all

x = 15, y = 15, rule = B3-cry4j5ci6c/S02ae3aijnr4r5ijny6ae
4bo2bo$3bo6bo$3b3o3b2o$9bobo2$o13bo2$2bo$obo$b2o6b3o$11bo$10bo3$7bo!
To go much faster than that you need different reactions in a different rule, but doing so with these bounce reactions is tricky. Search this thread for "fast*" to see what else is already known.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

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Re: Rules with small adjustable spaceships

Post by wildmyron » May 12th, 2020, 8:47 am

muzik wrote:
May 10th, 2020, 1:13 pm
Those are by far some of the nicest adjustable ships I've ever seen purely just to look at, even if it isnKt bringing any new speeds to the table.

<snip>

The third c/5648 spaceship ever:

Code: Select all

 x = 1133, y = 9, rule = B2ci3-ciqy4jnqrt5eqy6c8/S012eik3cejnr4ainrwz5ejry6ac8
1133o$o1131bo$o1131bo$o5bo1125bo$o5b2o1124bo$o5bo1125bo$o1131bo$o1131b
o$1133o!
I'm glad you like them, though I believe there are several other adjustable speed spaceships posted on this thread which can be made to move at c/5648. There was a fair bit of discussion about this idea and similar ships (quite a few of which were posted on MDiOCA by Saka) on the ConwayLife Lounge Discord server. That discussion provided most of the inspiration for these ships.

There was also a fair bit of discussion about various mechanisms to allow adjustable speed ships at >c/2, but so far nothing that looks like it will definitely work.
muzik wrote:
August 5th, 2019, 9:16 am
Have all orthogonal speeds 3c/n been proven yet?
As mentioned by "2718281828", they're definitely possible, but I don't think anyone has posted a set covering all periods here. I vaguely recall I even had some search results aiming to achieve that result, but I never completed them or posted them here.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

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Re: Rules with small adjustable spaceships

Post by yujh » May 12th, 2020, 8:53 am

wildmyron wrote:
May 12th, 2020, 8:28 am
yujh wrote:
May 11th, 2020, 11:09 pm
Can anyone make this faster?(orthorgonal)

Code: Select all

<snip>
Much faster compare to the original post
I'm not sure what you mean, and I also don't know which post is the original post you are referring to. Could you please link to older posts when you refer to them in future?

As for faster adjustable ships - it depends. This specific reaction in this rule can go up to c/8, p24:

Code: Select all

x = 15, y = 15, rule = B3-cry4j5ci6c/S02ae3aijnr4r5ijny6ae
4bo2bo$3bo6bo$3b3o3b2o$9bobo2$o13bo2$2bo$obo$b2o6b3o$11bo$10bo3$7bo!
To go much faster than that you need different reactions in a different rule, but doing so with these bounce reactions is tricky. Search this thread for "fast*" to see what else is already known.
AforAmpere wrote:
July 31st, 2018, 5:00 pm
calcyman wrote: Has anyone looked at the isotropic rulemin and rulemax to see whether there's a non-explosive rule supporting this family of ships?
Unfortunately, there doesn't seem to be a non-explosive rule in there. However, literally any rule with the same push reaction has this property, so if someone can find a rule with the push reaction that is non-explosive, we have adjustable-slope ships in a non-explosive rule.

EDIT, here's one:

Code: Select all

x = 135, y = 28, rule = B3-cry4j5ci6c/S02ae3aijnr4r5ijny6ae
o46bo$122bo$2bo46bo$3bo16bo29bo$b3o17bo26b3o$19b3o$51bo$5bo16bo105bo$
129bo$127b3o$110bo$109b2o$108bob2o$109b2o2$131bo2bo$130bo$130b3o5$117b
o$118bo$116b3o3$120bo!
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B34kz5e7c8/S23-a4ityz5k!!!

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wildmyron
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Re: Rules with small adjustable spaceships

Post by wildmyron » May 12th, 2020, 9:40 am

So assuming you meant 'make that orthogonal adjustable speed ship consisting of the glider + dot bounce reaction go much faster", the answer is in my previous reply: c/8 is as fast as it can be made to go. To go faster requires different reactions.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

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Re: Rules with small adjustable spaceships

Post by Saka » May 13th, 2020, 1:44 am

Some typical "bouncing ships" adjustable ships.
Speed of a ship with an n-cell gap between the 2 still lives is c/5+2n

Code: Select all

x = 14, y = 13, rule = B2-kn3cinqr4ikyz5ceijr6-ek/S01e2eik3acey4ckrtwyz5cnq6-ci78
2bo$4bo$o2b2o2bo$4bo$2bo3bo4$2bo$7bo$o5b2o5bo$7bo$2bo9bo!
Same speeds, but in a B1e rule

Code: Select all

x = 14, y = 13, rule = B1e2-ai3-ainq4jnqy5-cnqr6ack7c8/S01e2akn3aikn4-cijky5cei6ain8
2o$2ob2o$2obobob2o$2ob2ob3o$2o4b2o4$2o$2o3b2o$2o3bobo4b2o$2o3b2o4b3o$
2o9b2o!
Different set of speeds,
Speed of a ship with an n-cell gap between the 2 still lives is c/2n

Code: Select all

x = 16, y = 23, rule = B1e2-a3anqry4aceint5aceny6c7c8/S01e2ik3-eiqr4acjkqz5-acy6-an8
4o$4o2b2o$4o2bobo$4o3b3o$4o3b3o4$4o$4o2b2o$4o2bobo$4o2b2o2b2o$4o6b2o6$
4o$4o2b2o$4o2bobo$4o2b2o6b2o$4o10b2o!
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Re: Rules with small adjustable spaceships

Post by wildmyron » May 17th, 2020, 10:24 am

Following on from the ship inside a box adjustable spaceships, here is a ship inside a filled box adjustable spaceship.

(1, 0)c/(2+4n), p(2+4n); n >= 2

Code: Select all

x = 16, y = 20, rule = B2cei3ajny4ikqw5aein6-k7c/S12ei3ain4knr5ei6ace7c8
8o$8o$3o2b3o$ob2ob3o$2o2b4o$ob2ob3o$3o2b3o$8o$8o3$16o$16o$3o2b11o$ob2o
b11o$2o2b12o$ob2ob11o$3o2b11o$16o$16o!
(shown here at c/14 and c/30)

Similar idea, but wider box (same speeds)

Code: Select all

x = 15, y = 24, rule = B2cin3ajknr4-cknrw5-ajny6ein78/S01e2en3aikry4-ktwy5ceik6ai7c8
7o$7o$7o$2o2b3o$2obob2o$2obo2bo$2obob2o$2o2b3o$7o$7o$7o3$15o$15o$15o$
10o2b3o$10obob2o$10obo2bo$10obob2o$10o2b3o$15o$15o$15o!
It might be possible to find something like this which also has adjustable width - using a mechanism to lengthen the front and shorten the back by sending waves to do the job. The front seems easy enough (using B3a4a/S3a4a5i6a7c8) and a simple wave for the back uses B3j/S3a5i6a7c8, so this idea might be feasible.

Code: Select all

x = 7, y = 16, rule = B3aj4a/S3a4ar5i6a7c8
b5o$b5o$b5o$b5o$b5o$b5o$ob5o$2b5o$2b5o$ob5o$b5o$b5o$b5o$b5o$b5o$b5o!
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

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Saka
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Re: Rules with small adjustable spaceships

Post by Saka » May 21st, 2020, 4:27 am

5-cell adjustable wick ships, which also shows that 4-cell adjustable ships probably exist (although I haven't been able to find one, has one been found yet?), and maybe even 3 cells if we get lucky.

Code: Select all

x = 20, y = 27, rule = B2cei3ckqy4acejkt5-ir6-ce/S012ik3-cek4entyz5iknqr6-ck7e
2bo$2o4bo$2bo6$2bo$2o5bo$2bo6$2bo$2o9bo$2bo6$2bo$2o17bo$2bo!
Speed for a ship with gap of size n = 7+3n

EDIT:
A tad off topic, but
The minimum rule for those is non-explosive (apgsearchable) and has a small c/4d

Code: Select all

x = 4, y = 4, rule = B2cei3qy4aet5y/S012ik3-cekr4ent5ir6i7e
obo$o2bo2$2b2o!
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Re: Rules with small adjustable spaceships

Post by Saka » June 15th, 2020, 2:36 am

A new type of adjustable ships that is also slope-adjustable and size-adjustable.
Demonstration of speed and size adjustability

Code: Select all

x = 25, y = 57, rule = B2-ai3j4acqrwz5cenqr6ai7/S1e2-ae3akr4aeijkt5ceiny6aci78
18b3o$15bo2b5o$18b5o$16b5obo$16bob3obo$16bob4o$17b4o6$12b9o$12b9o$12b
9o$12b9o$11bob8o$11bob8o$11b10o$13b8o$10bo2b9o$13b8obo$13b8obo$13b10o$
13b8o$13b9obo$13b9o4$2b20o$2b20o$2b20o$2b20o$2b20o$2b20o$2b20o$2b20o$
2b20o$2b20o$2b20o$2b20o$2b20o$2b20o$2b20o$2b20o$2b20o$2b20o$2b20o$2b
20o$bob20o$bob19obo$b21obo$3b21o$o2b19o$3b20obo$3b20o!
M̶a̶x̶i̶m̶u̶m̶ ̶s̶p̶e̶e̶d̶ ̶i̶s̶ ̶2̶c̶/̶1̶2̶o̶,̶ (see edit below) and covered speeds are 2c/2(n-1) where n is the ship's "width" (So for example, a width 23 ship would be a 2c/2(23-1) = 2c/44o ship:

Code: Select all

x = 23, y = 8, rule = B2-ai3j4acqrwz5cenqr6ai7/S1e2-ae3akr4aeijkt5ceiny6aci78
bo$3b3o$2obo2bo$23o$23o$2bo2b18o$2b3o$o!
However... it is also slope-adjustable.
Here are three other slopes, a 2c/52d, (2,4)c/102, and (2,6)c/150 found by AforAmpere.

Code: Select all

x = 189, y = 32, rule = B2-ai3j4acqrwz5cenqr6ai7/S1e2-ae3akr4aeijkt5ceiny6aci78
27bo64bo$23b3o62b3o92bo$22bo2bob2o58bo2bob3o84b3o$3b26o14b52o83bo2bob
3o$o2b26o14b52o16b75o$3b26o14b52o16b75o$b28o14b52o16b75o$bob26o14b52o
16b75o$bob26o14b52o16b75o$2b27o14b52o16b75o$2b27o14b52o13bo2b75o$2b27o
11bo2b52o16b75o$2b27o14b52o14b77o$2b27o12b54o14bob75o$2b27o12bob52o14b
ob75o$2b27o12bob53o14b76o$2b27o13b53obo13b76o$2b27o13b53obo13b77o$2b
27o13b55o13b76obo$2b27o13b53o15b76obo$2b27o13b54obo12b78o$2b27o13b54o
14b76o$2b28o12b54o14b77obo$2b27obo11b54o14b77o$2b27obo11b54o14b77o$2b
29o11b54o14b77o$2b27o13b54o14b77o$2b28obo10b54o14b77o$2b28o12b54o14b
77o$7bo2b20o43bo2b20o20bo2b68o$7b3o63b3o40b3o$5bo65bo42bo!
EDIT: It can go to 2c/10o

Code: Select all

x = 9, y = 6, rule = B2-ai3j4acqrwz5cenqr6ai7/S1e2-ae3akr4aeijkt5ceiny6aci78
3b4o$3b4o$3b4obo$obob4o$3b5o$4b3o!
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Saka
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Re: Rules with small adjustable spaceships

Post by Saka » July 23rd, 2020, 9:37 am

So I was rulegolfing earlier today, no real goal set in mind, maybe find some cool but ultimately useless amoeba-ships, as usual...
I arrived upon this rule and apgsearched it, and found 3 natural ships in C1...

Code: Select all

x = 20, y = 20, rule = B2ci3-i4cit5-i6-i78/S3a4t5678
obo$obobo11b3o$6o10b4o$b6o9b4o$6o10b4o$8o8b3o$2b4o$2b2ob3o3$10bo3bo$
11b2o3bo$10b8o$10b9o$10b8o$11b7obo$10b8o$10b9o$12b7o$12b2ob3obo!
Hold on, take a close look on those 2 diagonals...
it's adjustable!

Code: Select all

x = 85, y = 82, rule = B2ci3-i4cit5-i6-i78/S3a4t5678
o3bo$b2o3bo$6o$6obo$6o$b6o$7o$2ob3obo4$10b3o3bo$10b5o3bo$10b8o$11b7obo
$10b8o$10b9o$10b9o$11b9o$10b10o$10b2ob3ob3o9$26bob3o3bo$27b6o3bo$26b
10o$26b10obo$26b10o$27b10o$26b11o$26b12o$26b12o$27b11o$26b11o$26b2ob3o
b3obo8$44b3ob3o3bo$44b9o3bo$44b12o$45b11obo$44b12o$44b13o$44b13o$45b
13o$44b14o$44b14o$44b13o$45b13o$44b14o5b3ob3ob3ob3o3bo$44b2ob3ob3ob3o
5b17o3bo$63b20o$64b19obo$63b20o$63b21o$63b21o$64b21o$63b22o$63b22o$63b
21o$64b21o$63b22o$63b22o$63b21o$64b21o$63b22o$63b22o$63b21o$64b21o$63b
22o$63b2ob3ob3ob3ob3ob3o!
Speeds available: (1,1)c/(9+4n) for all integer n>0

===
Those ships can have an extra little bit at the back, that makes them... a bit more wobbly, I guess.

Code: Select all

x = 86, y = 83, rule = B2ci3-i4cit5-i6-i78/S3a4t5678
bo3bo$2b2o3bo$b6o$b6obo$b6o$2b6o$b7o$b2ob3obo$o3$11b3o3bo$11b5o3bo$11b
8o$12b7obo$11b8o$11b9o$11b9o$12b9o$11b10o$11b2ob3ob3o$10bo8$27bob3o3bo
$28b6o3bo$27b10o$27b10obo$27b10o$28b10o$27b11o$27b12o$27b12o$28b11o$
27b11o$27b2ob3ob3obo$26bo7$45b3ob3o3bo$45b9o3bo$45b12o$46b11obo$45b12o
$45b13o$45b13o$46b13o$45b14o$45b14o$45b13o$46b13o$45b14o5b3ob3ob3ob3o
3bo$45b2ob3ob3ob3o5b17o3bo$44bo19b20o$65b19obo$64b20o$64b21o$64b21o$
65b21o$64b22o$64b22o$64b21o$65b21o$64b22o$64b22o$64b21o$65b21o$64b22o$
64b22o$64b21o$65b21o$64b22o$64b2ob3ob3ob3ob3ob3o$63bo!
c/9d and c/13d's can have some period-specific "adornments" at the back as well

Code: Select all

x = 54, y = 13, rule = B2ci3-i4cit5-i6-i78/S3a4t5678
2bo3bo13b3o3bo17b3o3bo$3b2o3bo11b5o3bo15b5o3bo$2b6o12b8o16b8o$2b6obo
11b7obo15b7obo$2b6o12b8o16b8o$b8o11b9o15b9o$2b7o11b9o13bob9o$b7obo9b
11o13b11o$3obo14b11o12b12o$2o16b8ob3o11b9ob3o$19b4o18b6o$20bo21b4obo$
41bob2o!
===
I believe this is the first rule with adjustable ships that was found without the initial intention of finding adjustable ships. Unfortunately you'll have to take my word for it :P , but here are some things to consider before deciding that I just did an LLS search:
1. The surface of the square is period 2
2. The corners are period 4, with the back corners being different than the side corners
3. The ship requires 3 different signals to work and 3 different reactions, too
3a. And the signals aren't exactly normal like in my adjustable ships above this post. In this one, one signal adds on 2 cells and one removes one layer.
4. This rule is only 10 transitions away from Diamoeba (my usual starting point for rulegolfing)
Currently taking a little break, but still hanging around on the Discord server.
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silversmith
Posts: 80
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Re: Rules with small adjustable spaceships

Post by silversmith » July 31st, 2020, 10:36 am

Here is a non-explosive rule with spaceships of speeds 2c/2n, n>6, using a wick perpendicular to the direction of movement.

Code: Select all

x = 81, y = 3, rule = 1e2iack3ar/2iec3j4w
3o4b4o4b5o4b6o4b7o4b8o4b9o4b10o$3bo7bo8bo9bo10bo11bo12bo13bo$2bo7bo8b
o9bo10bo11bo12bo13bo!

kiho park
Posts: 65
Joined: September 24th, 2010, 12:16 am

Re: Rules with small adjustable spaceships

Post by kiho park » August 3rd, 2020, 7:16 am

After few days of LLS searching, I found new type of adjustable spaceship using c2o wickstretcher and a c2o spaceship.
If following spaceship hits the tail of the wickstretcher, then chasing spaceship is delayed and the line wickstretcher start to burning while the "fire" reach to the front of wickstretcher then wickstretcher delayed too.

Delaying an 1 generation for every collision, speed is (12+2*n)c/(25+4*n) for n>=0

Code: Select all

x = 13, y = 35, rule = B2ce3akqry4aekwyz5-jr6ce7e8/S12aik3-aikr4acnqty5ejnry6ace7c
4bo7bo$4b2o4b2o$4bo7bo6$3bo8bo$3b2o5b2o$3bo8bo6$2bo9bo$2b2o6b2o$2bo9bo
6$bo10bo$b2o7b2o$bo10bo6$o11bo$2o8b2o$o11bo!
Delaying 2 generations for every collisions, speed is (8+2*n)c/(18+4*n) for n >= 0

Code: Select all

x = 22, y = 99, rule = B2-ak3acn4-ktwy5-kqr7c/S12aik3ekny4akrtz5ny6acn7
12b2o6bo$12bo4b3obo$12b2o6bo6$11b2o7bo$11bo5b3obo$11b2o7bo6$10b2o8bo$
10bo6b3obo$10b2o8bo6$9b2o9bo$9bo7b3obo$9b2o9bo6$8b2o10bo$8bo8b3obo$8b
2o10bo6$7b2o11bo$7bo9b3obo$7b2o11bo6$6b2o12bo$6bo10b3obo$6b2o12bo6$5b
2o13bo$5bo11b3obo$5b2o13bo6$4b2o14bo$4bo12b3obo$4b2o14bo6$3b2o15bo$3bo
13b3obo$3b2o15bo6$2b2o16bo$2bo14b3obo$2b2o16bo6$b2o17bo$bo15b3obo$b2o
17bo6$2o18bo$o16b3obo$2o18bo!
I also trying to find other adjustable spaceships advancing or shifting instead of delaying them or using other speed such as c3o, c4o, c5o, 2c5 and 2c3o or faster speeds.
Furthermore, I'll also try diagonal or oblique design if possible.
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

wildmyron
Posts: 1518
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: Rules with small adjustable spaceships

Post by wildmyron » August 3rd, 2020, 10:08 am

wildmyron wrote:
May 12th, 2020, 8:47 am
muzik wrote:
August 5th, 2019, 9:16 am
Have all orthogonal speeds 3c/n been proven yet?
As mentioned by "2718281828", they're definitely possible, but I don't think anyone has posted a set covering all periods here. I vaguely recall I even had some search results aiming to achieve that result, but I never completed them or posted them here.
Here's a full set covering all periods. They all use the push-reflect + pull-reflect mechanism with a small c/2 ship and SL reflectors. They were discovered some months ago and originally posted to the ConwayLife Discord server on 2020-05-30.

(3,0)c/(4n), p(4n); n>=6 - 3c/24

Code: Select all

x = 11, y = 3, rule = B2cen3jkr4-knqty5-cein6ac78/S01c2in3ajry4-jkwyz5-acik6aik8
2o2b2o$2obobo4bo$4b2o!
(3,0)c/(4n+1), p(4n+1); n>=6 - 3c/25

Code: Select all

x = 11, y = 3, rule = B2cin3-cej4aciz5-cjry6kn7/S01e2ain3cjkr4aknr5-eikn6ak78
o2bo$ob2o6bo$3bo!
(3,0)c/(4n+2), p(4n+2); n>=4 - 3c/18 (Uses the same SL for push and pull)

Code: Select all

x = 11, y = 3, rule = B2-ak3ery4ackqr5jnqy6cek8/S01c2aei3-acr4-atwz5akqr6ckn7e8
bo2b2o4bo$2obobo3b2o$bo2b2o4bo!
(3,0)c/(4n+3), p(4n+3); n>=5 - 3c/23

Code: Select all

x = 11, y = 3, rule = B2ck3-knqr4acknw5jkq6-ek78/S1e2eik3-aejn4inqrtw5knqry6e7e
3bo$ob2o5b2o$o2bo!
These were all found with LLS. The searches didn't take too long to run - once the actual search file had been set up (which is a bit tedious). It also took a bit of trial and error to find the right reaction times for the searches to start giving results. I haven't tried to optimise for reaction speed and space so it's possible that there are 3c/p adjustable saceships for p(4n) and p(4n+1) which have lower minimum periods.

I considered extending this further, but it starts to get trickier for higher displacements because it just physically takes longer for the reaction to shift the SL the required number of cells and reform the reflected spaceship (particularly for the pull where the ship has to form a long way in front of where the reaction initially occurs). I expect 5c/N would be doable with LLS, but I'm not sure how far that idea can be pushed. A better idea IMO is to find a mechanism with adjustable displacement. It just so happens that my earlier post regarding antiphotons in a box suggests a method to find precisely such a mechanism. Expect a follow-up post on this topic in a day or two.
kiho park wrote:
August 3rd, 2020, 7:16 am
After few days of LLS searching, I found new type of adjustable spaceship using c2o wickstretcher and a c2o spaceship.
If following spaceship hits the tail of the wickstretcher, then chasing spaceship is delayed and the line wickstretcher start to burning while the "fire" reach to the front of wickstretcher then wickstretcher delayed too.

<snip>

I also trying to find other adjustable spaceships advancing or shifting instead of delaying them or using other speed such as c3o, c4o, c5o, 2c5 and 2c3o or faster speeds.
Furthermore, I'll also try diagonal or oblique design if possible.
This is a very nice idea and great to see it working with such a simple design. You've prompted me to make this post which has been in draft form for some time now - all the spaceships here have been previously posted to the ConwayLife Discord server, but I never got around to posting them here.

In particular there has been a fair bit of discussion about adjustable spaceships with speeds > c/2 on the Discord server. After unsuccessful exploration of several proposed designs by A for Awesome, AforAmpere, myself and others; I found this solution where a c/2 diagonal bounces between two c/2 orthogonal ships and the phase of each is advanced with each bounce (prompted by a discussion with AforAmpere):

(n+1)c/(2n+1), p(4n+2), n>=3, 19 cells (discovered 2020-06-22)

Code: Select all

x = 8, y = 57, rule = B2ac3aekqy4ent5y6ae8/S12n3-ai4aeijn5ae6n7e
4bo$6bo$3b3o$6bo$4bo2$2bobo$4bo$o4bo2$2bo2$4bobo$o2bob3o$4bobo6$4bo$6b
o$3b3o$6bo$4bo2$2bobo$4bo$5bo5$4bobo$3bob3o$4bobo5$4bo$6bo$3b3o$6bo$4b
o2$2bobo$4bo$5bo6$4bobo$3bob3o$4bobo!
The resulting family of spaceships all have speed c/2 < v <= 4c/7. I called this reaction a bounce+nudge. Another idea I tried was a bounce shift - where the bounce reaction produces a lane shift in the orthogonal ship (no phase change). A for Awesome originally proposed this idea and found component reactions (bounce+push and bounce+pull) at c/3, but not both in a single rule. I tried the same idea at c/2 and was also able to find component reactions but the combined search was ultimately unsuccessful. I also tried the idea at 2c/3 with a p3 knightship (before I tried c/2) and managed to find a bounce+pull, but couldn't even find a bounce+push let alone both in a single rule.

Explosive, paired bounce+pull reaction at 2c/3 (discovered 2020-06-27):

Code: Select all

x = 5, y = 20, rule = B2aci3cejy4jnyz5ejq7c8/S12ci3cknqr4cikntz5aeqr6ein7c
o2bo$2b2o$bobo5$bobo$2bobo$5o$bo2bo7$bobo$2b2o$o2bo!
However, I had been able to find adjustable period 2c/3 spaceships which just require a single bounce reaction:

2c/3, p(6n), n>=3 (discovered 2020-06-23)

Code: Select all

x = 13, y = 59, rule = B2aci3cejy4ejn5ajq6aek78/S12cn3-aeiy4ikntyz5-cikq6n
12bo$10bo$9bo2bo$10bo3$9bobo$10bobo$3bo4b5o$6bo2bo2bo3$8bobo$obo4bobo
2bo$b4o3bobo$2b4o6bo5$12bo$10bo$9bo2bo$10bo3$9bobo$10bobo$8b5o$9bo2bo
4$10bo$9bo2bo$10bo$12bo5$12bo$10bo$9bo2bo$10bo3$9bobo$10bobo$8b5o$9bo
2bo5$10bo$9bo2bo$10bo$12bo!
There were several other similar results found with slight variations of this search:

Same ships, different reaction

Code: Select all

x = 5, y = 16, rule = B2aci3cejy4eijn5aj6aei7c/S12cn3-eiy4ikntz5-cjky6-ac7c8
4bo$2bo$bo2bo$2bo3$bobo$2bobo$5o$bo2bo3$2bo$bo2bo$2bo$4bo!
Different ships

Code: Select all

x = 5, y = 16, rule = B2acn3ej4ceinwyz5ikqry6acn7e/S01e2-ae3kn4eiknq5ejny6ikn7
bobo$obo$bobo4$bobo$4bo$3b2o$4bo4$bobo$obo$bobo!
One other, earlier, failed attempt at finding adjustable > c/2 spaceships was bouncing a photon between two orthogonal c/2 spaceships, nudging forward at each reflection. Here's a bounce+push reaction found 2020-06-14:

Code: Select all

x = 12, y = 16, rule = B2-in3ceik4cjkqrt5aqy6-ci7c8/S2cen3ceiny4aeiktyz5knqy6ci78
10bo$9bo$8b2obo$9bo$10bo7$10bo$2bo6bo$obo5b2obo$2bo6bo$10bo!
I'm sure that I found a corresponding bounce+pull reaction but I don't have an example to hand. I was definitely unable to find a pair of reactions which worked in a single rule.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

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LaundryPizza03
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Re: Rules with small adjustable spaceships

Post by LaundryPizza03 » August 4th, 2020, 12:16 am

c/3 ships with period 6n for all n≥2:

Code: Select all

x = 3, y = 49, rule = B3aijn4aeiky5eiy6-ei78/S2-an3-ekny4cjqw5ij6ci
2o$b2o$2o2$o$2o$b2o3$2o$b2o$2o6$2o$b2o$2o2$o$2o$b2o4$2o$b2o$2o6$2o$b2o
$2o2$o$2o$b2o5$2o$b2o$2o!

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!
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The latest edition of new-gliders.db.txt and oscillators.db.txt have 31531 spaceships and 1293 oscillators from outer-totalistic rules. You are invited to help!

kiho park
Posts: 65
Joined: September 24th, 2010, 12:16 am

Re: Rules with small adjustable spaceships

Post by kiho park » August 4th, 2020, 4:26 am

wildmyron wrote:
August 3rd, 2020, 10:08 am
(n+1)c/(2n+1), p(4n+2), n>=3, 19 cells (discovered 2020-06-22)

Code: Select all

x = 8, y = 57, rule = B2ac3aekqy4ent5y6ae8/S12n3-ai4aeijn5ae6n7e
4bo$6bo$3b3o$6bo$4bo2$2bobo$4bo$o4bo2$2bo2$4bobo$o2bob3o$4bobo6$4bo$6b
o$3b3o$6bo$4bo2$2bobo$4bo$5bo5$4bobo$3bob3o$4bobo5$4bo$6bo$3b3o$6bo$4b
o2$2bobo$4bo$5bo6$4bobo$3bob3o$4bobo!
The resulting family of spaceships all have speed c/2 < v <= 4c/7. I called this reaction a bounce+nudge. Another idea I tried was a bounce shift - where the bounce reaction produces a lane shift in the orthogonal ship (no phase change). A for Awesome originally proposed this idea and found component reactions (bounce+push and bounce+pull) at c/3, but not both in a single rule. I tried the same idea at c/2 and was also able to find component reactions but the combined search was ultimately unsuccessful. I also tried the idea at 2c/3 with a p3 knightship (before I tried c/2) and managed to find a bounce+pull, but couldn't even find a bounce+push let alone both in a single rule.
That's awesome :) I also imagined and tried that design using two c2 diagonal spaceships and a c1 orthogonal spaceship but I couldn't get any satisfiable result.

LaundryPizza03 wrote:
August 4th, 2020, 12:16 am
c/3 ships with period 6n for all n≥2:

Code: Select all

x = 3, y = 49, rule = B3aijn4aeiky5eiy6-ei78/S2-an3-ekny4cjqw5ij6ci
2o$b2o$2o2$o$2o$b2o3$2o$b2o$2o6$2o$b2o$2o2$o$2o$b2o4$2o$b2o$2o6$2o$b2o
$2o2$o$2o$b2o5$2o$b2o$2o!
I used c3o and c3d used in your pattern instead of c2o and c2d, and I got this result.
Speed : (6+2*n)c/(16+6*n)

Code: Select all

x = 43, y = 17, rule = B3-kqry4-nqt5-aceq6-ae7c/S2cek3acijr4cnqtwz5aj6an78
2o6b2o6b2o6b2o6b2o6b2o$b2o6b2o6b2o6b2o6b2o6b2o$2o6b2o6b2o6b2o6b2o6b2o
2$40bo$o7bo7bo7bo7bo7b2o$2o6b2o6b2o6b2o6b2o7b2o$b2o6b2o6b2o6b2o6b2o2$
41b2o$33b2o5bobo$25b2o5bobo6b2o$17b2o5bobo6b2o$9b2o5bobo6b2o$b2o5bobo
6b2o$obo6b2o$b2o!

Edit : Here is faster design with speed of (12 + 2*n)c/(32 + 6*n), n>=0
n=0 means the minimal design, not the interval between two orthogonal spaceships.

Code: Select all

x = 28, y = 15, rule = B3-enry4-aktyz5-akry6aci78/S2-an3acijr4jnrwyz5aijn6-i7e
2bo7bo7bo7bo$2obo4b2obo4b2obo4b2obo$2bo7bo7bo7bo2$3o5b3o5b3o5b3o$2bo7b
o7bo7bo$obo5bobo5bobo5bobo3$26b2o$18b2o5bobo$10b2o5bobo6b2o$2b2o5bobo
6b2o$bobo6b2o$2b2o!
Edit : Nope. It crashes.

Code: Select all

x = 40, y = 15, rule = B3-enry4-aktyz5-akry6aci78/S2-an3acijr4jnrwyz5aijn6-i7e
2bo11bo11bo11bo$2obo8b2obo8b2obo8b2obo$2bo11bo11bo11bo2$3o9b3o9b3o9b3o
$2bo11bo11bo11bo$obo9bobo9bobo9bobo3$38b2o$26b2o9bobo$14b2o9bobo10b2o$
2b2o9bobo10b2o$bobo10b2o$2b2o!
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

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LaundryPizza03
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Re: Rules with small adjustable spaceships

Post by LaundryPizza03 » August 4th, 2020, 11:55 am

kiho park wrote:
August 4th, 2020, 4:26 am
I also imagined and tried that design using two c2 diagonal spaceships and a c1 orthogonal spaceship but I couldn't get any satisfiable result.
What are the largest ships you tried (e.g. 4*4 photon and 4*4 c/2d?)
kiho park wrote: Edit : Nope. It crashes.

Code: Select all

x = 40, y = 15, rule = B3-enry4-aktyz5-akry6aci78/S2-an3acijr4jnrwyz5aijn6-i7e
2bo11bo11bo11bo$2obo8b2obo8b2obo8b2obo$2bo11bo11bo11bo2$3o9b3o9b3o9b3o
$2bo11bo11bo11bo$obo9bobo9bobo9bobo3$38b2o$26b2o9bobo$14b2o9bobo10b2o$
2b2o9bobo10b2o$bobo10b2o$2b2o!
Try lining up the spaceships sideways. It's clearer that way.

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!
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The latest edition of new-gliders.db.txt and oscillators.db.txt have 31531 spaceships and 1293 oscillators from outer-totalistic rules. You are invited to help!

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LaundryPizza03
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Re: Rules with small adjustable spaceships

Post by LaundryPizza03 » August 4th, 2020, 8:07 pm

c/4, p(8n), n≥2

Code: Select all

x = 3, y = 45, rule = B2cei3ceiy4ceinrt5-cinr6ak/S12-kn3cijq4cejyz5ekqr6-ei7c8
2bo$3o$2bo2$b2o2$2bo3$2bo$3o$2bo4$2bo$3o$2bo2$b2o2$2bo4$2bo$3o$2bo4$2b
o$3o$2bo2$b2o2$2bo5$2bo$3o$2bo!
Another c/3, p(6n), n≥2

Code: Select all

x = 3, y = 45, rule = B2ckn3aeqry4aeqty5ajnqy6eik/S02ei3jr4anrtw5ejny6cek
o$2bo$o2$o$2o$b2o3$o$2bo$o4$o$2bo$o2$o$2o$b2o4$o$2bo$o4$o$2bo$o2$o$2o$
b2o5$o$2bo$o!
This one requires a bit of explanation. Let N≥1. This family of spaceships consists of two parallel 10c/20 diagonal puffers whose tracks are offset by 5N cells in the direction perpendicular to travel. 2N photons bounce back and forth between the two tracks, deleting the puffers’ output as they do so. The resulting spaceship has period 20N.

Code: Select all

x = 124, y = 74, rule = B2aci3cin4ejnrw5a6akn/S12-ak3ejnr4ajnrtwz5aeijk6ain78
19bo29bo39bo29bo$20b2o28b2o38b2o28b2o$20b3o27b3o37b3o27b3o$19bob2o26bo
b2o36bob2o26bob2o$20bo2bo26bo2bo36bo2bo26bo2bo3$14bo29bo39bo29bo$15bo
29bo39bo29bo$16bo29bo39bo29bo$19bo39bo$20b2o38b2o$9bo10b3o16bo4b3o13b
3o23bo22bo$10bo8bob2o17bo4bo13bob2o22b2o23bo$11bo8bo2bo17bo18bo2bo22bo
24bo3$4bo4b3o2bo19bo19bo19bo29bo$5bo4bo4bo19bo19bo19bo29bo$6bo9bo19bo
19bo19bo29bo3$34b3o9bo2bo19bo29bo$35bo9b2o3bo19bo29bo$46bo4bo19bo29bo
3$bo2bo59bo29bo$2o3bo59bo29bo$bo4bo59bo29bo3$36bo2bo26bo17b3o2bo$35b2o
3bo24b2o18bo4bo$36bo4bo24bo24bo13$44bo29bo$45bo29bo$46bo29bo3$46bo17b
3o2bo$45b2o18bo4bo$46bo24bo18$44b3o$45bo!

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!
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The latest edition of new-gliders.db.txt and oscillators.db.txt have 31531 spaceships and 1293 oscillators from outer-totalistic rules. You are invited to help!

lemon41625
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Re: Rules with small adjustable spaceships

Post by lemon41625 » October 20th, 2020, 6:57 am

Not really ships but whatever...

Code: Select all

x = 86, y = 82, rule = R2,C0,S15-28,B9-11,17-28,NW0010003330130310333000100
14b3o$11b6o$12b7o$10b9o$10b11o$8b13o$8b13o$7b13o$7b13o$5b13obo$5b13o$
3b13o$3b13o11b3o$b13o10b6o$b11o13b7o$b11o11b9o$10o13b11o$2b8o11b13o$2b
6o13b15o$4b4o12b16o$4bo15b18o$18b20o$18b20o$16b21o$16b21o$14b21obo$14b
21o$14b19o$13b20o12b3o$15b16o11b6o$15b14o14b7o$17b12o12b9o$17b10o14b
11o$19b8o12b13o$19b6o14b15o$21b4o13b16o$21bo16b18o$36b20o$36b22o$34b
24o$34b26o$32b28o$32b28o$32b27o$31b28o$33b24obo$33b24o$35b20o$35b20o$
37b16o14b3o$37b14o13b6o$39b12o14b7o$39b10o14b9o$41b8o14b11o$41b6o14b
13o$43b4o14b15o$43bo16b16o$60b18o$58b20o$58b22o$56b24o$56b26o$54b28o$
54b30o$54b30o$53b33o$55b31o$55b31o$57b28o$57b28o$59b24obo$59b24o$61b
20o$61b20o$63b16o$63b14o$65b12o$65b10o$67b8o$67b6o$69b4o$69bo!
I believe this is the 1st HROT rule with adjustable things. Can someone find a suitable backend to make it a ship?

I also found this rule without the intention of finding adjustable wickstrechers.
If you don't want to take my word for it, consider the fact that no search programs for LtL / HROT support partial rules.
Download CAViewer: https://github.com/jedlimlx/Cellular-Automaton-Viewer

Supports:
BSFKL, Extended Generations, Regenerating Generations, Naive Rules, R1 Moore, R2 Cross and R2 Von Neumann INT
And some others...

wwei23

Re: Rules with small adjustable spaceships

Post by wwei23 » October 21st, 2020, 12:18 am

I tried to make one of these as a challenge, here's a simple c/(2n+1) diagonal adjustable ship. Fastest is c/7 diagonal (n=3).

Code: Select all

x = 50, y = 50, rule = B2in3acij4enq5a6ce/S01c2n3cjn4ciq5ay6e
2bo9bo9bo9bo9bo$b2o8b2o8b2o8b2o8b2o$3o7b3o7b3o7b3o7b3o$3bo9bo9bo9bo9bo
$5bo8bo9bo9bo9bo$4bo11bo8bo9bo9bo$15bo11bo8bo9bo$26bo11bo8bo$37bo11bo$
48bo11$2bo$b2o$3o$3bo$4bo$5bo$6bo$7bo$8bo$9bo$10bo$11bo$12bo$13bo$14bo
$15bo$16bo$17bo$18bo$19bo$20bo$21bo$22bo$23bo$24bo$25bo$26bo$27bo$29bo
$28bo!
I also tried fixed speed but adjustable period, here is nc/2n, minimum period 16 (n=8).

Code: Select all

x = 70, y = 13, rule = B2ci3aenr4ajnqr5ainq/S12kn3aen4jy5ci6a8
5bo19bo18bo19bo$bo2b3o14bo2b3o16b3o2bo14b3o2bo$3o4bobo10b3o4bobo10bobo
4b3o10bobo4b3o$4b2o2bo15b2o2bo12bo2b2o15bo2b2o$4b2o18b2o18b2o18b2o3$ob
o4bobo51bo6bo$bo6bo51b3o4b3o3$20bobo4bobo11bo6bo$21bo6bo11b3o4b3o!
EDIT: The minimum population for the second set of ships is 20 if n is odd and 21 if n is even.
I'd like to see a version where the back "helper" ships get pushed back by 1 cell so that we have something that slows down over time LOL

AforAmpere
Posts: 1215
Joined: July 1st, 2016, 3:58 pm

Re: Rules with small adjustable spaceships

Post by AforAmpere » November 13th, 2020, 9:55 am

C/(11+4n), n>1:

Code: Select all

x = 35, y = 17, rule = B2ce3aj4t5i6i7e/S12cik3ejr4i5iy7e
o$7o$o5$o$33o$o5$o$35o$o!
C/(10+4n), n>1:

Code: Select all

x = 35, y = 17, rule = B2ce3aj4t5i6ci7e/S12cik3ejr4i5iy7e
o$7o$o5$o$33o$o5$o$35o$o!
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

muzik
Posts: 3962
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Rules with small adjustable spaceships

Post by muzik » November 14th, 2020, 12:24 pm

Quoting from another thread for completion's sake:
FWKnightship wrote:
June 19th, 2020, 6:27 am
c/29+6n:

Code: Select all

x = 18, y = 37, rule = B2cek3aiq4aekntw5ciny6c7e/S02c3enr4acz5ijy6ci
o2bobob2o4bo9$o2bobob2o5bo9$o2bobob2o6bo9$o2bobob2o7bo9$o2bobob2o8bo!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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