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Rules with small adjustable spaceships

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Re: Rules with small adjustable spaceships

Postby nolovoto » February 11th, 2019, 4:16 pm

I discovered a rule: g3b34s3-i4-i5-ak

Most of the spaceships share the same period and are made from a similar structure.

a single haul ended up uncovering 11 different spaceships (one is not shown)
x = 44, y = 66, rule = 3-i4-i5-ak/34/3
$22.BA$22.3A$21.B.2A$18.B.A2.2A$19.6A$21.BA4$21.BA$9.B2A7.B4A$9.AB2A
5.B2A.2A$8.B2.BA9.2A$8.4A8.B3A$7.B2.2A9.A$7.B.2A$8.3A4$21.3A$20.B.2A$
7.BA8.B.A2.2A$5.B3A9.6A$7.B2A8.BA.BA$5.BA.BA$5.A.4A$5.B2A2.A$6.AB.2A
9.B2A$8.3A9.AB2A$17.ABA.B2A$17.B5A$19.BA5$7.BA11.3A$7.3A9.B.2A$6.B.2A
9.B.2A$7.A.2A9.3A$7.BA.A9.BA$7.B.2A$8.3A$8.BA11.B$20.3A$19.B.2A$19.B.
2A$20.3A$21.B3$21.B$20.3A$19.B.2A$20.A.2A$20.B3A$20.A2.BA$21.4A$20.B.
BA$20.AB2A$20.B2A!


I call it tanksntowers
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Re: Rules with small adjustable spaceships

Postby muzik » February 11th, 2019, 4:28 pm

nolovoto wrote:I discovered a rule: g3b34s3-i4-i5-ak

Most of the spaceships share the same period and are made from a similar structure.

a single haul ended up uncovering 11 different spaceships (one is not shown)

I call it tanksntowers

So what part of this rule, exactly, allows the speed and/or slope of the spaceships to be modified to an infinite different amout of unique slopes/speeds?
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Re: Rules with small adjustable spaceships

Postby 77topaz » February 11th, 2019, 7:14 pm

Yeah, those aren't adjustable spaceships.
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Re: Rules with small adjustable spaceships

Postby nolovoto » February 11th, 2019, 7:29 pm

oh sorry
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Re: Rules with small adjustable spaceships

Postby 2718281828 » February 19th, 2019, 11:59 am

A simple class of adjustable ships:
x = 43, y = 56, rule = B2ac3-aeqy4cjnyz5-ciky6aei7e/S12eik3-cij4-aeknw5-ckny6ae7e
2$38bo$39bo$37b4o$38bo6$38bo$37b4o$39bo$38bo5$38bo$39bo$37b4o$38bo7$3b
o5bo$2b3o3bo14bo14bo$15bo6b3o12b4o$14b3o22bo$38bo2$24bo$14b3o6bo$15bo$
38bo$39bo$37b4o$38bo10$38bo$37b4o$39bo$38bo!

I am not sure if adjustable slope ships are possible in this rule.
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Re: Rules with small adjustable spaceships

Postby Moosey » February 19th, 2019, 1:00 pm

2718281828 wrote:A simple class of adjustable ships:
x = 43, y = 56, rule = B2ac3-aeqy4cjnyz5-ciky6aei7e/S12eik3-cij4-aeknw5-ckny6ae7e
2$38bo$39bo$37b4o$38bo6$38bo$37b4o$39bo$38bo5$38bo$39bo$37b4o$38bo7$3b
o5bo$2b3o3bo14bo14bo$15bo6b3o12b4o$14b3o22bo$38bo2$24bo$14b3o6bo$15bo$
38bo$39bo$37b4o$38bo10$38bo$37b4o$39bo$38bo!

I am not sure if adjustable slope ships are possible in this rule.

Those don’t need bilateral symmetry:
x = 3, y = 27, rule = B2ac3-aeqy4cjnyz5-ciky6aei7e/S12eik3-cij4-aeknw5-ckny6ae7e
bo$2bo17$3o$bo2$bo$3o3$2bo$bo!


Well behaved at first:
x = 24, y = 22, rule = B2ac3-aeqy4cjnyz5-ciky6aei7e/S12eik3-cij4-aeknw5-ckny6ae7e
bo7bo7bo4bo$o8b2o5b2o5bo$9bo7bo10$21b3o$22bo2$22bo$21b3o4$23bo$22bo!


A variant of a different rule by aforampere:
x = 30, y = 12, rule = B2ce3a5y7e8/S01c2-e3-i4-c5-r6-c7c8
2o$bo$bob27o$bob26o$bob27o$bo$2o3$22b8o$23b6o$23b7o!

(The top is a methuselah)

Short “codes” tend to stop spontaneously:
x = 6, y = 4, rule = B2ce3a5y7e8/S01c2-e3-i4-c5-r6-c7c8
b5o$b4o$b5o$o!


And a variant with “fake loops”.
x = 14, y = 10, rule = B2ce3a5y6aci78/S01c2-e3-i4-c56-c7c8
10o$10o$10o$3o4b3o$3o4b3o$3o4b3o$3o4b3o$14o$8ob5o$14o!

I kinda want a loop rule based on this.
Basically there’d be another dead state that can destroy living cells in some extra ways.
Anyways, the rule has fairly nice behavior and is not explosive:
x = 80, y = 62, rule = B2ce3a5y6aci78/S01c2-e3-i4-c56-c7c8
2o2b4o2bo3b2obo2b5o2bo2bo3bo2b4ob11o2bob2obo2b3o3bo2bobobob2o$6b8obo2b
3o2bo5bob4o2bob5ob2obobobo2bobobobob3ob2o2b7o$3b3obo2bo2bobobobo3bo2bo
2bo2bo3b3obo3bobo2b2o2bobobob6obob2obo3b4o$2b3obo5bob2o2b3ob4obo2b2o4b
2obo5b2o3bob4o4b3o5bob2obob3obo$ob2o2bobo4bobo2bobo4bob2o2bobo2b2ob3o
2b3obo2b3obob2o2b3ob3o4b4o2bo$4ob2o2b9ob3o2b2obo3bob2obob3obo3b3o2bobo
b3o2bo2bo5bobob4ob2o$bobobobobo2bo6b3o2b3o4b2o3b2o2b5o2b2obo4b2o2b3o2b
3obo2bo2bobobo$2bo4bob2o4b3o4b2o3bo2b3obobo6bob3o2bob6o4b2o2b3o2b2ob3o
$o3b2o2bo2bo3bo2b4o2b4ob5o2b2ob2obo2b2o2b2ob2obob3obobob5ob2o5bo$5ob2o
bobo3bo2bobo2bob4obo2b2obob5o3b2obobo2bobo2bo6b5obo2b3obo$o2bo2bobo4bo
b3ob2ob4obob2ob4obo3bob2ob5obo2b3obo3bo3b3o2bobo2bobo$2b3ob2o2bo2bob3o
b2o2bo2bo2b4o2b3o2b5obobobo2b3obo3b2o3bob2o2bob2ob3o$bobo2bob2ob2ob2o
4b15o6bo4bobo6bob6o2bo2b2o5b2o2bo$o2bobo4b4obobo4bo3b2o2bobo3bobob3ob
4ob2obobobob2ob2o5bo3b4o2b2o$2b3o2bob2o2bo2b2obobo2bo2b5o3b2ob3ob3o2bo
bob2o4bobo3bo2b3obobobo2bobo$2obobo5b2ob2o5bo2bo3b2ob2obobob2obo4b7o3b
2o4bob4o5b2o4bo$o2bo2b2obobo2b2o4b2o2bob2o3bobo2bo4bob3o2bo3b2obo2b6o
2b4o2bo2bo$b2o3b2obobo2bobo3bobo4bo3b3obo5b3o2bobo2bobo2b6obo3b2obob2o
2b2obo$7bob4o3bobob2ob5o3b2ob4o2bobobo4bob2o2bo6b3obobo5bobo2bo$o6bob
3ob2o2b2obob3o4bo3b3o3bobobobo2bobobob3o2b2obo2b3ob2o2b2o4bo$b2o3bo6b
3ob2o4bo2bobo2b2o4bob3obo2bo3b5obo3bob2obob3ob2o2bo3bo$bo2b2obob6o2bo
3b2ob7ob4ob3o2bo2b6o5bo2b7o3b2obobo2bobo$o3bo2bob2o3bobo2bobob2o6b2ob
4o2bo2bo3bobob2ob4ob2obob2o2bo5b2o2b2o$bo3b2obob4ob3o2b4ob2o3bob4o5b2o
bobo3b3ob3ob6obo3b3ob5obo$2bo5b2o2bobobo2bob2o3bobobo3b2o3b2o2b2ob7obo
2bobo3bob5ob2ob3o2bo$b6ob2ob4ob3o3bob2obobo3bobo3bobobobob3o5bob3obob
8ob3o3bo$2bo4b5obob2o4b2o3b3obob3obo2b2o2b2ob2ob3o3bob2o2bob3ob2obo2b
2o3b2o$2bo2b4o3bo4bo10b2obobo4bobob2o3b3ob2ob2obobob2o3bo2b3o2b2ob2o$
6b2o2bo2b4obob2ob4ob2obobob2obobo2bo3b2ob6ob5o3bo3b2o4b2o$ob3ob2o2b3o
2b3ob6obo3b6ob2ob2o3b4o4b3ob2o2bo2b2o4b3o2b2ob2o$5o3bobo8b3obobo2bo3b
2obo3b2o3bo2bo5b2o3b2o2bo6b4ob2o2bo$3o3bo2bobobo2b2o3b2obo4bobob2obo2b
2obo4b3o2bo2bobo3b3o5bobob4o2bo$bob3o2b3o2bobobob2obo2b5o2bo2bo2bo2bo
4b2o6b2o2b2o5b3o3b3obo$2o3bob2o2b2obo2b4ob6o2bo2b2ob2o2bo4bo5b3o4bo2b
2o2b2ob2o3bobob3o$3ob2ob4ob2o6b4ob2o2bob3ob3o5b2o2b4o2b5obo3b4o2b6o2bo
$3bobob2obo2b2ob2o2bob2ob2o2b3o6bobo4bobo2bobo2bobob3ob3o2b4o5bo$4b2ob
o3bob3obo3bo3bob3o2b2ob2obob2o2b2obo2b6o2b6o5b3obo2bo2bo$ob2obo2b3o6bo
2bo2bobo5b2o2b2ob3o3bo2b3o3bobo3bob7obo4bo2bo$ob2o3b5o3b2obobo2bo2b6ob
o3bobob3obo2bobo2b2o4b3o4bo3b9o$2bo2b4o4bo2b3o2b2o4bo3bobo2bo4b6o2b2o
3bobobob4o5b2obo2b2o$bo3b11obo3bo3b2ob2obo2b5o3bo4b2o7bobo3b4o4b5o3b2o
$bobobo3b3ob6o3b5ob2o2bo2b2o2bobob4ob7o3b3o2bob3o3bo2b2obo$bobo3bob2ob
3o2b5o2b2o3b10o2bob3o3b4o2b3o3b5ob3o2bob2o2bo$2b2o2bo3b3o5bo3b6o2bo2b
3ob3ob4ob3ob3obo2b6o2b2ob2obo2bob2o$obobo3bobobobo3bo3bobo2b2obo3b2ob
6o2bo3b2o2b3o2b3obo2b2o2bo2b8o$b2obo2bo2b2ob2o3b2o5b4obobobo4bob2obo2b
2o2bo2bo4b4o8bo4b3o$bobo2bo2bo7bob3o2bobobo3b3obo4b3ob2o2b3ob2o2bobobo
3b2ob2obob3obo$2b2o4bobo2bo3b3o2bob4o2b2obo2bo2b2ob9ob3ob4ob2o3bo6bo2b
2o$o3b2o2b2o2b2o2b2o2b3obo6bo2bo2b5o2bob2o2bo5b5obo2b2obo3bo3b2o$o2b2o
2b2o2bob2ob2o2b2o3bob3o5bo3b3ob2ob2obo6b3obo2bob2obob5obobo$4b3ob2ob2o
bobobo2bo2bo2b2o2bob6ob2o3b4obo2bobo3b5obo3bo3b7o$4obobo4b3obobo5b2o3b
o5bobob4obo2bobob2o2bob3o2b2obob2obob3o2b3o$ob2obo2bo4bobo7b2o2b6o5bo
7b2ob3o9b7o3b3o$b5o3b3ob3ob2o2b5o2bo3b2ob2o2bobo5b2ob5o2bo2bob2o3b5ob
2o2b2o$o3bobobo5bob2ob2ob5ob2o5bo2b4o2b3obo2b2o5bo4b5o2bobo3bob2o$3b5o
3b2obob2obob2o4bo3bo4b5obo3b4ob4obo2b2o4b2o2bobob3o$o3b2obob2o2bob3ob
2o6bob2o6bo2b2o2bo3b2obob5o2b2obo3bob4obobob2o$ob5obobo2b3o3b2o4b3o5b
4obobobob2ob2o2bo3b2o2bo4bo5bo2b2o2bobo$4obobo2bo6b3o2b2obobo2b5obo2b
4ob3o4bo2bo3b2ob4o3bob3o2b5o$ob5obo2bobobob2obo2bo3b2obo3b4ob3o3b2o4b
2o2b2o2bob2o7bo4b3obo$bobo2b2o2bobobo2b2ob2o3bobo2bobo3b4o5bo3b3o3b4o
3b2o3bob3ob2o4bo$2bo8bo2bo2b5ob2ob3o6bob2o6b6o2bo2bo3bob4ob6obobob2o!


Becomes a solid rectangle:
x = 3, y = 9, rule = B2ce3a5y6aci78/S01c2-e3-i4-c56-c7c8
3o$3o$3o$obo$3o$3o$3o$3o$o!


Sadly, this rule does not have adjustable spaceships. (As far as I can see)

It does have irregular wickstretchers:
x = 5, y = 5, rule = B2ce3a5y6aci78/S01c2-e3-i4-c56-c7c8
b3o$bobo$2bo$5o$o3bo!

These seem to have overall linear growth.
My rules:
They can be found here

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Re: Rules with small adjustable spaceships

Postby AbhpzTa » February 22nd, 2019, 5:52 pm

(1,0)c/2m p(2m) and (1,0)c/(2n+1) p(2n+1) [m>=4, n>=5]:
x = 10, y = 94, rule = B2c3ajq4ijk5n6c7e8/S12-en3-jkqy4etw5ry6ci7e
5bo3bo$5b4o$5bo3bo18$4bo4bo$4b5o$4bo4bo7$3b3o$5bo3bo$2bob5o$5bo3bo$3b
3o7$3bo5bo$3b6o$3bo5bo7$2b2o$4bo4bo$3b6o$4bo4bo$2b2o7$2bo6bo$2b7o$2bo
6bo7$b2o$9bo$2b7o$9bo$b2o7$bo7bo$b8o$bo7bo7$2o$9bo$b8o$9bo$2o!

(Unfortunately this rule (minimum) is explosive...)
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
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Re: Rules with small adjustable spaceships

Postby AforAmpere » March 9th, 2019, 2:00 pm

Methods for making (2n,2)c/x ships in an adjustable slope ships rule

There are a few ways to make adjustable slope ships in various rules, but for minimum population, the rule B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e seems to be a good candidate.

To make many of the speeds, we want this base ship, a (2,2)c/20:
x = 20, y = 21, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e
4$6bo$5bo6bo$4bo8bo$6bo4bo2bo5$2bo2bo$4bo6bo$3bo8bo$13bo$11bo!


Constructing other diagonal speeds from here (of the form (2,2)c/(2n+18), where n>=1) is easy. Simply move the left two sections left one cell, and the bottom two down one cell to get a (2,2)c/22:

x = 61, y = 14, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e
4bo46bo$3bo6bo22bo16bo7bo$2bo8bo37bo9bo$4bo4bo2bo22bo15bo5bo2bo2$28bob
obo4bo2$35bo$o2bo$2bo6bo23bo13bo2bo$bo8bo38bo7bo$11bo36bo9bo$9bo49bo$
57bo!


Using this base ship, we can make ships with speeds of the form (4m-2,2)c/(36m-18+4mn-2n) for m>=1. By taking the base ship and moving the bottom two parts down 20 cells, we get a ship of slope (6,2). For general diagonal ships of speed (2,2)c/(2n+18), to get a slope (6,2) ship, move the bottom bits down 18+2n cells. This operation changes a (2,2)c/22 ship into a (6,2)c/66 ship, and a (2,2)c/20 ship into a (6,2)c/60:
x = 42, y = 66, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e
4bo28bo$3bo7bo20bo6bo$2bo9bo18bo8bo$4bo5bo2bo19bo4bo2bo5$29bo2bo$o2bo
27bo6bo$2bo7bo19bo8bo$bo9bo28bo$12bo25bo$10bo17$4bo28bo$3bo7bo20bo6bo$
2bo9bo18bo8bo$4bo5bo2bo19bo4bo2bo25$29bo2bo$31bo6bo$30bo8bo$o2bo36bo$
2bo7bo27bo$bo9bo$12bo$10bo!


If you want to increase n for higher slope ships, instead of moving the left two bits one cell left and the bottom two one cell down, move the left two one cell left and the bottom two 2m-1 cells down, where the m is the m in the general formula (4m-2,2)c/(36m-18+4mn-2n). Here is the transformation from (10,2)c/100 to (10,2)c/110:
x = 56, y = 58, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e
4bo41bo$3bo6bo34bo7bo$2bo8bo32bo9bo$4bo4bo2bo33bo5bo2bo22$24bo2$26bo2$
21bobobo2bo2$26bo2$24bo15$o2bo$2bo6bo$bo8bo$11bo$9bo$42bo2bo$44bo7bo$
43bo9bo$54bo$52bo!


Using the steps above, it is possible to construct any ship of a speed of the form (4m-2,2)c/(36m-18+4mn-2n) in only 16 cells. There is a way to construct some other periods, but that will be in the next post.
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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Re: Rules with small adjustable spaceships

Postby AforAmpere » March 9th, 2019, 4:59 pm

The next set of adjustables are more complicated. The speeds attainable with these are of the form (2m+2,2)c/(16m+18+2mn+2n), where m>=1 and n>=1.

The base ship here is this (4,2)c/38:
x = 12, y = 22, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e
3bo$2bo6bo$bo8bo$3bo4bo2bo9$b2o$o2bo5$3bo$2bobo5bo2$4bo!


For increasing period but not displacement (increasing n in the above function), we do a very similar thing to the last set of ships. Take the left side of a ship that you want to increase n for and shift it one cell to the left. Then take the bottom and shift it m+1 cells down. Next, change the bottom to its predecessor (a predecessor that is in the sequence that the bottom ship part would follow). This is a bit strange, but it makes it not misalign with multiple n increases.

A change from (4,2)c/38 to (4,2)c/42 would look like:
x = 52, y = 24, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e
3bo38bo$2bo6bo31bo7bo$bo8bo29bo9bo$3bo4bo2bo30bo5bo2bo3$27bo2$29bo2$
24bobobo2bo2$b2o26bo10b2o$o2bo35bo2bo$27bo4$3bo$2bobo5bo$43bo$4bo37bo
7bo$41bo$43bo!


Changing from one slope to the next is more annoying. To do this, with a ship with some n in the above formula, to add one to m, take the bottom section, move it down n+9 cells, and evolve only the bottom section n+9 generations forward.
The transformation from (4,2)c/38 to (6,2)c/56 is like:
x = 54, y = 31, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e
3bo41bo$2bo6bo34bo6bo$bo8bo32bo8bo$3bo4bo2bo33bo4bo2bo5$29bo2$31bo2$b
2o22bobobo3bo9b2o$o2bo38bo2bo$31bo2$29bo2$3bo$2bobo5bo2$4bo6$50b3o$44b
o$51bo$50bo!


Those two rules allow you to make any ship of the form (2m+2,2)c/(16m+18+2mn+2n) in 27 cells or less. Unfortunately there does not seem to be a way to do this that has a constant size with this period.

As something worth mentioning, the type of ships in the previous post are actually able to be constructed in a different rule with only 12 cells. The operations are the same, and it can actually support ships where n = 0 as well as n = 1 and so on. This is the base ship:
x = 13, y = 13, rule = B2aei3-aij4-aiknr5-jny678/S01e2ein3-aijq4-nqtwy5-eiy6-ac78
3bo$9bo$3bo6bobo$2bo6$bobo6bo$o$10bo$11bo!


This means that all ships of the form (4m-2,2)c/(36m-18+4mn-2n) for m>=1 and n>=0 are possible with 12 cells, and all ships of the form (2m+2,2)c/(16m+18+2mn+2n) for m>=1 and n>=1 is possible with 27 or less cells.
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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