## Rules with small adjustable spaceships

For discussion of other cellular automata.
nolovoto
Posts: 30
Joined: January 5th, 2019, 1:22 pm

### Re: Rules with small adjustable spaceships

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)

Code: Select all

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

muzik
Posts: 3772
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

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?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

77topaz
Posts: 1467
Joined: January 12th, 2018, 9:19 pm

### Re: Rules with small adjustable spaceships

Yeah, those aren't adjustable spaceships.

nolovoto
Posts: 30
Joined: January 5th, 2019, 1:22 pm

### Re: Rules with small adjustable spaceships

oh sorry

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Rules with small adjustable spaceships

A simple class of adjustable ships:

Code: Select all

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.

Moosey
Posts: 3033
Joined: January 27th, 2019, 5:54 pm
Location: A house, or perhaps the OCA board. Or [click to not expand]
Contact:

### Re: Rules with small adjustable spaceships

2718281828 wrote:A simple class of adjustable ships:

Code: Select all

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:

Code: Select all

x = 3, y = 27, rule = B2ac3-aeqy4cjnyz5-ciky6aei7e/S12eik3-cij4-aeknw5-ckny6ae7e
bo$2bo17$3o$bo2$bo$3o3$2bo$bo!  Well behaved at first: Code: Select all x = 24, y = 22, rule = B2ac3-aeqy4cjnyz5-ciky6aei7e/S12eik3-cij4-aeknw5-ckny6ae7e bo7bo7bo4bo$o8b2o5b2o5bo$9bo7bo10$21b3o$22bo2$22bo$21b3o4$23bo$22bo!  A variant of a different rule by aforampere: Code: Select all x = 30, y = 12, rule = B2ce3a5y7e8/S01c2-e3-i4-c5-r6-c7c8 2o$bo$bob27o$bob26o$bob27o$bo$2o3$22b8o$23b6o$23b7o!

(The top is a methuselah)

Short “codes” tend to stop spontaneously:

Code: Select all

x = 6, y = 4, rule = B2ce3a5y7e8/S01c2-e3-i4-c5-r6-c7c8
b5o$b4o$b5o$o!  And a variant with “fake loops”. Code: Select all 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:

Code: Select all

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$bobo2b2o2bobobo2b2ob2o3bobo2bobo3b4o5bo3b3o3b4o
6bo7$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). AforAmpere Posts: 1074 Joined: July 1st, 2016, 3:58 pm ### Re: Rules with small adjustable spaceships 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: Code: Select all 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:

Code: Select all

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: Code: Select all 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:

Code: Select all

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.
I and wildmyron 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
- Finish a rule with ships with period >= f_e_0(n) (in progress)

AforAmpere
Posts: 1074
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

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:

Code: Select all

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:

Code: Select all

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: Code: Select all 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: Code: Select all 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.
I and wildmyron 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
- Finish a rule with ships with period >= f_e_0(n) (in progress)

fluffykitty
Posts: 652
Joined: June 14th, 2014, 5:03 pm

### Re: Rules with small adjustable spaceships

A constructed example of a rule supporting XOR-extendable spaceships:

Code: Select all

x = 38, y = 133, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8
2b36o$bob5ob3ob3obob19o$2b36o3$b36o$b31obobobo$b36o9$2b31o$b2obobob5ob ob3obobobobob3ob2o$2b31o3$2b31o$bob5ob3ob3obob9obobobo$2b31o3$b33o$2bo b3obobobobob3ob7ob5o$b33o3$2b31o$4obob9obobob5obob3ob2o$2b31o3$2b32o$o bob3ob7ob5ob3ob3obob3o$2b32o3$3b31o$2b2obobob5obob3obobobobob3ob2o$3b 31o5$b20o$2bob3obobobobob3ob2o$b20o3$2b19o$4obob9obobobo$2b19o3$2b20o$obob3ob7ob5o$2b20o3$3b18o$2b2obobob5obob3ob2o$3b18o3$3b19o$2bob5ob3ob 3obob3o$3b19o3$2b20o$3bob3obobobobob3ob2o$2b20o5$4b6o$3b2obobobo$4b6o
3$4b7o$3bob5o$4b7o3$3b7o$4bob3ob2o$3b7o3$4b7o$2b4obob3o$4b7o3$4b7o$2bo bob3ob2o$4b7o3$5b6o$4b2obobobo$5b6o3$5b7o$4bob5o$5b7o3$4b7o$5bob3ob2o$4b7o3$5b7o$3b4obob3o$5b7o3$5b7o$3bobob3ob2o$5b7o3$6b6o$5b2obobobo$6b6o
!

I like making rules

A for awesome
Posts: 1948
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Rules with small adjustable spaceships

fluffykitty wrote:A constructed example of a rule supporting XOR-extendable spaceships
c/7:

Code: Select all

x = 4, y = 14, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8
bob$bob$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$bob$3b! c/9: Code: Select all x = 4, y = 42, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 bob$bob$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$o bo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3b$bob!
c/11:

Code: Select all

x = 4, y = 106, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8
bob$bob$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$
3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3 o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$
3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$
obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3b! 2c/12: Code: Select all x = 4, y = 134, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 bob$bob$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$ob o$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$
3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$o bo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3
o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$bob$3b!
c/13:

Code: Select all

x = 4, y = 436, y = 134, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8
bob$bob$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o
$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3 o$3o$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$
3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o
$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$
obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$
3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3 o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$bob! 3c/17: Code: Select all x = 4, y = 539, y = 134, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 bob$bob$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$
3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$
3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3
o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$
3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o
$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$
3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3
o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$
3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o
$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$
3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$
3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3
o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$o bo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$3 o$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$obo$3o
$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$o bo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o
$3o$3o$obo$3o$obo$3o$3o$bob$bob! It seems likely that there's a ship for every Nc/P orthogonal speed where N+P is even, N and P are coprime, and N/P <= 1/5, although I don't know how to prove this. x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce AforAmpere Posts: 1074 Joined: July 1st, 2016, 3:58 pm ### Re: Rules with small adjustable spaceships This takes around 28 million generations to stabilize: Code: Select all x = 94, y = 3, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 94o$92obo$94o!  p45980: Code: Select all x = 3, y = 79, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$
3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o!  p64996: Code: Select all x = 3, y = 97, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$
3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$
3o$3o$3o$3o$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o
$3o$3o$3o$3o$3o$3o$3o!  p210068: Code: Select all x = 3, y = 99, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$ob
o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$o
bo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo
$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$
3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$bo!  I and wildmyron 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 - Finish a rule with ships with period >= f_e_0(n) (in progress) dani Posts: 982 Joined: October 27th, 2017, 3:43 pm Location: New Jersey, USA Contact: ### Re: Rules with small adjustable spaceships AforAmpere wrote:This takes around 28 million generations to stabilize: Code: Select all x = 94, y = 3, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 94o$92obo$94o!  Adding B3e yields a small c/4 glider, while (I think) preserving every pattern you posted: Code: Select all x = 2, y = 3, rule = B2cei3ej4c5i6c8/S1e2i3-ckqr4air5i6ci8 bo$o$bo!  moose#0915 AforAmpere Posts: 1074 Joined: July 1st, 2016, 3:58 pm ### Re: Rules with small adjustable spaceships Wow, a p113725632: Code: Select all x = 3, y = 199, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 bo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$
3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o
$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$
3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$
3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$
3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$
3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$o bo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$bo!  I and wildmyron 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 - Finish a rule with ships with period >= f_e_0(n) (in progress) AforAmpere Posts: 1074 Joined: July 1st, 2016, 3:58 pm ### Re: Rules with small adjustable spaceships All of the ships I could find in fluffykitty's rule: Code: Select all x = 2311, y = 483, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8 2304b6o$2303b2obobobo$2304b6o18$1774b535o$1772b4obob5obobobob7ob3obobo bob3obob3obob5ob3obobobob3ob3ob3obob5ob5ob5obob3obob3ob3obobobobobobob obobobobob11ob3ob3obobobobobob3ob5ob11ob7obob3ob7obobob3ob9ob7ob5obobo bob3obob5obob3obob3obobobob5ob9obobobob11ob7obobob7ob7ob5obobobobobob 3obob5ob7ob3ob7ob3obobobobob9obobob3obob3obobob3obobob3ob3ob5ob9ob11ob 3ob3ob3obobobobob3obob15obob9ob5ob3obob2o$1774b535o18$2179b130o$2178b
2obobob5ob7obob5ob5ob3ob9obob3obob5obobobobobob13ob3obob3obob3ob3obobo
b3obob7ob3obob2o$2179b130o18$648b1661o$647bob9ob5obobobobob3obob3obob 3ob3ob3obob9obob7obob5obob3ob5obobobobobobobob5ob5ob3obobobobobob5obob 3ob3obob3obobob3ob3ob11ob7obobob3ob3obobob11obobob5ob3ob9obob5obob3ob 3obobob3obobobobob7ob7obob7ob5ob3ob3obobob5obobob9obob11obob5obob3ob5o b9obob3ob3obob3ob9obob15obob3obobobob5obob3ob9obobobobobobobobobobobob 5ob3obob3obobob5ob3obob9ob3ob5obob13ob3ob3ob3obob5ob9ob3obob9obob3obob 5ob5obobobobob3ob7ob13ob3ob3obob3obobob7obobobob3obobob13ob3obob7ob7ob 9ob13ob9ob5ob5ob3ob3ob11obobob3ob3obob5ob3ob3obobob7ob3ob3obobobobobob obob5obob7ob3ob3ob9obobobob5ob5obobob5obobob3ob3obobob3obobobob3ob5obo bob3ob3obob3obobobobobobobob9ob3obob5obob5ob11obobob27obobob17ob5obobo bob3ob11ob3ob9obobob3obob5ob7obobob5ob3obobobob3ob15ob7ob3obobobob5obo b3obob5obobobobobobobob5ob3ob7ob3ob3obob3obob5obobob5ob9ob3ob3ob5ob5ob 5ob7ob3ob11obobobobobob3obobobob5ob5obob3obobob3ob5obobobobobob7ob3ob 3obob3ob5ob3ob3ob3obobobobobobobobobobobob3obobob5ob7obobob3ob5ob7ob3o bob3ob3obobobobobobobob7obobobob3ob3ob3ob9ob3ob3ob3obob5ob3ob7obobobob ob5obob5ob5obobobobob7obob3obob2o$648b1661o18$b2308o$2obobob7ob3ob3obo
b5obobob5ob3ob3obob3obobobob3obobobob3obob3ob9obob5obobob3ob3obobobobo
b3ob3obobob3obob3ob3ob9obob7obobob11obobobobob5ob17ob7obobob3ob7ob5obo
b3obob3obob3obobobob5ob5ob9obob3obobobobob3obobob5ob3obobobob9obob3obo
b5obob7obobobob5obob9obob3ob3ob5ob3obobobobobobobob3ob13ob7ob3ob5obob
9obob3obobob3obobob3ob3obob11obob3ob5ob7obobob3obob9obob5obob3obobob3o
bobobobob3ob11ob5obob3ob5obobobobobob3ob13obobobobobobobob3obobobobobo
b3ob3ob5obob9ob3obob3obob11obob3ob3ob3ob7ob3ob3obobob3ob3obobobobob5ob
3obobob9ob3ob5ob15obob5obobob5ob3obob3obobobobobob9ob3ob7obob3obobob3o
bob3obob3obobob3obobob3ob5obob7obob3obob3obob3obob3obob5obobob3ob9ob
11obob9ob3obob9ob3ob7obobob3ob7ob3ob3obob3obobob3ob5obob3obobob3ob3ob
3obobob5obob9ob7ob7ob5ob7obob5ob3obobob9obob3obobob3ob5obob3ob3ob3ob3o
b9obob5obobobobobob3ob3ob7ob3ob5ob3ob5ob3obob5obob3ob3obob3obobob3ob3o
bobob5obobobobobobobob5ob13ob5obobob3ob5ob7ob3ob5obobob3obobob3obob5ob
ob3ob3obobobob5ob3ob7obobob3obob5ob17ob3obob3ob3ob5obobob7obobobobob3o
b3obobob7obobobobob5ob3ob11ob3obob3ob9obobobob7ob3obobob3obobobob13ob
5ob9ob3obobobobobobobob7ob7obobob5ob3obobobobobob5obob5obobob3ob7ob3ob
obobobobob3obobob9ob3obobobobobobob3ob5ob13obob3obobobob7obob13obob3ob
13obobobob5ob3ob3obob9ob9obob3ob3obobob3ob7ob3ob9obobobob3obob3ob3ob3o
bob7obobobob3obob5obobobobob3obob3ob7obobobobob9ob5obobob5ob5ob3obob7o
bob7obobobob9obob5ob15ob3obob3obobob5obobob3ob7ob3ob3ob7obob3obobob3ob
ob7ob5ob3obob15ob7obobobob5ob3ob3obob3obob3ob5obobob3obob2o$b2308o18$
2299b10o$2298b2obob3obob2o$2299b10o18$2086b223o$2084b4ob5ob11obobob3ob
7obob3ob3ob5ob3obobobob7ob3ob13ob9ob3obobob3obob3ob3ob3ob7obob7ob3obob
3ob19obob5obob5obob5obob9ob5ob3obobob2o$2086b223o18$2236b73o$2235bob5o b7obobobobobobob7ob3ob3ob3ob5ob3ob3obob3obobobob2o$2236b73o18$2053b 256o$2052b2obob3ob7obob3obobobob13obobobobob3obobob3obobobob3ob5ob5ob
3ob5ob3obobobobob3obob5ob3obobobob3obob3obob5ob5obob5ob5ob19ob5ob5ob5o
b5ob5obob3obob3obob3ob5ob5ob3obobobob2o$2053b256o18$2267b42o$2266b6obo bobob3ob5ob5ob3obobobobobob2o$2267b42o18$2271b38o$2269bob5ob3obob3obob
5obob3ob3obobob2o$2271b38o18$1898b411o$1897b3ob3obobob3obobobob3ob3ob 3obob5obob5ob7ob13obobob3obob5ob3ob3obobob3obob3obob17obobob5obob3ob3o bob3ob3ob3obob3ob3obobob5ob3ob5obob5obobobob3obobobobob7obob3ob5ob3obo b5obob13ob3obobob3obobob9ob3obobobobob5obob7ob3obob5obobob5obobob3obob obobobobobobob3ob3obobobobob3obobob5obob3ob3ob6o$1898b411o18$419b1890o$417bob7ob5obobob5obobob9ob7obob7ob9ob7ob3obobob7ob9obobob3ob3ob3obob
3ob7obob3ob5ob13ob7ob3obob3ob11obobobobob3ob5ob11obob3ob5obobobob3ob3o
b3obobobobobob3obobobobob3ob5ob3ob5obob3obob3ob5ob9ob3obobobob9ob3obob
5obobobobobob3obob3ob3ob3obob5obob3ob7ob3ob5ob7ob3obobobobob3ob3ob9obo
bobobobobobob3ob5obobob3obobobob3obob13ob5ob5ob9obobobobob5ob3ob3ob5ob
obobobob7ob3ob5ob5obobob3obob3ob3obob5ob3ob3ob3obob3ob3ob3obob5obob3ob
ob3obobobobob7obob3ob3obobobobobobob5ob3ob7obob11obobob3obobobobobob7o
bobob3obob3obobobob5ob5ob5ob3obob3obob7ob7ob9obob7ob7ob3obobob5ob7ob3o
bob5obobob3obobob5obobob3ob5ob3ob5ob7ob9obob3ob3ob5obob3ob3obob7ob9ob
3ob5ob3obobobob3ob3obobob3ob3ob9ob7ob7ob3obobobobobob3obob9obobob7ob5o
bobob9ob3ob3ob7obob5obobob5ob3obobobob5obob3obobobobob7obobob3ob5ob7ob
ob3obobobobobobob3obob3ob11ob5obobobobobob5ob11obob7ob5ob11ob5obobobob
obobob3obobob5ob3ob5obobobobob5ob5ob11ob5obob3obob7ob9obobobobobobobob
3ob5ob3ob3ob3obob5ob3obob7ob19ob3obobobobobobobob5ob3obobobobobob5ob5o
bob3obobobobobobobobobobobob3ob9ob3obob7ob5ob3ob5ob9obobobobobobob5ob
9ob9obob9obob7obob11ob3obobob3obob15obobob5obob7ob5obob5ob5ob15obob3ob
obobobob5ob9ob5ob5ob5ob3obobobob7obob5obobob9ob3obobobobobob2o$419b 1890o18$2206b103o$2207bob5obobob5ob9obob7obobob5ob3ob3obob7ob5ob3obobo b7obobob3obobobob2o$2206b103o18$2238b71o$2237b5ob3ob3ob3obobobobob3ob
3ob7obobobobob7ob3obobob8o$2238b71o18$1876b433o$1875bob3ob3ob5ob9obobo bob3obobobobob5obobob3ob3obob9obobob3ob3obobobob9obobob3obobobobob7obo b7ob3obobobob5ob3ob3obob9obob3ob3obobobob5ob3obob5ob9obobobobob7obob3o bob3obobobob5obobobobob5obobobobob3ob7obob7ob5obobobob3obob3ob5obob5ob ob3obob3obob3obobobob3ob7obob3obob3ob3obob3obobob7obob5obobob3ob3obobo bobob2o$1876b433o18$1383b926o$1382b8obobobob5ob5ob3ob7ob3ob5ob5obobobo
b3ob9ob5ob7ob3obobobob5obob3ob7obob9obob5obobob7obob15obobobobobob5ob
3obob3obobobob5ob3obobob3obobobob5ob5ob11ob3ob3ob3ob3obobobob5ob7obobo
b5obob5obob3ob3ob5obobobob3obobobob3ob7ob3ob3obobobob3ob3obob5ob3obobo
b3obob3ob3obob7ob3obob3obob5obobob3obob3obob11ob3obobobob3obobobobob3o
bob5ob3ob3obobob5obob5ob3obob3obob5ob3obobob3ob3obob3obobobobob3obobob
ob3obobob7ob5obob3ob7ob3ob3obobobob3ob9ob3ob3ob3ob5ob11ob3obob3ob3ob9o
bob3ob5ob3ob5obob5obob3obob3ob9obob9ob7obob7obobobobobob3ob3obobobob3o
b3ob9ob7ob9ob3ob3ob5ob3ob3obobob3obobobob5obob3ob15obob3obob7ob7obob6o
$1383b926o18$2193b116o$2193b9ob3obobob3obobobobob5obob3ob3ob3obobob9ob obobobobob3obobobobob5obobobobobob3obobobobobob2o$2193b116o18$2272b37o$2271bobob3ob3obobob15obobob4o$2272b37o18$1968b341o$1967b3ob3obob11obo bob5obobob5ob9obobob3obob7ob5ob3obobobob7ob3ob3ob3ob5obobob3obobobob7o b3obob3obobob3ob23ob7obobob5ob3ob3obobobob3ob7obobob5ob3obobob5obobobo b3ob3ob3ob5obobob7ob7ob5obobob7ob13ob9ob3obobobob4o$1968b341o18$2273b 36o$2273b3obob5ob5obobob3obobob8o$2273b36o18$1894b415o$1892b2obob5ob3o bob7obobobobob7ob5ob3obob5obobobob3obobobob11ob3ob5obobob3obobob3ob3ob 3obobobobobob5ob3ob11ob5obob5obobob5ob7ob3ob7obob5obobobob3ob3obobobob ob5obob3obobobob3ob3obob3ob13ob7ob11ob3obobobob5ob5ob13ob9obob7obobob 7ob3ob3obob7ob3obobob3ob3obob3obobob3ob3ob6o$1894b415o18$2201b108o$
2200b4obobobob3obob3ob5ob5obobobob5obob3ob3ob9obobob3ob3obobob3obob5ob
5obob10o$2201b108o18$2137b172o$2137bobob5obob5ob11obob13obob3obobob3ob 3ob3obob5obobob9obobobobob3ob5ob7obobob3obob3ob3ob7obobob3ob3ob3obob7o b6o$2137b172o18$1853b456o$1852b2obobobob3obob5obob3ob3obobob3obobobobo
bob3obob7obob11obobobob3ob5obobobobobobob3ob3obob3obob7ob7obobobob3obo
b19obobobob7ob9ob5obob3ob9obobob3obobob5ob3ob3ob3obobobobobob3ob3ob5ob
7ob3obob7ob11ob3ob3ob3obob3ob3ob9ob5ob3ob5ob3ob3obob3ob3obobobob5obobo
b3obob3ob3obobobobobob7ob3obob5obob3obobobob13ob4o$1853b456o!  ntzfind breaks after p30. I and wildmyron 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 - Finish a rule with ships with period >= f_e_0(n) (in progress) 2718281828 Posts: 738 Joined: August 8th, 2017, 5:38 pm ### Re: Rules with small adjustable spaceships AbhpzTa wrote: (m/g,0)c/(n/g) , period n [g=gcd(m,n) , (m=1 AND n=5) OR (0<5m<n AND m==n(mod 2))] m=1 and n={5,7,9,11} (reaction={(5),(7),(9),(11)}): Code: Select all x = 114, y = 36, rule = B2a3jkq/S01c3e 103bo$102bo10bo$106bo5bo$106bo5bo$102bo10bo$103bo5$79bo$78bo34bo$85bob o5bo3bo7bobobo$85bobo5bo3bo7bobobo$78bo34bo$79bo5$bo$o112bo$3bobo5bo7b o3bobo7bobo3bobobo7bobo9bobo5bo3bobo3bo3bobo11bo5bobo$3bobo5bo7bo3bobo
7bobo3bobobo7bobo9bobo5bo3bobo3bo3bobo11bo5bobo$o112bo$bo5$7bo$6bo106b
o$13bobo9bo5bobo5bo3bo3bo5bo11bo3bobobo3bo3bo9bobo5bo3bobobobo$13bobo
9bo5bobo5bo3bo3bo5bo11bo3bobobo3bo3bo9bobo5bo3bobobobo$6bo106bo$7bo!
m=3 and n=17 (reaction=(5,5,7)):

Code: Select all

x = 540, y = 6, rule = B2a3jkq/S01c3e
bo$o538bo$7bobo3bo5bo9bobo11bo3bo5bobobobo3bo3bobobo9bo3bo3bo3bo3bo3bo
bobobo7bobo11bo3bo3bobo7bo3bo5bo3bo3bobo3bo5bo5bobo3bobo3bobobo17bobo
5bo7bobo3bobobo5bobobo3bobo3bo9bobobo3bo5bo13bobo3bobo3bo5bobo5bo9bobo
3bo7bobo3bobo3bobobo3bobo5bobobo5bo5bobo9bo3bobo7bo11bobobo5bobo11bobo
bo9bobo3bobo9bo3bo3bo5bobo11bobo7bo3bobo3bobo$7bobo3bo5bo9bobo11bo3bo 5bobobobo3bo3bobobo9bo3bo3bo3bo3bo3bobobobo7bobo11bo3bo3bobo7bo3bo5bo 3bo3bobo3bo5bo5bobo3bobo3bobobo17bobo5bo7bobo3bobobo5bobobo3bobo3bo9bo bobo3bo5bo13bobo3bobo3bo5bobo5bo9bobo3bo7bobo3bobo3bobobo3bobo5bobobo 5bo5bobo9bo3bobo7bo11bobobo5bobo11bobobo9bobo3bobo9bo3bo3bo5bobo11bobo 7bo3bobo3bobo$o538bo$bo! A relative seems to have all velocities c/n. Code: Select all x = 271, y = 456, rule = B2a3ejkq4ekrtw5ijn6ein7c8/S01c2cen3ejq4ikntyz5-ce6-ai8 68b2ob2o6bobo7bo5bo8bobo14bo2bo8bo2bo5bo2bo8bo2bo8bo2bo12bo2bo6bo2bo7b o2bo4bo2bo4bo2bo5bo2bo$59b3o7bobo8bo10b3o13bo11bo6bo$58b2obo28bobobo 12b3o11bo2bo87b2o$58bob3o26bob3obo9b2obo$58b3o31bo13b2o11b2o4b2o7b2o 123b2o$60bo28bo2bo2bo10bo60b2o35b2o56bo7bo$90bo3bo10b2o12b2ob2ob2o7b2o 7b2o10b2o26b2o27b2o48bo2bo4bo$106b2obo94b2o59bo$104bob2o14b2o19b2o10b 2o26b2o27b2o45b2o$107b3o110b2o7b2o$104bo3bo25b2o7b2o10b2o36b2o17b2o$
104bob2o24bo4bo29b2o51b2o7b2o$102b3obo12b2ob2ob2o6bo2bo46b2o8b2o17b2o$
105b2o60b2o60b2o$103b4o15b2o19b2o48b2o$100bo3b4obo57b2o35b2o$101b2ob2o 2bo34b2o10b2o26b2o27b2o$102bobobo97b2o$108bo10b2ob2ob2o56b2o8b2o17b2o$
204b2o23b2o$bo2bo5bo2bo4bo5bo5bo3bo6bobo3bobo50b4o2b2o11b2ob2ob2o28b2o 26b2o8b2o17b2o$o4bo3bo4bo91bo15b2o105b2o$2b2o37b2o4b2o51bob2o2bo12b2o 4b2o28b2o$11b2o24bo10b2o52b2o2bo60b2o35b2o14b2o$17b2o5b2o3b2o3b2o65b2o 3bo12b2o4b2o16b2o38b2o8b2o17b2o$23b2o8b2o68b2obo15b2o80b2o$101b2o16b2o 4b2o27b4o35b2o$42b2o56bo2b2obo$36b2o63bo3bo16b2o19b2o10b2o36b2o$121bo
2bo42b2o51b2o7b2o$103b2o14b2ob2ob2o56b2o27b2o$120bob2obo41b2o$101bo4bo 86b2o$102bo2bo98b2o23b2o$183b2o8b2o17b2o$181bo4bo17b2o14b2o$120b2o2b2o 29b2o25bo2bo26b2o$220b2o7b2o$120b2o2b2o67b2o17b2o$122b2o80b2o14b2o$155b2o36b2o17b2o$167b2o51b2o7b2o$120b2o2b2o17b2o67b2o$122b2o43b2o$155b 2o36b2o17b2o$167b2o51b2o$143b2o10b2o$122b2o43b2o35b2o23b2o$120b2o2b2o 17b2o48b2o$122b2o105b2o$193b2o$220b2o$120b2o2b2o29b2o53bo4bo$122b2o80b
2o5bo2bo$193b2o$167b2o35b2o23b2o$193b2o$167b2o33bo4bo12b2o7b2o$143b2o 58bo2bo2$122b2o19b2o10b2o36b2o$167b2o$120bo4bo17b2o48b2o$121bo2bo42b2o$143b2o10b2o$220b2o$143b2o9bo2bo35b2o$227bo4bo$143b2o48b2o33bo2bo$220b 2o$143b2o10b2o$167b2o$155b2o36b2o$167b2o$155b2o36b2o$153bo4bo61b2o$
154bo2bo3$220b2o$143b2o$167b2o$143b2o$167b2o51b2o2$167b2o51b2o2$167b2o 3$143b2o2$143b2o48b2o2$193b2o$167b2o$143b2o2$143b2o48b2o2$143b2o48b2o$167b2o51b2o$143b2o$167b2o51b2o$143b2o48b2o3$220b2o$193b2o$167b2o$143b
2o$167b2o51b2o$143b2o48b2o$167b2o51b2o$193b2o$167b2o51b2o2$167b2o51b2o
$143b2o48b2o$220b2o$143b2o$167b2o$193b2o2$143b2o48b2o$167b2o51b2o$143b
2o$220b2o$193b2o$167b2o$193b2o2$143b2o3$167b2o51b2o2$166bo2bo$193b2o$220b2o$143b2o22b2o24b2o2$193b2o$220b2o$167b2o2$167b2o24b2o2$167b2o2$
143b2o22b2o24b2o$220b2o$143b2o48b2o2$143b2o2$167b2o$220b2o$167b2o23b4o
2$143b2o22b2o22b2o2b2o$193b2o25b2o$143b2o22b2o22b2o2b2o$220b2o$143b2o 46b2o2b2o$220b2o$143b2o46b2o2b2o2$165b6o20b2o2b2o$166bo2bo$191b2o2b2o$193b2o$143b2o2$143b2o$193b2o$191b2o2b2o$220b2o$143b2o$193b2o25b2o3$143b2o2$143b2o$218bo4bo$191b2o2b2o22bo2bo2$191b2o2b2o$193b2o3$191b2o2b 2o2$191b2o2b2o2$143b2o46b2o2b2o2$191b2o2b2o2$143b2o2$143b2o4$191b2o2b 2o$193b2o$143b2o2$143b2o46b2o2b2o$193b2o$191b2o2b2o4$143b2o2$191b2o2b
2o4$143b2o3$193b2o3$143b2o46b2o2b2o2$143b2o46b2o2b2o2$191b2o2b2o4$191b
o4bo2$191bob2obo2$143b2o46bob2obo2$191bo4bo2$191bob2obo2$191bo4bo2$
143b2o46bo4bo2$191bo4bo2$191bob2obo2$191bo4bo2$143b2o46bo4bo2$143b2o 46bo4bo2$191bob2obo2$143b2o46bo4bo2$191bo4bo2$191bob2obo$142b4o$191bo 4bo$143b2o$191bob2obo2$191bob2obo$143b2o$191bob2obo$143b2o$191bob2obo$143b2o$191bo4bo$143b2o$191bob2obo2$191bo4bo2$191bo4bo2$191bob2obo$143b
2o$191bob2obo$143b2o$191bob2obo$143b2o$191bob2obo2$191bob2obo$143b2o$
191bo4bo$143b2o$191bob2obo$143b2o$191bob2obo2$191bo4bo$141bo4bo$142bo 2bo45bo4bo2$191bo4bo2$191bo4bo2$191bo4bo2$191bo4bo2$191bob2obo2$191bo 4bo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bo b2obo2$191bob2obo2$191bo4bo2$191bob2obo2$191bob2obo2$191bob2obo2$191bo b2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bo4bo2$191bo 4bo2$191bo4bo2$191bo4bo2$192bo2bo6$193b2o2$193b2o12$193b2o4$193b2o10$193b2o6$193b2o5$192bo2bo$193b2o6$193b2o2$193b2o2$193b2o4$193b2o10$193b 2o2$193b2o6$193b2o10$193b2o8$191b6o$192bo2bo!


2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Rules with small adjustable spaceships

Adjustable ships in B2a with increasing population:

Code: Select all

x = 69, y = 12, rule = B2-cn3aeqry4inqrtwz5aciy6ak/S2e3aq4ajkz5iq
b4o14b4o5b4o5b4o5b4o5b4o5b4o2$2o2b2o12b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o 3b2o2b2o3b2o2b2o$bo2bo14bo2bo5bo2bo5bo2bo5bo2bo5bo2bo5bo2bo$o4bo12bo4b o3bo4bo3bo4bo3bo4bo3bo4bo3bo4bo$19bo2bo5bo2bo5bo2bo5bo2bo5bo2bo5bo2bo$18bo4bo3bo4bo3bo4bo3bo4bo3bo4bo3bo4bo$28bo2bo5bo2bo5bo2bo5bo2bo5bo2bo$36bo4bo3bo4bo3bo4bo3bo4bo$46bo2bo5bo2bo5bo2bo$54bo4bo3bo4bo$64bo2bo!


2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Rules with small adjustable spaceships

A rule which has adjustable ships for all speeds c/n for n>8. I think the first rule of this kind. Maybe there is a relative rule (keeping the three reflecting elements) which allows for all c/n speeds. however c/2 seems to be tricky.

Code: Select all

x = 204, y = 92, rule = B2akn3cn4ijnrw5cij6a8/S1c2-ak3ceiy4acenw5iqr6c8
9$119bobo4bobo15bo4bo$17bobo2bobo75bobo2bobo12bo6bo17bo2bo$4bo4bo8bo4b o20bobo2bobo7bobobobo7bobobobo7bobobobo7bo4bo14bo4bo16bobo2bobo19bobob obo14b2o$3bo6bo6bobo2bobo7bo4bo7bo4bo48bo8bo11bo2b2o2bo17b4o$31bo6bo5b obo2bobo7bo5bo13bo7bo35b2o18bobo2bobo25bo13bo2bo$99b2o2b2o2b2o9bobo6bo
bo9bo3bobo2bobo3bo$59bobobobo11bo9bobobobo6b2ob2ob2o11b2obo2bob2o9bo2b 2o2bo2bo2b2o2bo14bobobobo$101bo4bo11bob2o4b2obo12b2o6b2o$59bo5bo9bo11b o5bo8b4o13bo2b4o2bo9bo3bo3b2o3bo3bo14bo$4bob2obo8bob2obo8bob2obo7bob2o
bo50bob2obo12b2o6b2o15b2o2b2o$3b8o6b8o6b8o5b8o7bobobobo7bo13bobobobo8b 4o13bo3b2o3bo9b2o4bo4bo4b2o14bobobobo$4bob2obo8bob2obo8bob2obo7bob2obo
48bob6obo7bo2bobo4bobo2bo10b2o6b2o$3bobo2bobo6bobo2bobo6bobo2bobo5bobo 2bobo49bo4bo14b2o2b2o13b2o10b2o$4bo4bo8bo4bo8bo4bo7bo4bo48bob2o2b2obo
7b3o10b3o9bobobo2bobobo$101bo4bo8bobo3b2o2b2o3bobo6b3o10b3o$121bo4bo
11bo2bob2o4b2obo2bo$123b2o15bobo8bobo$117bobo2bo2bo2bobo7bo3bo8bo3bo$123b2o14bo2b2obo2bob2o2bo15bob3o2bo13b2o$121bo4bo13bo2b2o4b2o2bo13b2o
2bobo2bo$120bo6bo12b2o10b2o13b3ob3o3b2o12bo$119bob6obo10bo3bo2b2o2bo3b
o10bo2bo6bobobo$120bob4obo18b2o18b2o2b2obo2bobo$121b2o2b2o11bo2bo2bo4b
o2bo2bo11bo2b2obo$117bo4bo2bo4bo9bo2bo6bo2bo15bo$123b2o15b2ob3o2b3ob2o
15b3o6bo$116b2ob2o6b2ob2o12bo4bo16b2obobo3b3o$117bo3b2o2b2o3bo14b4o16b
o4b2o2bobo3bo$116bo2b2o6b2o2bo8bo4bo2bo4bo9bo4b2o2bobob2o$116bo4bo4bo
4bo7bobo3bo2bo3bobo9bobo5bob2obo3bo$115bobobobo4bobobobo6b2o5b2o5b2o7b 2obo3bo2b3obo2bobo$116bo2b2o6b2o2bo6bo6bo2bo6bo12bo3bob2o3bo2bo$122b4o 14bo2bobo2bobo2bo11b2o3b2ob2o3b2o$119b2o2b2o2b2o9b2o6b2o6b2o7bo5bo4b2o
2bo3bo$120bobo2bobo11bo2b2o6b2o2bo10bo3bo4bo3b2o$120bobo2bobo12b3o3b2o
3b3o9bo8b2obo3bo$120bo6bo12bob2obo2bob2obo8b2o2bo2bo2b2o2bobob3o$119bo
8bo11bobo8bobo9bo3b2o5bob2o$141b2o8b2o11b2o2b2obo4bo3bobo$119bo8bo14bo
bo2bobo19b4o3bo$120b2o4b2o13b4o4b4o11b4o3b2o5bo$121b6o17bo4bo11bob2obo
bo2b3obo3bob3o$121bo4bo15b4o2b4o8bob4o3bo2bo6bo$121bob2obo14b2o2bo2bo
2b2o15bo2b2ob2obobo2bobo$121bob2obo35b4o3b3o3bo3bobo$123b2o20b4o12bob
3o10b4obobo$142b10o14bo9b2o$121bo4bo18bo2bo15bo3bo5bo5b2obo$122bo2bo 16b2o2b2o2b2o13bo4bo4bo3b2o$120b3o2b3o11bob2o3b2o3b2obo13b2o4bo4bo$140bobobo4bobobo11bo2bobo$123b2o14bobo2bo4bo2bobo9bo2b2o5b4o$116bobo2b o4bo2bobo37b3o5bob2o$116bo14bo9bo10bo14bo3bob2o2b2o$116b2o4bo2bo4b2o 36bobo2bo3bo$118b3o6b3o36b2o2bobo4bo$118bo10bo39bo5bo2bo$166b2o$168b2o 7b2o$166bobo2$163b5o9bobobo$166bo12b2o$179bobo$166b2o9b4o$166bo12b2o$
180bo!


muzik
Posts: 3772
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

Adjustable speed via rule changes:

Code: Select all

x = 7, y = 7, rule = 1c23-y4c5e6c/34e6in/15
2.3A$A5BA$7B$AB3DBA$.A3DA$2.ADA$3.A!
[[ THEME Blues ]]

Code: Select all

x = 7, y = 7, rule = 1c23-y4c5e6c/34e6in/150
2.3A$A5BA$7B$AB3DBA$.A3DA$2.ADA$3.A!
[[ THEME Blues ]]
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Hdjensofjfnen
Posts: 1471
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Rules with small adjustable spaceships

muzik wrote:Adjustable speed via rule changes:

Code: Select all

x = 7, y = 7, rule = 1c23-y4c5e6c/34e6in/15
2.3A$A5BA$7B$AB3DBA$.A3DA$2.ADA$3.A!
[[ THEME Blues ]]

Code: Select all

x = 7, y = 7, rule = 1c23-y4c5e6c/34e6in/150
2.3A$A5BA$7B$AB3DBA$.A3DA$2.ADA$3.A!
[[ THEME Blues ]]
That's doable in almost any appropriate Generations rule.
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!


LaundryPizza03
Posts: 507
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

### Re: Rules with small adjustable spaceships

Hdjensofjfnen wrote: That's doable in almost any appropriate Generations rule.
Indeed, here is a much smaller example, 2c/g orthogonal from 126/345/g, g≥2:

Code: Select all

x = 3, y = 2, rule = 126/345/2
3A$.A!  Code: Select all x = 3, y = 2, rule = 126/345/3 3A$.A!

...

Code: Select all

x = 3, y = 2, rule = 126/345/16
3A$.A!  ... etc.! Code: Select all x = 4, y = 3, rule = B3-q4z5y/S234k5j 2b2o$b2o$2o!  LaundryPizza03 at Wikipedia wildmyron Posts: 1341 Joined: August 9th, 2013, 12:45 am ### Re: Rules with small adjustable spaceships 2718281828 wrote:A rule which has adjustable ships for all speeds c/n for n>8. I think the first rule of this kind. Maybe there is a relative rule (keeping the three reflecting elements) which allows for all c/n speeds. however c/2 seems to be tricky. Code: Select all <snip rle>  Very nice! Looking through this thread I only found one other such rule - near the top of this page. AbhpzTa wrote:(1,0)c/2m p(2m) and (1,0)c/(2n+1) p(2n+1) [m>=4, n>=5] I haven't seen any such rules with a bounded population for all c/n ships for all n greater than some value. The adjustable ships in AbhpzTa's rule cover c/8, and c/n for all n >= 10. I don't think anyone tried to find ships at the other speeds. I'm a bit surprised the ships in your rule are as large as they are, though I expect you would have found smaller ones if it were easy to do so. Here are c/3, c/4, c/5, and c/6 in AbhpzTa's rule. I haven't found a c/7 or c/8. I'm not sure if c/2 is possible in this rule either. At p2 it seems very unlikely and for p4 ntzfind doesn't reach a depth beyond 22 rows up to w13. [ For your rule c/2 looks possible - the ntzfind partials are steadily increasing in length with increasing width, up to 102 rows for "p4 k2 w13 u". Code: Select all x = 72, y = 35, rule = B2c3ajq4ijk5n6c7e8/S12-en3-jkqy4etw5ry6ci7e 4bo8bo13bo2bo14b3o2b3o14bo2bo$3bob3o2b3obo13b2o13bo4b2o4bo11bob2obo$3b 3o2b2o2b3o12bo2bo12bob3o2b3obo11bob2obo$7bo2bo14bobo2bobo11bo8bo14b2o$4b2obo2bob2o10bo3b2o3bo10bo2bo2bo2bo$3b2obo4bob2o7b2o10b2o7bo3bo2bo3bo
$3ob2o6b2ob3o2bo6bo2bo6bo9bo2bo$o4bo6bo4bo3b2o12b2o5bo2bobo2bobo2bo$bo 4bo4bo4bo5b2o10b2o6bo2bobo2bobo2bo$bo2bobo4bobo2bo5b2o10b2o11bo2bo$2bo 3bo4bo3bo5bo2bo8bo2bo7b4o2b4o$ob2o2bo4bo2b2obo3bobobo6bobobo7bo2bo2bo
2bo$o3b3o4b3o3bo3bobobo6bobobo6bo2bo4bo2bo$o2b2obo4bob2o2bo3bo2bobo4bo
bo2bo6bo2bo4bo2bo$o2bo2bo4bo2bo2bo3bo3b2o4b2o3bo5bo4bo2bo4bo$obo12bobo
3bo3b2o4b2o3bo5bo4bo2bo4bo$obobobo4bobobobo3bob3o6b3obo$o6bo2bo6bo3bob
obo6bobobo6b4o4b4o$o2bobo6bobo2bo3bo2bobo4bobo2bo$o2bobobo2bobobo2bo4b
2obo2b2o2bob2o6bo4bo2bo4bo$o2b3o6b3o2bo10b2o$o6bo2bo6bo9b4o$o3b2o2b2o 2b2o3bo6bob6obo$o3b2o6b2o3bo8b6o$o2bo2bo4bo2bo2bo$o3b2o6b2o3bo$2obo10b ob2o$2bo12bo$bob4o4b4obo$3b2o2b4o2b2o$2bo2bobo2bobo2bo$2bo4bo2bo4bo$2b 3o2bo2bo2b3o2$4bo8bo!
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.

AforAmpere
Posts: 1074
Joined: July 1st, 2016, 3:58 pm

### Re: Rules with small adjustable spaceships

Adjustable lightspeed ships with period 3^n:

Code: Select all

x = 26, y = 42, rule = B2ain3ackr4eijkrw5cnry6e/S02aei3-ciky4jt5cnry6e7e
25bo$21bobobo7$25bo$16b4obobobo7$25bo$12b8obobobo7$25bo$8b12obobobo7$
25bo$4b16obobobo7$25bo$20obobobo!  Increasing the length by 4 multiplies the period by 3. I and wildmyron 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 - Finish a rule with ships with period >= f_e_0(n) (in progress) Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Rules with small adjustable spaceships 4 adjustable ships with the "colliding wicks" format. I've only found the "formula" for the first, I'm too lazy right now to find for the other 3. 1. P = 27+11n ; n >= 0, V = c/Pd, Spacing = n*2+1 Code: Select all x = 70, y = 20, rule = B2ce3cnqry4aeijkyz5cj6a7c/S12ik3aejqy4ijnw5jnq6a 3bo29bo29bo$3o27b3o27b3o$3bo29bo29bo4$67bobo$68bo$68bo$68bo3$43bobo$44bo$44bo$44bo$17bobo$18bo$18bo$18bo! 2. Code: Select all x = 67, y = 20, rule = B2ce3y4ejkr5i/S12ei3ry4r 3bo29bo29bo$3o27b3o27b3o$3bo29bo29bo$64bobo$65bo$65bo$65bo6$43bobo$44b o$44bo$44bo$17bobo$18bo$18bo$18bo!  3. Code: Select all x = 70, y = 20, rule = B2ce3akq4ejrwz5aein8/S012eik3enry4cqz5c6ae8 3bo29bo29bo$3o27b3o27b3o$3bo29bo29bo4$67bobo$68bo$68bo$68bo3$43bobo$44bo$44bo$44bo$17bobo$18bo$18bo$18bo!  4. Code: Select all x = 70, y = 20, rule = B2-an3kq4aejnw5ceinq6in7e/S12ik3cqy4ceknz5eir6c 3bo29bo29bo$3o27b3o27b3o$3bo29bo29bo4$67bobo$68bo$68bo$68bo3$43bobo$44bo$44bo$44bo$17bobo$18bo$18bo$18bo!  Airy Clave White It Nay Code: Select all x = 17, y = 10, rule = B3/S23 b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

muzik
Posts: 3772
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with small adjustable spaceships

Have all orthogonal speeds 3c/n been proven yet?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!