For discussion of other cellular automata.

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)
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.AB2A5.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.2A9.B2A$8.3A9.AB2A$17.ABA.B2A$17.B5A$19.BA5$7.BA11.3A$7.3A9.B.2A$6.B.2A9.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
nolovoto

Posts: 14
Joined: January 5th, 2019, 1:22 pm

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!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Rules with small adjustable spaceships

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

Re: Rules with small adjustable spaceships

oh sorry
nolovoto

Posts: 14
Joined: January 5th, 2019, 1:22 pm

Re: Rules with small adjustable spaceships

A simple class of adjustable ships:
x = 43, y = 56, rule = B2ac3-aeqy4cjnyz5-ciky6aei7e/S12eik3-cij4-aeknw5-ckny6ae7e2$38bo$39bo$37b4o$38bo6$38bo$37b4o$39bo$38bo5$38bo$39bo$37b4o$38bo7$3bo5bo$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.

2718281828

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

Re: Rules with small adjustable spaceships

2718281828 wrote:A simple class of adjustable ships:
x = 43, y = 56, rule = B2ac3-aeqy4cjnyz5-ciky6aei7e/S12eik3-cij4-aeknw5-ckny6ae7e2$38bo$39bo$37b4o$38bo6$38bo$37b4o$39bo$38bo5$38bo$39bo$37b4o$38bo7$3bo5bo$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-ckny6ae7ebo$2bo17$3o$bo2$bo$3o3$2bo$bo! Well behaved at first: x = 24, y = 22, rule = B2ac3-aeqy4cjnyz5-ciky6aei7e/S12eik3-cij4-aeknw5-ckny6ae7ebo7bo7bo4bo$o8b2o5b2o5bo$9bo7bo10$21b3o$22bo2$22bo$21b3o4$23bo$22bo! A variant of a different rule by aforampere: x = 30, y = 12, rule = B2ce3a5y7e8/S01c2-e3-i4-c5-r6-c7c82o$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-c7c8b5o$b4o$b5o$o! And a variant with “fake loops”. x = 14, y = 10, rule = B2ce3a5y6aci78/S01c2-e3-i4-c56-c7c810o$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-c7c82o2b4o2bo3b2obo2b5o2bo2bo3bo2b4ob11o2bob2obo2b3o3bo2bobobob2o$6b8obo2b3o2bo5bob4o2bob5ob2obobobo2bobobobob3ob2o2b7o$3b3obo2bo2bobobobo3bo2bo2bo2bo3b3obo3bobo2b2o2bobobob6obob2obo3b4o$2b3obo5bob2o2b3ob4obo2b2o4b2obo5b2o3bob4o4b3o5bob2obob3obo$ob2o2bobo4bobo2bobo4bob2o2bobo2b2ob3o2b3obo2b3obob2o2b3ob3o4b4o2bo$4ob2o2b9ob3o2b2obo3bob2obob3obo3b3o2bobob3o2bo2bo5bobob4ob2o$bobobobobo2bo6b3o2b3o4b2o3b2o2b5o2b2obo4b2o2b3o2b3obo2bo2bobobo$2bo4bob2o4b3o4b2o3bo2b3obobo6bob3o2bob6o4b2o2b3o2b2ob3o$o3b2o2bo2bo3bo2b4o2b4ob5o2b2ob2obo2b2o2b2ob2obob3obobob5ob2o5bo$5ob2obobo3bo2bobo2bob4obo2b2obob5o3b2obobo2bobo2bo6b5obo2b3obo$o2bo2bobo4bob3ob2ob4obob2ob4obo3bob2ob5obo2b3obo3bo3b3o2bobo2bobo$2b3ob2o2bo2bob3ob2o2bo2bo2b4o2b3o2b5obobobo2b3obo3b2o3bob2o2bob2ob3o$bobo2bob2ob2ob2o4b15o6bo4bobo6bob6o2bo2b2o5b2o2bo$o2bobo4b4obobo4bo3b2o2bobo3bobob3ob4ob2obobobob2ob2o5bo3b4o2b2o$2b3o2bob2o2bo2b2obobo2bo2b5o3b2ob3ob3o2bobob2o4bobo3bo2b3obobobo2bobo$2obobo5b2ob2o5bo2bo3b2ob2obobob2obo4b7o3b2o4bob4o5b2o4bo$o2bo2b2obobo2b2o4b2o2bob2o3bobo2bo4bob3o2bo3b2obo2b6o2b4o2bo2bo$b2o3b2obobo2bobo3bobo4bo3b3obo5b3o2bobo2bobo2b6obo3b2obob2o2b2obo$7bob4o3bobob2ob5o3b2ob4o2bobobo4bob2o2bo6b3obobo5bobo2bo$o6bob3ob2o2b2obob3o4bo3b3o3bobobobo2bobobob3o2b2obo2b3ob2o2b2o4bo$b2o3bo6b3ob2o4bo2bobo2b2o4bob3obo2bo3b5obo3bob2obob3ob2o2bo3bo$bo2b2obob6o2bo3b2ob7ob4ob3o2bo2b6o5bo2b7o3b2obobo2bobo$o3bo2bob2o3bobo2bobob2o6b2ob4o2bo2bo3bobob2ob4ob2obob2o2bo5b2o2b2o$bo3b2obob4ob3o2b4ob2o3bob4o5b2obobo3b3ob3ob6obo3b3ob5obo$2bo5b2o2bobobo2bob2o3bobobo3b2o3b2o2b2ob7obo2bobo3bob5ob2ob3o2bo$b6ob2ob4ob3o3bob2obobo3bobo3bobobobob3o5bob3obob8ob3o3bo$2bo4b5obob2o4b2o3b3obob3obo2b2o2b2ob2ob3o3bob2o2bob3ob2obo2b2o3b2o$2bo2b4o3bo4bo10b2obobo4bobob2o3b3ob2ob2obobob2o3bo2b3o2b2ob2o$6b2o2bo2b4obob2ob4ob2obobob2obobo2bo3b2ob6ob5o3bo3b2o4b2o$ob3ob2o2b3o2b3ob6obo3b6ob2ob2o3b4o4b3ob2o2bo2b2o4b3o2b2ob2o$5o3bobo8b3obobo2bo3b2obo3b2o3bo2bo5b2o3b2o2bo6b4ob2o2bo$3o3bo2bobobo2b2o3b2obo4bobob2obo2b2obo4b3o2bo2bobo3b3o5bobob4o2bo$bob3o2b3o2bobobob2obo2b5o2bo2bo2bo2bo4b2o6b2o2b2o5b3o3b3obo$2o3bob2o2b2obo2b4ob6o2bo2b2ob2o2bo4bo5b3o4bo2b2o2b2ob2o3bobob3o$3ob2ob4ob2o6b4ob2o2bob3ob3o5b2o2b4o2b5obo3b4o2b6o2bo$3bobob2obo2b2ob2o2bob2ob2o2b3o6bobo4bobo2bobo2bobob3ob3o2b4o5bo$4b2obo3bob3obo3bo3bob3o2b2ob2obob2o2b2obo2b6o2b6o5b3obo2bo2bo$ob2obo2b3o6bo2bo2bobo5b2o2b2ob3o3bo2b3o3bobo3bob7obo4bo2bo$ob2o3b5o3b2obobo2bo2b6obo3bobob3obo2bobo2b2o4b3o4bo3b9o$2bo2b4o4bo2b3o2b2o4bo3bobo2bo4b6o2b2o3bobobob4o5b2obo2b2o$bo3b11obo3bo3b2ob2obo2b5o3bo4b2o7bobo3b4o4b5o3b2o$bobobo3b3ob6o3b5ob2o2bo2b2o2bobob4ob7o3b3o2bob3o3bo2b2obo$bobo3bob2ob3o2b5o2b2o3b10o2bob3o3b4o2b3o3b5ob3o2bob2o2bo$2b2o2bo3b3o5bo3b6o2bo2b3ob3ob4ob3ob3obo2b6o2b2ob2obo2bob2o$obobo3bobobobo3bo3bobo2b2obo3b2ob6o2bo3b2o2b3o2b3obo2b2o2bo2b8o$b2obo2bo2b2ob2o3b2o5b4obobobo4bob2obo2b2o2bo2bo4b4o8bo4b3o$bobo2bo2bo7bob3o2bobobo3b3obo4b3ob2o2b3ob2o2bobobo3b2ob2obob3obo$2b2o4bobo2bo3b3o2bob4o2b2obo2bo2b2ob9ob3ob4ob2o3bo6bo2b2o$o3b2o2b2o2b2o2b2o2b3obo6bo2bo2b5o2bob2o2bo5b5obo2b2obo3bo3b2o$o2b2o2b2o2bob2ob2o2b2o3bob3o5bo3b3ob2ob2obo6b3obo2bob2obob5obobo$4b3ob2ob2obobobo2bo2bo2b2o2bob6ob2o3b4obo2bobo3b5obo3bo3b7o$4obobo4b3obobo5b2o3bo5bobob4obo2bobob2o2bob3o2b2obob2obob3o2b3o$ob2obo2bo4bobo7b2o2b6o5bo7b2ob3o9b7o3b3o$b5o3b3ob3ob2o2b5o2bo3b2ob2o2bobo5b2ob5o2bo2bob2o3b5ob2o2b2o$o3bobobo5bob2ob2ob5ob2o5bo2b4o2b3obo2b2o5bo4b5o2bobo3bob2o$3b5o3b2obob2obob2o4bo3bo4b5obo3b4ob4obo2b2o4b2o2bobob3o$o3b2obob2o2bob3ob2o6bob2o6bo2b2o2bo3b2obob5o2b2obo3bob4obobob2o$ob5obobo2b3o3b2o4b3o5b4obobobob2ob2o2bo3b2o2bo4bo5bo2b2o2bobo$4obobo2bo6b3o2b2obobo2b5obo2b4ob3o4bo2bo3b2ob4o3bob3o2b5o$ob5obo2bobobob2obo2bo3b2obo3b4ob3o3b2o4b2o2b2o2bob2o7bo4b3obo$bobo2b2o2bobobo2b2ob2o3bobo2bobo3b4o5bo3b3o3b4o3b2o3bob3ob2o4bo$2bo8bo2bo2b5ob2ob3o6bob2o6b6o2bo2bo3bob4ob6obobob2o! Becomes a solid rectangle: x = 3, y = 9, rule = B2ce3a5y6aci78/S01c2-e3-i4-c56-c7c83o$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-c7c8b3o$bobo$2bo$5o$o3bo! These seem to have overall linear growth. I am a prolific creator of many rather pathetic googological functions My CA rules can be found here Also, the tree game Bill Watterson once wrote: "How do soldiers killing each other solve the world's problems?" Moosey Posts: 2352 Joined: January 27th, 2019, 5:54 pm Location: A house, or perhaps the OCA board. Re: Rules with small adjustable spaceships (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-jkqy4etw5ry6ci7e5bo3bo$5b4o$5bo3bo18$4bo4bo$4b5o$4bo4bo7$3b3o$5bo3bo$2bob5o$5bo3bo$3b3o7$3bo5bo$3b6o$3bo5bo7$2b2o$4bo4bo$3b6o$4bo4bo$2b2o7$2bo6bo$2b7o$2bo6bo7$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). AbhpzTa Posts: 473 Joined: April 13th, 2016, 9:40 am Location: Ishikawa Prefecture, Japan 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: x = 20, y = 21, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e4$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-jkqr6ik7e4bo46bo$3bo6bo22bo16bo7bo$2bo8bo37bo9bo$4bo4bo2bo22bo15bo5bo2bo2$28bobobo4bo2$35bo$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-jkqr6ik7e4bo28bo$3bo7bo20bo6bo$2bo9bo18bo8bo$4bo5bo2bo19bo4bo2bo5$29bo2bo$o2bo27bo6bo$2bo7bo19bo8bo$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-jkqr6ik7e4bo41bo$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: 1047
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:
x = 12, y = 22, rule = B2ae3acnqy4aint5aj6c7e8/S01e2ce3cjnqr4acejknr5-jkqr6ik7e3bo$2bo6bo$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-jkqr6ik7e3bo38bo$2bo6bo31bo7bo$bo8bo29bo9bo$3bo4bo2bo30bo5bo2bo3$27bo2$29bo2$24bobobo2bo2$b2o26bo10b2o$o2bo35bo2bo$27bo4$3bo$2bobo5bo$43bo$4bo37bo7bo$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-jkqr6ik7e3bo41bo$2bo6bo34bo6bo$bo8bo32bo8bo$3bo4bo2bo33bo4bo2bo5$29bo2$31bo2$b2o22bobobo3bo9b2o$o2bo38bo2bo$31bo2$29bo2$3bo$2bobo5bo2$4bo6$50b3o$44bo$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-ac783bo$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)
AforAmpere

Posts: 1047
Joined: July 1st, 2016, 3:58 pm

Re: Rules with small adjustable spaceships

A constructed example of a rule supporting XOR-extendable spaceships:
x = 38, y = 133, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci82b36o$bob5ob3ob3obob19o$2b36o3$b36o$b31obobobo$b36o9$2b31o$b2obobob5obob3obobobobob3ob2o$2b31o3$2b31o$bob5ob3ob3obob9obobobo$2b31o3$b33o$2bob3obobobobob3ob7ob5o$b33o3$2b31o$4obob9obobob5obob3ob2o$2b31o3$2b32o$obob3ob7ob5ob3ob3obob3o$2b32o3$3b31o$2b2obobob5obob3obobobobob3ob2o$3b31o5$b20o$2bob3obobobobob3ob2o$b20o3$2b19o$4obob9obobobo$2b19o3$2b20o$obob3ob7ob5o$2b20o3$3b18o$2b2obobob5obob3ob2o$3b18o3$3b19o$2bob5ob3ob3obob3o$3b19o3$2b20o$3bob3obobobobob3ob2o$2b20o5$4b6o$3b2obobobo$4b6o3$4b7o$3bob5o$4b7o3$3b7o$4bob3ob2o$3b7o3$4b7o$2b4obob3o$4b7o3$4b7o$2bobob3ob2o$4b7o3$5b6o$4b2obobobo$5b6o3$5b7o$4bob5o$5b7o3$4b7o$5bob3ob2o$4b7o3$5b7o$3b4obob3o$5b7o3$5b7o$3bobob3ob2o$5b7o3$6b6o$5b2obobobo$6b6o!
I like making rules
fluffykitty

Posts: 625
Joined: June 14th, 2014, 5:03 pm

Re: Rules with small adjustable spaceships

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

c/7:
x = 4, y = 14, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8bob$bob$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$bob$3b! c/9: x = 4, y = 42, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8bob$bob$obo$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3b$bob!

c/11:
x = 4, y = 106, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8bob$bob$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$3o$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$3b! 2c/12: x = 4, y = 134, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8bob$bob$obo$3o$obo$3o$3o$3o$obo$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$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$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$3o$3o$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:
x = 4, y = 436, y = 134, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8bob$bob$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$3o$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$3o$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$bob! 3c/17: x = 4, y = 539, y = 134, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8bob$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$3o$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$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$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$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$3o$3o$obo$3o$3o$3o$obo$3o$obo$3o$3o$3o$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$3o$obo$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 A for awesome Posts: 1880 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Re: Rules with small adjustable spaceships This takes around 28 million generations to stabilize: x = 94, y = 3, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci894o$92obo$94o! p45980: x = 3, y = 79, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci83o$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: x = 3, y = 97, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci83o$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: x = 3, y = 99, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci83o$3o$3o$3o$3o$3o$3o$3o$3o$3o$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$obo$3o$3o$3o$3o$3o$obo$3o$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) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm Re: Rules with small adjustable spaceships AforAmpere wrote:This takes around 28 million generations to stabilize: x = 94, y = 3, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci894o$92obo$94o! Adding B3e yields a small c/4 glider, while (I think) preserving every pattern you posted: x = 2, y = 3, rule = B2cei3ej4c5i6c8/S1e2i3-ckqr4air5i6ci8bo$o$bo! she/they // Please stop using my full name. Refer to me as dani. "I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D. danny Posts: 966 Joined: October 27th, 2017, 3:43 pm Location: New Jersey, USA Re: Rules with small adjustable spaceships Wow, a p113725632: x = 3, y = 199, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci8bo$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$3o$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$3o$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: 1047 Joined: July 1st, 2016, 3:58 pm Re: Rules with small adjustable spaceships All of the ships I could find in fluffykitty's rule: x = 2311, y = 483, rule = B2cei3j4c5i6c8/S1e2i3-ckqr4air5i6ci82304b6o$2303b2obobobo$2304b6o18$1774b535o$1772b4obob5obobobob7ob3obobobob3obob3obob5ob3obobobob3ob3ob3obob5ob5ob5obob3obob3ob3obobobobobobobobobobobob11ob3ob3obobobobobob3ob5ob11ob7obob3ob7obobob3ob9ob7ob5obobobob3obob5obob3obob3obobobob5ob9obobobob11ob7obobob7ob7ob5obobobobobob3obob5ob7ob3ob7ob3obobobobob9obobob3obob3obobob3obobob3ob3ob5ob9ob11ob3ob3ob3obobobobob3obob15obob9ob5ob3obob2o$1774b535o18$2179b130o$2178b2obobob5ob7obob5ob5ob3ob9obob3obob5obobobobobob13ob3obob3obob3ob3obobob3obob7ob3obob2o$2179b130o18$648b1661o$647bob9ob5obobobobob3obob3obob3ob3ob3obob9obob7obob5obob3ob5obobobobobobobob5ob5ob3obobobobobob5obob3ob3obob3obobob3ob3ob11ob7obobob3ob3obobob11obobob5ob3ob9obob5obob3ob3obobob3obobobobob7ob7obob7ob5ob3ob3obobob5obobob9obob11obob5obob3ob5ob9obob3ob3obob3ob9obob15obob3obobobob5obob3ob9obobobobobobobobobobobob5ob3obob3obobob5ob3obob9ob3ob5obob13ob3ob3ob3obob5ob9ob3obob9obob3obob5ob5obobobobob3ob7ob13ob3ob3obob3obobob7obobobob3obobob13ob3obob7ob7ob9ob13ob9ob5ob5ob3ob3ob11obobob3ob3obob5ob3ob3obobob7ob3ob3obobobobobobobob5obob7ob3ob3ob9obobobob5ob5obobob5obobob3ob3obobob3obobobob3ob5obobob3ob3obob3obobobobobobobob9ob3obob5obob5ob11obobob27obobob17ob5obobobob3ob11ob3ob9obobob3obob5ob7obobob5ob3obobobob3ob15ob7ob3obobobob5obob3obob5obobobobobobobob5ob3ob7ob3ob3obob3obob5obobob5ob9ob3ob3ob5ob5ob5ob7ob3ob11obobobobobob3obobobob5ob5obob3obobob3ob5obobobobobob7ob3ob3obob3ob5ob3ob3ob3obobobobobobobobobobobob3obobob5ob7obobob3ob5ob7ob3obob3ob3obobobobobobobob7obobobob3ob3ob3ob9ob3ob3ob3obob5ob3ob7obobobobob5obob5ob5obobobobob7obob3obob2o$648b1661o18$b2308o$2obobob7ob3ob3obob5obobob5ob3ob3obob3obobobob3obobobob3obob3ob9obob5obobob3ob3obobobobob3ob3obobob3obob3ob3ob9obob7obobob11obobobobob5ob17ob7obobob3ob7ob5obob3obob3obob3obobobob5ob5ob9obob3obobobobob3obobob5ob3obobobob9obob3obob5obob7obobobob5obob9obob3ob3ob5ob3obobobobobobobob3ob13ob7ob3ob5obob9obob3obobob3obobob3ob3obob11obob3ob5ob7obobob3obob9obob5obob3obobob3obobobobob3ob11ob5obob3ob5obobobobobob3ob13obobobobobobobob3obobobobobob3ob3ob5obob9ob3obob3obob11obob3ob3ob3ob7ob3ob3obobob3ob3obobobobob5ob3obobob9ob3ob5ob15obob5obobob5ob3obob3obobobobobob9ob3ob7obob3obobob3obob3obob3obobob3obobob3ob5obob7obob3obob3obob3obob3obob5obobob3ob9ob11obob9ob3obob9ob3ob7obobob3ob7ob3ob3obob3obobob3ob5obob3obobob3ob3ob3obobob5obob9ob7ob7ob5ob7obob5ob3obobob9obob3obobob3ob5obob3ob3ob3ob3ob9obob5obobobobobob3ob3ob7ob3ob5ob3ob5ob3obob5obob3ob3obob3obobob3ob3obobob5obobobobobobobob5ob13ob5obobob3ob5ob7ob3ob5obobob3obobob3obob5obob3ob3obobobob5ob3ob7obobob3obob5ob17ob3obob3ob3ob5obobob7obobobobob3ob3obobob7obobobobob5ob3ob11ob3obob3ob9obobobob7ob3obobob3obobobob13ob5ob9ob3obobobobobobobob7ob7obobob5ob3obobobobobob5obob5obobob3ob7ob3obobobobobob3obobob9ob3obobobobobobob3ob5ob13obob3obobobob7obob13obob3ob13obobobob5ob3ob3obob9ob9obob3ob3obobob3ob7ob3ob9obobobob3obob3ob3ob3obob7obobobob3obob5obobobobob3obob3ob7obobobobob9ob5obobob5ob5ob3obob7obob7obobobob9obob5ob15ob3obob3obobob5obobob3ob7ob3ob3ob7obob3obobob3obob7ob5ob3obob15ob7obobobob5ob3ob3obob3obob3ob5obobob3obob2o$b2308o18$2299b10o$2298b2obob3obob2o$2299b10o18$2086b223o$2084b4ob5ob11obobob3ob7obob3ob3ob5ob3obobobob7ob3ob13ob9ob3obobob3obob3ob3ob3ob7obob7ob3obob3ob19obob5obob5obob5obob9ob5ob3obobob2o$2086b223o18$2236b73o$2235bob5ob7obobobobobobob7ob3ob3ob3ob5ob3ob3obob3obobobob2o$2236b73o18$2053b256o$2052b2obob3ob7obob3obobobob13obobobobob3obobob3obobobob3ob5ob5ob3ob5ob3obobobobob3obob5ob3obobobob3obob3obob5ob5obob5ob5ob19ob5ob5ob5ob5ob5obob3obob3obob3ob5ob5ob3obobobob2o$2053b256o18$2267b42o$2266b6obobobob3ob5ob5ob3obobobobobob2o$2267b42o18$2271b38o$2269bob5ob3obob3obob5obob3ob3obobob2o$2271b38o18$1898b411o$1897b3ob3obobob3obobobob3ob3ob3obob5obob5ob7ob13obobob3obob5ob3ob3obobob3obob3obob17obobob5obob3ob3obob3ob3ob3obob3ob3obobob5ob3ob5obob5obobobob3obobobobob7obob3ob5ob3obob5obob13ob3obobob3obobob9ob3obobobobob5obob7ob3obob5obobob5obobob3obobobobobobobobob3ob3obobobobob3obobob5obob3ob3ob6o$1898b411o18$419b1890o$417bob7ob5obobob5obobob9ob7obob7ob9ob7ob3obobob7ob9obobob3ob3ob3obob3ob7obob3ob5ob13ob7ob3obob3ob11obobobobob3ob5ob11obob3ob5obobobob3ob3ob3obobobobobob3obobobobob3ob5ob3ob5obob3obob3ob5ob9ob3obobobob9ob3obob5obobobobobob3obob3ob3ob3obob5obob3ob7ob3ob5ob7ob3obobobobob3ob3ob9obobobobobobobob3ob5obobob3obobobob3obob13ob5ob5ob9obobobobob5ob3ob3ob5obobobobob7ob3ob5ob5obobob3obob3ob3obob5ob3ob3ob3obob3ob3ob3obob5obob3obob3obobobobob7obob3ob3obobobobobobob5ob3ob7obob11obobob3obobobobobob7obobob3obob3obobobob5ob5ob5ob3obob3obob7ob7ob9obob7ob7ob3obobob5ob7ob3obob5obobob3obobob5obobob3ob5ob3ob5ob7ob9obob3ob3ob5obob3ob3obob7ob9ob3ob5ob3obobobob3ob3obobob3ob3ob9ob7ob7ob3obobobobobob3obob9obobob7ob5obobob9ob3ob3ob7obob5obobob5ob3obobobob5obob3obobobobob7obobob3ob5ob7obob3obobobobobobob3obob3ob11ob5obobobobobob5ob11obob7ob5ob11ob5obobobobobobob3obobob5ob3ob5obobobobob5ob5ob11ob5obob3obob7ob9obobobobobobobob3ob5ob3ob3ob3obob5ob3obob7ob19ob3obobobobobobobob5ob3obobobobobob5ob5obob3obobobobobobobobobobobob3ob9ob3obob7ob5ob3ob5ob9obobobobobobob5ob9ob9obob9obob7obob11ob3obobob3obob15obobob5obob7ob5obob5ob5ob15obob3obobobobob5ob9ob5ob5ob5ob3obobobob7obob5obobob9ob3obobobobobob2o$419b1890o18$2206b103o$2207bob5obobob5ob9obob7obobob5ob3ob3obob7ob5ob3obobob7obobob3obobobob2o$2206b103o18$2238b71o$2237b5ob3ob3ob3obobobobob3ob3ob7obobobobob7ob3obobob8o$2238b71o18$1876b433o$1875bob3ob3ob5ob9obobobob3obobobobob5obobob3ob3obob9obobob3ob3obobobob9obobob3obobobobob7obob7ob3obobobob5ob3ob3obob9obob3ob3obobobob5ob3obob5ob9obobobobob7obob3obob3obobobob5obobobobob5obobobobob3ob7obob7ob5obobobob3obob3ob5obob5obob3obob3obob3obobobob3ob7obob3obob3ob3obob3obobob7obob5obobob3ob3obobobobob2o$1876b433o18$1383b926o$1382b8obobobob5ob5ob3ob7ob3ob5ob5obobobob3ob9ob5ob7ob3obobobob5obob3ob7obob9obob5obobob7obob15obobobobobob5ob3obob3obobobob5ob3obobob3obobobob5ob5ob11ob3ob3ob3ob3obobobob5ob7obobob5obob5obob3ob3ob5obobobob3obobobob3ob7ob3ob3obobobob3ob3obob5ob3obobob3obob3ob3obob7ob3obob3obob5obobob3obob3obob11ob3obobobob3obobobobob3obob5ob3ob3obobob5obob5ob3obob3obob5ob3obobob3ob3obob3obobobobob3obobobob3obobob7ob5obob3ob7ob3ob3obobobob3ob9ob3ob3ob3ob5ob11ob3obob3ob3ob9obob3ob5ob3ob5obob5obob3obob3ob9obob9ob7obob7obobobobobob3ob3obobobob3ob3ob9ob7ob9ob3ob3ob5ob3ob3obobob3obobobob5obob3ob15obob3obob7ob7obob6o$1383b926o18$2193b116o$2193b9ob3obobob3obobobobob5obob3ob3ob3obobob9obobobobobob3obobobobob5obobobobobob3obobobobobob2o$2193b116o18$2272b37o$2271bobob3ob3obobob15obobob4o$2272b37o18$1968b341o$1967b3ob3obob11obobob5obobob5ob9obobob3obob7ob5ob3obobobob7ob3ob3ob3ob5obobob3obobobob7ob3obob3obobob3ob23ob7obobob5ob3ob3obobobob3ob7obobob5ob3obobob5obobobob3ob3ob3ob5obobob7ob7ob5obobob7ob13ob9ob3obobobob4o$1968b341o18$2273b36o$2273b3obob5ob5obobob3obobob8o$2273b36o18$1894b415o$1892b2obob5ob3obob7obobobobob7ob5ob3obob5obobobob3obobobob11ob3ob5obobob3obobob3ob3ob3obobobobobob5ob3ob11ob5obob5obobob5ob7ob3ob7obob5obobobob3ob3obobobobob5obob3obobobob3ob3obob3ob13ob7ob11ob3obobobob5ob5ob13ob9obob7obobob7ob3ob3obob7ob3obobob3ob3obob3obobob3ob3ob6o$1894b415o18$2201b108o$2200b4obobobob3obob3ob5ob5obobobob5obob3ob3ob9obobob3ob3obobob3obob5ob5obob10o$2201b108o18$2137b172o$2137bobob5obob5ob11obob13obob3obobob3ob3ob3obob5obobob9obobobobob3ob5ob7obobob3obob3ob3ob7obobob3ob3ob3obob7ob6o$2137b172o18$1853b456o$1852b2obobobob3obob5obob3ob3obobob3obobobobobob3obob7obob11obobobob3ob5obobobobobobob3ob3obob3obob7ob7obobobob3obob19obobobob7ob9ob5obob3ob9obobob3obobob5ob3ob3ob3obobobobobob3ob3ob5ob7ob3obob7ob11ob3ob3ob3obob3ob3ob9ob5ob3ob5ob3ob3obob3ob3obobobob5obobob3obob3ob3obobobobobob7ob3obob5obob3obobobob13ob4o$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) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 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)}): x = 114, y = 36, rule = B2a3jkq/S01c3e103bo$102bo10bo$106bo5bo$106bo5bo$102bo10bo$103bo5$79bo$78bo34bo$85bobo5bo3bo7bobobo$85bobo5bo3bo7bobobo$78bo34bo$79bo5$bo$o112bo$3bobo5bo7bo3bobo7bobo3bobobo7bobo9bobo5bo3bobo3bo3bobo11bo5bobo$3bobo5bo7bo3bobo7bobo3bobobo7bobo9bobo5bo3bobo3bo3bobo11bo5bobo$o112bo$bo5$7bo$6bo106bo$13bobo9bo5bobo5bo3bo3bo5bo11bo3bobobo3bo3bo9bobo5bo3bobobobo$13bobo9bo5bobo5bo3bo3bo5bo11bo3bobobo3bo3bo9bobo5bo3bobobobo$6bo106bo$7bo!
m=3 and n=17 (reaction=(5,5,7)):
x = 540, y = 6, rule = B2a3jkq/S01c3ebo$o538bo$7bobo3bo5bo9bobo11bo3bo5bobobobo3bo3bobobo9bo3bo3bo3bo3bo3bobobobo7bobo11bo3bo3bobo7bo3bo5bo3bo3bobo3bo5bo5bobo3bobo3bobobo17bobo5bo7bobo3bobobo5bobobo3bobo3bo9bobobo3bo5bo13bobo3bobo3bo5bobo5bo9bobo3bo7bobo3bobo3bobobo3bobo5bobobo5bo5bobo9bo3bobo7bo11bobobo5bobo11bobobo9bobo3bobo9bo3bo3bo5bobo11bobo7bo3bobo3bobo$7bobo3bo5bo9bobo11bo3bo5bobobobo3bo3bobobo9bo3bo3bo3bo3bo3bobobobo7bobo11bo3bo3bobo7bo3bo5bo3bo3bobo3bo5bo5bobo3bobo3bobobo17bobo5bo7bobo3bobobo5bobobo3bobo3bo9bobobo3bo5bo13bobo3bobo3bo5bobo5bo9bobo3bo7bobo3bobo3bobobo3bobo5bobobo5bo5bobo9bo3bobo7bo11bobobo5bobo11bobobo9bobo3bobo9bo3bo3bo5bobo11bobo7bo3bobo3bobo$o538bo$bo! A relative seems to have all velocities c/n. x = 271, y = 456, rule = B2a3ejkq4ekrtw5ijn6ein7c8/S01c2cen3ejq4ikntyz5-ce6-ai868b2ob2o6bobo7bo5bo8bobo14bo2bo8bo2bo5bo2bo8bo2bo8bo2bo12bo2bo6bo2bo7bo2bo4bo2bo4bo2bo5bo2bo$59b3o7bobo8bo10b3o13bo11bo6bo$58b2obo28bobobo12b3o11bo2bo87b2o$58bob3o26bob3obo9b2obo$58b3o31bo13b2o11b2o4b2o7b2o123b2o$60bo28bo2bo2bo10bo60b2o35b2o56bo7bo$90bo3bo10b2o12b2ob2ob2o7b2o7b2o10b2o26b2o27b2o48bo2bo4bo$106b2obo94b2o59bo$104bob2o14b2o19b2o10b2o26b2o27b2o45b2o$107b3o110b2o7b2o$104bo3bo25b2o7b2o10b2o36b2o17b2o$104bob2o24bo4bo29b2o51b2o7b2o$102b3obo12b2ob2ob2o6bo2bo46b2o8b2o17b2o$105b2o60b2o60b2o$103b4o15b2o19b2o48b2o$100bo3b4obo57b2o35b2o$101b2ob2o2bo34b2o10b2o26b2o27b2o$102bobobo97b2o$108bo10b2ob2ob2o56b2o8b2o17b2o$204b2o23b2o$bo2bo5bo2bo4bo5bo5bo3bo6bobo3bobo50b4o2b2o11b2ob2ob2o28b2o26b2o8b2o17b2o$o4bo3bo4bo91bo15b2o105b2o$2b2o37b2o4b2o51bob2o2bo12b2o4b2o28b2o$11b2o24bo10b2o52b2o2bo60b2o35b2o14b2o$17b2o5b2o3b2o3b2o65b2o3bo12b2o4b2o16b2o38b2o8b2o17b2o$23b2o8b2o68b2obo15b2o80b2o$101b2o16b2o4b2o27b4o35b2o$42b2o56bo2b2obo$36b2o63bo3bo16b2o19b2o10b2o36b2o$121bo2bo42b2o51b2o7b2o$103b2o14b2ob2ob2o56b2o27b2o$120bob2obo41b2o$101bo4bo86b2o$102bo2bo98b2o23b2o$183b2o8b2o17b2o$181bo4bo17b2o14b2o$120b2o2b2o29b2o25bo2bo26b2o$220b2o7b2o$120b2o2b2o67b2o17b2o$122b2o80b2o14b2o$155b2o36b2o17b2o$167b2o51b2o7b2o$120b2o2b2o17b2o67b2o$122b2o43b2o$155b2o36b2o17b2o$167b2o51b2o$143b2o10b2o$122b2o43b2o35b2o23b2o$120b2o2b2o17b2o48b2o$122b2o105b2o$193b2o$220b2o$120b2o2b2o29b2o53bo4bo$122b2o80b2o5bo2bo$193b2o$167b2o35b2o23b2o$193b2o$167b2o33bo4bo12b2o7b2o$143b2o58bo2bo2$122b2o19b2o10b2o36b2o$167b2o$120bo4bo17b2o48b2o$121bo2bo42b2o$143b2o10b2o$220b2o$143b2o9bo2bo35b2o$227bo4bo$143b2o48b2o33bo2bo$220b2o$143b2o10b2o$167b2o$155b2o36b2o$167b2o$155b2o36b2o$153bo4bo61b2o$154bo2bo3$220b2o$143b2o$167b2o$143b2o$167b2o51b2o2$167b2o51b2o2$167b2o3$143b2o2$143b2o48b2o2$193b2o$167b2o$143b2o2$143b2o48b2o2$143b2o48b2o$167b2o51b2o$143b2o$167b2o51b2o$143b2o48b2o3$220b2o$193b2o$167b2o$143b2o$167b2o51b2o$143b2o48b2o$167b2o51b2o$193b2o$167b2o51b2o2$167b2o51b2o$143b2o48b2o$220b2o$143b2o$167b2o$193b2o2$143b2o48b2o$167b2o51b2o$143b2o$220b2o$193b2o$167b2o$193b2o2$143b2o3$167b2o51b2o2$166bo2bo$193b2o$220b2o$143b2o22b2o24b2o2$193b2o$220b2o$167b2o2$167b2o24b2o2$167b2o2$143b2o22b2o24b2o$220b2o$143b2o48b2o2$143b2o2$167b2o$220b2o$167b2o23b4o2$143b2o22b2o22b2o2b2o$193b2o25b2o$143b2o22b2o22b2o2b2o$220b2o$143b2o46b2o2b2o$220b2o$143b2o46b2o2b2o2$165b6o20b2o2b2o$166bo2bo$191b2o2b2o$193b2o$143b2o2$143b2o$193b2o$191b2o2b2o$220b2o$143b2o$193b2o25b2o3$143b2o2$143b2o$218bo4bo$191b2o2b2o22bo2bo2$191b2o2b2o$193b2o3$191b2o2b2o2$191b2o2b2o2$143b2o46b2o2b2o2$191b2o2b2o2$143b2o2$143b2o4$191b2o2b2o$193b2o$143b2o2$143b2o46b2o2b2o$193b2o$191b2o2b2o4$143b2o2$191b2o2b2o4$143b2o3$193b2o3$143b2o46b2o2b2o2$143b2o46b2o2b2o2$191b2o2b2o4$191bo4bo2$191bob2obo2$143b2o46bob2obo2$191bo4bo2$191bob2obo2$191bo4bo2$143b2o46bo4bo2$191bo4bo2$191bob2obo2$191bo4bo2$143b2o46bo4bo2$143b2o46bo4bo2$191bob2obo2$143b2o46bo4bo2$191bo4bo2$191bob2obo$142b4o$191bo4bo$143b2o$191bob2obo2$191bob2obo$143b2o$191bob2obo$143b2o$191bob2obo$143b2o$191bo4bo$143b2o$191bob2obo2$191bo4bo2$191bo4bo2$191bob2obo$143b2o$191bob2obo$143b2o$191bob2obo$143b2o$191bob2obo2$191bob2obo$143b2o$191bo4bo$143b2o$191bob2obo$143b2o$191bob2obo2$191bo4bo$141bo4bo$142bo2bo45bo4bo2$191bo4bo2$191bo4bo2$191bo4bo2$191bo4bo2$191bob2obo2$191bo4bo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bo4bo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bob2obo2$191bo4bo2$191bo4bo2$191bo4bo2$191bo4bo2$192bo2bo6$193b2o2$193b2o12$193b2o4$193b2o10$193b2o6$193b2o5$192bo2bo$193b2o6$193b2o2$193b2o2$193b2o4$193b2o10$193b2o2$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:
x = 69, y = 12, rule = B2-cn3aeqry4inqrtwz5aciy6ak/S2e3aq4ajkz5iqb4o14b4o5b4o5b4o5b4o5b4o5b4o2$2o2b2o12b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o$bo2bo14bo2bo5bo2bo5bo2bo5bo2bo5bo2bo5bo2bo$o4bo12bo4bo3bo4bo3bo4bo3bo4bo3bo4bo3bo4bo$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.

x = 204, y = 92, rule = B2akn3cn4ijnrw5cij6a8/S1c2-ak3ceiy4acenw5iqr6c89$119bobo4bobo15bo4bo$17bobo2bobo75bobo2bobo12bo6bo17bo2bo$4bo4bo8bo4bo20bobo2bobo7bobobobo7bobobobo7bobobobo7bo4bo14bo4bo16bobo2bobo19bobobobo14b2o$3bo6bo6bobo2bobo7bo4bo7bo4bo48bo8bo11bo2b2o2bo17b4o$31bo6bo5bobo2bobo7bo5bo13bo7bo35b2o18bobo2bobo25bo13bo2bo$99b2o2b2o2b2o9bobo6bobo9bo3bobo2bobo3bo$59bobobobo11bo9bobobobo6b2ob2ob2o11b2obo2bob2o9bo2b2o2bo2bo2b2o2bo14bobobobo$101bo4bo11bob2o4b2obo12b2o6b2o$59bo5bo9bo11bo5bo8b4o13bo2b4o2bo9bo3bo3b2o3bo3bo14bo$4bob2obo8bob2obo8bob2obo7bob2obo50bob2obo12b2o6b2o15b2o2b2o$3b8o6b8o6b8o5b8o7bobobobo7bo13bobobobo8b4o13bo3b2o3bo9b2o4bo4bo4b2o14bobobobo$4bob2obo8bob2obo8bob2obo7bob2obo48bob6obo7bo2bobo4bobo2bo10b2o6b2o$3bobo2bobo6bobo2bobo6bobo2bobo5bobo2bobo49bo4bo14b2o2b2o13b2o10b2o$4bo4bo8bo4bo8bo4bo7bo4bo48bob2o2b2obo7b3o10b3o9bobobo2bobobo$101bo4bo8bobo3b2o2b2o3bobo6b3o10b3o$121bo4bo11bo2bob2o4b2obo2bo$123b2o15bobo8bobo$117bobo2bo2bo2bobo7bo3bo8bo3bo$123b2o14bo2b2obo2bob2o2bo15bob3o2bo13b2o$121bo4bo13bo2b2o4b2o2bo13b2o2bobo2bo$120bo6bo12b2o10b2o13b3ob3o3b2o12bo$119bob6obo10bo3bo2b2o2bo3bo10bo2bo6bobobo$120bob4obo18b2o18b2o2b2obo2bobo$121b2o2b2o11bo2bo2bo4bo2bo2bo11bo2b2obo$117bo4bo2bo4bo9bo2bo6bo2bo15bo$123b2o15b2ob3o2b3ob2o15b3o6bo$116b2ob2o6b2ob2o12bo4bo16b2obobo3b3o$117bo3b2o2b2o3bo14b4o16bo4b2o2bobo3bo$116bo2b2o6b2o2bo8bo4bo2bo4bo9bo4b2o2bobob2o$116bo4bo4bo4bo7bobo3bo2bo3bobo9bobo5bob2obo3bo$115bobobobo4bobobobo6b2o5b2o5b2o7b2obo3bo2b3obo2bobo$116bo2b2o6b2o2bo6bo6bo2bo6bo12bo3bob2o3bo2bo$122b4o14bo2bobo2bobo2bo11b2o3b2ob2o3b2o$119b2o2b2o2b2o9b2o6b2o6b2o7bo5bo4b2o2bo3bo$120bobo2bobo11bo2b2o6b2o2bo10bo3bo4bo3b2o$120bobo2bobo12b3o3b2o3b3o9bo8b2obo3bo$120bo6bo12bob2obo2bob2obo8b2o2bo2bo2b2o2bobob3o$119bo8bo11bobo8bobo9bo3b2o5bob2o$141b2o8b2o11b2o2b2obo4bo3bobo$119bo8bo14bobo2bobo19b4o3bo$120b2o4b2o13b4o4b4o11b4o3b2o5bo$121b6o17bo4bo11bob2obobo2b3obo3bob3o$121bo4bo15b4o2b4o8bob4o3bo2bo6bo$121bob2obo14b2o2bo2bo2b2o15bo2b2ob2obobo2bobo$121bob2obo35b4o3b3o3bo3bobo$123b2o20b4o12bob3o10b4obobo$142b10o14bo9b2o$121bo4bo18bo2bo15bo3bo5bo5b2obo$122bo2bo16b2o2b2o2b2o13bo4bo4bo3b2o$120b3o2b3o11bob2o3b2o3b2obo13b2o4bo4bo$140bobobo4bobobo11bo2bobo$123b2o14bobo2bo4bo2bobo9bo2b2o5b4o$116bobo2bo4bo2bobo37b3o5bob2o$116bo14bo9bo10bo14bo3bob2o2b2o$116b2o4bo2bo4b2o36bobo2bo3bo$118b3o6b3o36b2o2bobo4bo$118bo10bo39bo5bo2bo$166b2o$168b2o7b2o$166bobo2$163b5o9bobobo$166bo12b2o$179bobo$166b2o9b4o$166bo12b2o$180bo!

2718281828

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

Re: Rules with small adjustable spaceships

x = 7, y = 7, rule = 1c23-y4c5e6c/34e6in/152.3A$A5BA$7B$AB3DBA$.A3DA$2.ADA$3.A![[ THEME Blues ]]

x = 7, y = 7, rule = 1c23-y4c5e6c/34e6in/1502.3A$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!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Rules with small adjustable spaceships

muzik wrote:Adjustable speed via rule changes:

x = 7, y = 7, rule = 1c23-y4c5e6c/34e6in/152.3A$A5BA$7B$AB3DBA$.A3DA$2.ADA$3.A![[ THEME Blues ]]

x = 7, y = 7, rule = 1c23-y4c5e6c/34e6in/1502.3A$A5BA$7B$AB3DBA$.A3DA$2.ADA$3.A![[ THEME Blues ]]

That's doable in almost any appropriate Generations rule.
That that is, is. That that is not, is not. Is that it? It is.
A predecessor to my favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i4b3o$6bo$o3b3o$2o$bo!

Hdjensofjfnen

Posts: 1297
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

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:
x = 3, y = 2, rule = 126/345/23A$.A! x = 3, y = 2, rule = 126/345/33A$.A!

...
x = 3, y = 2, rule = 126/345/163A$.A! ... etc.! x = 4, y = 3, rule = B3-q4z5y/S234k5j2b2o$b2o$2o! LaundryPizza03 at Wikipedia LaundryPizza03 Posts: 457 Joined: December 15th, 2017, 12:05 am Location: Unidentified location "https://en.wikipedia.org/wiki/Texas" 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. <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". x = 72, y = 35, rule = B2c3ajq4ijk5n6c7e8/S12-en3-jkqy4etw5ry6ci7e4bo8bo13bo2bo14b3o2b3o14bo2bo$3bob3o2b3obo13b2o13bo4b2o4bo11bob2obo$3b3o2b2o2b3o12bo2bo12bob3o2b3obo11bob2obo$7bo2bo14bobo2bobo11bo8bo14b2o$4b2obo2bob2o10bo3b2o3bo10bo2bo2bo2bo$3b2obo4bob2o7b2o10b2o7bo3bo2bo3bo$3ob2o6b2ob3o2bo6bo2bo6bo9bo2bo$o4bo6bo4bo3b2o12b2o5bo2bobo2bobo2bo$bo4bo4bo4bo5b2o10b2o6bo2bobo2bobo2bo$bo2bobo4bobo2bo5b2o10b2o11bo2bo$2bo3bo4bo3bo5bo2bo8bo2bo7b4o2b4o$ob2o2bo4bo2b2obo3bobobo6bobobo7bo2bo2bo2bo$o3b3o4b3o3bo3bobobo6bobobo6bo2bo4bo2bo$o2b2obo4bob2o2bo3bo2bobo4bobo2bo6bo2bo4bo2bo$o2bo2bo4bo2bo2bo3bo3b2o4b2o3bo5bo4bo2bo4bo$obo12bobo3bo3b2o4b2o3bo5bo4bo2bo4bo$obobobo4bobobobo3bob3o6b3obo$o6bo2bo6bo3bobobo6bobobo6b4o4b4o$o2bobo6bobo2bo3bo2bobo4bobo2bo$o2bobobo2bobobo2bo4b2obo2b2o2bob2o6bo4bo2bo4bo$o2b3o6b3o2bo10b2o$o6bo2bo6bo9b4o$o3b2o2b2o2b2o3bo6bob6obo$o3b2o6b2o3bo8b6o$o2bo2bo4bo2bo2bo$o3b2o6b2o3bo$2obo10bob2o$2bo12bo$bob4o4b4obo$3b2o2b4o2b2o$2bo2bobo2bobo2bo$2bo4bo2bo4bo$2b3o2bo2bo2b3o2$4bo8bo!
The latest version of the 5S Project contains over 221,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
wildmyron

Posts: 1238
Joined: August 9th, 2013, 12:45 am

Re: Rules with small adjustable spaceships

Adjustable lightspeed ships with period 3^n:
x = 26, y = 42, rule = B2ain3ackr4eijkrw5cnry6e/S02aei3-ciky4jt5cnry6e7e25bo$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) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm 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 x = 70, y = 20, rule = B2ce3cnqry4aeijkyz5cj6a7c/S12ik3aejqy4ijnw5jnq6a3bo29bo29bo$3o27b3o27b3o$3bo29bo29bo4$67bobo$68bo$68bo$68bo3$43bobo$44bo$44bo$44bo$17bobo$18bo$18bo$18bo! 2. x = 67, y = 20, rule = B2ce3y4ejkr5i/S12ei3ry4r3bo29bo29bo$3o27b3o27b3o$3bo29bo29bo$64bobo$65bo$65bo$65bo6$43bobo$44bo$44bo$44bo$17bobo$18bo$18bo$18bo! 3. x = 70, y = 20, rule = B2ce3akq4ejrwz5aein8/S012eik3enry4cqz5c6ae83bo29bo29bo$3o27b3o27b3o$3bo29bo29bo4$67bobo$68bo$68bo$68bo3$43bobo$44bo$44bo$44bo$17bobo$18bo$18bo$18bo! 4. x = 70, y = 20, rule = B2-an3kq4aejnw5ceinq6in7e/S12ik3cqy4ceknz5eir6c3bo29bo29bo$3o27b3o27b3o$3bo29bo29bo4$67bobo$68bo$68bo$68bo3$43bobo$44bo$44bo$44bo$17bobo$18bo$18bo$18bo! If you're the person that uploaded to Sakagolue illegally, please PM me. x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Saka

Posts: 3117
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

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!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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