Rules with small adjustable spaceships

[NimbleRogue]

I have been doing more investigation into rules based on My sideways mealworm rule from a while ago

In this rule length 7+10n is a rightward adjustable ship that moves at 2+4nc/192n^2+304n+90, length 24+10n is a adjustable knightship that moves at (1+n,2+n)c/24n^2+140n+200, and length 22+10n is an adjustable ship that moves downward at 2+2nc/48n^2+296n+426, lastly 9+10n is an adjustable oscillator in addition lengths 5 and 12 are oscillators

Code: Select all

x = 291, y = 123, rule = B2cik3ajkq4ajr5cy6n/S1e2ce3acjnr4aky5aeij6ack78
263b4o$262b5o$260b2ob4o28$263b11o$262b12o$260b2ob11o28$3b6o74b23o77b
31o49b8o$2b7o73b24o76b32o48b9o$2ob6o71b2ob23o74b2ob31o46b2ob8o28$3b26o
54b33o67b41o39b18o$2b27o53b34o66b42o38b19o$2ob26o51b2ob33o64b2ob41o36b
2ob18o28$3b46o34b43o57b21o59b28o$2b47o33b44o56b22o58b29o$2ob46o31b2ob
43o54b2ob21o56b2ob28o!

This rule has 5 adjustable ships at lengths 34+20n, 35+20n, 39+20n, 42+20n, and 43+20n that move at 2c/120n+186, 2c/120n+188,c/40n+86, c/40n+94, and c/40n+96 respectively

Code: Select all

x = 410, y = 103, rule = B2ck3ajq4aijkry5cenr6e/S1e2cei3acknr4ajkyz5aeij6ac78
35o43b36o43b40o43b43o43b44o$2b33o45b34o45b38o45b41o45b42o$b34o44b35o
44b39o44b42o44b43o48$55o23b56o23b60o23b63o23b64o$2b53o25b54o25b58o25b
61o25b62o$b54o24b55o24b59o24b62o24b63o48$75o3b76o3b80o3b83o3b84o$2b73o
5b74o5b78o5b81o5b82o$b74o4b75o4b79o4b82o4b83o!

Here are some rules with some more cursed adjustability reactions:

I still have yet to figure out the overarching pattern for adjustable ships in this rule. The mechanics of this rule are bases around a c/14d wickstretcher+signal injector. Signals bounce up and down, and when they hit the c/14d again they either destroy the reaction completely, rephase the c/14d or destroy the c/14d and send out signals that will "reset the pattern"

Code: Select all

x = 3976, y = 142, rule = B2cik3aj4ajr5ceq/S1e2-ak3acjnr4aktwy5aeij6ack78
2bo101bo101bo101bo99b16o104bo101bo101bo101bo101bo99b37o104bo99b49o102b
25o102b61o104bo99b73o104bo99b78o102b85o104bo99b88o102b97o104bo99b109o
104bo99b121o102b133o102b145o$2bo101bo101bo101bo99b17o103bo101bo101bo
101bo101bo99b38o103bo99b50o101b26o101b62o103bo99b74o103bo99b79o101b86o
103bo99b89o101b98o103bo99b110o103bo99b122o101b134o101b146o$bo101bo101b
o101bo100b16ob2o100bo101bo101bo101bo101bo100b37ob2o100bo100b49ob2o99b
25ob2o99b61ob2o100bo100b73ob2o100bo100b78ob2o99b85ob2o100bo100b88ob2o
99b97ob2o100bo100b109ob2o100bo100b121ob2o99b133ob2o99b145ob2o$3o99b3o
99b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b
3o$3o99b3o99b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o
488b3o310b3o$3o99b3o99b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o
274b3o466b3o488b3o310b3o$3o99b3o99b3o99b3o217b3o99b3o99b3o99b3o99b3o
238b3o540b3o274b3o466b3o488b3o310b3o$3o99b3o99b3o99b3o217b3o99b3o99b3o
99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$3o99b3o99b3o99b3o217b3o
99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$3o99b3o99b3o
99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$
102b3o99b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b
3o310b3o$102b3o99b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o
466b3o488b3o310b3o$102b3o99b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o
540b3o274b3o466b3o488b3o310b3o$102b3o99b3o99b3o217b3o99b3o99b3o99b3o
99b3o238b3o540b3o274b3o466b3o488b3o310b3o$102b3o99b3o99b3o217b3o99b3o
99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$102b3o99b3o99b3o
217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$102b3o
99b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b
3o$102b3o99b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o
488b3o310b3o$102b3o99b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o
274b3o466b3o488b3o310b3o$102b3o99b3o99b3o217b3o99b3o99b3o99b3o99b3o
238b3o540b3o274b3o466b3o488b3o310b3o$102b3o99b3o99b3o217b3o99b3o99b3o
99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$102b3o99b3o99b3o217b3o
99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$204b3o99b3o
217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$204b3o
99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$
204b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o
310b3o$204b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o
488b3o310b3o$204b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o274b3o
466b3o488b3o310b3o$204b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o540b3o
274b3o466b3o488b3o310b3o$204b3o99b3o217b3o99b3o99b3o99b3o99b3o238b3o
540b3o274b3o466b3o488b3o310b3o$204b3o99b3o217b3o99b3o99b3o99b3o99b3o
238b3o540b3o274b3o466b3o488b3o310b3o$204b3o99b3o217b3o99b3o99b3o99b3o
99b3o238b3o540b3o274b3o466b3o488b3o310b3o$204b3o99b3o217b3o99b3o99b3o
99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$204b3o99b3o217b3o99b3o
99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$204b3o99b3o217b3o
99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o
99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o
99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o
99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o
99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o
99b3o99b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o
201b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o201b
3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o201b3o99b
3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o201b3o99b3o99b
3o238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o201b3o99b3o99b3o
238b3o540b3o274b3o466b3o488b3o310b3o$306b3o217b3o201b3o99b3o99b3o238b
3o540b3o274b3o466b3o488b3o310b3o$306b3o421b3o99b3o99b3o238b3o540b3o
274b3o466b3o488b3o310b3o$730b3o99b3o99b3o238b3o540b3o274b3o466b3o488b
3o310b3o$730b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$730b3o
99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$730b3o99b3o99b3o238b3o
540b3o274b3o466b3o488b3o310b3o$730b3o99b3o99b3o238b3o540b3o274b3o466b
3o488b3o310b3o$730b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$
730b3o99b3o99b3o238b3o540b3o274b3o466b3o488b3o310b3o$730b3o99b3o99b3o
238b3o540b3o274b3o466b3o488b3o310b3o$730b3o99b3o99b3o238b3o540b3o274b
3o466b3o488b3o310b3o$730b3o201b3o238b3o540b3o274b3o466b3o488b3o310b3o$
730b3o201b3o238b3o540b3o274b3o466b3o488b3o310b3o$730b3o201b3o238b3o
540b3o274b3o466b3o488b3o310b3o$934b3o238b3o540b3o274b3o466b3o488b3o
310b3o$934b3o238b3o540b3o274b3o466b3o488b3o310b3o$934b3o238b3o540b3o
274b3o466b3o488b3o310b3o$934b3o238b3o540b3o274b3o466b3o488b3o310b3o$
934b3o238b3o540b3o274b3o466b3o488b3o310b3o$934b3o238b3o540b3o274b3o
466b3o488b3o310b3o$934b3o238b3o540b3o274b3o466b3o488b3o310b3o$934b3o
238b3o540b3o274b3o466b3o488b3o310b3o$934b3o238b3o540b3o274b3o466b3o
488b3o310b3o$934b3o238b3o540b3o274b3o466b3o488b3o310b3o$934b3o238b3o
540b3o274b3o466b3o488b3o310b3o$934b3o238b3o540b3o274b3o466b3o488b3o
310b3o$1175b3o540b3o274b3o466b3o488b3o310b3o$1175b3o540b3o274b3o466b3o
488b3o310b3o$1175b3o540b3o274b3o466b3o488b3o310b3o$1175b3o540b3o274b3o
466b3o488b3o310b3o$1175b3o540b3o274b3o466b3o488b3o310b3o$1175b3o540b3o
274b3o466b3o488b3o310b3o$1175b3o540b3o274b3o466b3o488b3o310b3o$1175b3o
540b3o274b3o466b3o488b3o310b3o$1175b3o540b3o274b3o466b3o488b3o310b3o$
1175b3o540b3o274b3o466b3o488b3o310b3o$1175b3o540b3o274b3o466b3o488b3o
310b3o$1175b3o540b3o274b3o466b3o488b3o310b3o$1718b3o274b3o466b3o488b3o
310b3o$1718b3o274b3o466b3o488b3o310b3o$1718b3o274b3o466b3o488b3o310b3o
$1718b3o274b3o466b3o488b3o310b3o$1718b3o274b3o466b3o488b3o310b3o$1718b
3o274b3o466b3o488b3o310b3o$1718b3o274b3o466b3o488b3o310b3o$1718b3o274b
3o466b3o488b3o310b3o$1718b3o274b3o466b3o488b3o310b3o$1718b3o274b3o466b
3o488b3o310b3o$1718b3o274b3o466b3o488b3o310b3o$1718b3o274b3o466b3o488b
3o310b3o$1995b3o466b3o488b3o310b3o$1995b3o466b3o488b3o310b3o$1995b3o
466b3o488b3o310b3o$1995b3o466b3o488b3o310b3o$1995b3o466b3o488b3o310b3o
$1995b3o466b3o488b3o310b3o$1995b3o466b3o488b3o310b3o$1995b3o466b3o488b
3o310b3o$1995b3o466b3o488b3o310b3o$1995b3o466b3o488b3o310b3o$1995b3o
466b3o488b3o310b3o$1995b3o466b3o488b3o310b3o$2464b3o488b3o310b3o$2464b
3o488b3o310b3o$2464b3o488b3o310b3o$2464b3o488b3o310b3o$2464b3o488b3o
310b3o$2464b3o488b3o310b3o$2464b3o488b3o310b3o$2464b3o488b3o310b3o$
2464b3o488b3o310b3o$2464b3o488b3o310b3o$2464b3o488b3o310b3o$2464b3o
488b3o310b3o$2955b3o310b3o$2955b3o310b3o$2955b3o310b3o$2955b3o310b3o$
2955b3o310b3o$2955b3o310b3o$2955b3o310b3o$2955b3o310b3o$2955b3o310b3o$
2955b3o310b3o$2955b3o310b3o$2955b3o310b3o$3268b3o$3268b3o$3268b3o$
3268b3o$3268b3o$3268b3o$3268b3o$3268b3o$3268b3o$3268b3o$3268b3o$3268b
3o!

Here is what I have so far
Length 7+12n is an adjustable ship that move at 4+2n/56n^2+284n+326
Length 13+12n is an adjustable ship that move at 2n/2n+56n^2+228n+198
Length 16+72n is an adjustable ship that move at 4+26n/5096n^2+3608n+584
Length 52+72n is an adjustable ship that move at 20+26n/5096n^2+8704n+3662
Length 42+72n is an adjustable ship that move at 16+26n/5096n^2+7192n+2478
Length 78+72n is an adjustable ship that move at 26+26n/5096n^2+12288n+7348

They seem to fall into groups based on the number of times the c/14d wickstrecher+signal injector is hit before being destroyed. Specifically the number of cells needed to adjusts ships seems to be 2*6^(n) where n is the number of times the wickstretcher+signal injector is hit. The adjustable ships also always seem to come in pairs where when one ship with base length m works there is an adjustable ship with base length (m+6^(n))%2*6^(n) that moves perpendicularly to the original.

I am unsure if there is a limit to the number of times the signal injector is hit before being destroyed. This 654c/1454580o involves 6 collisions

Code: Select all

x = 434, y = 3, rule = B2cik3aj4ajr5ceq/S1e2-ak3acjnr4aktwy5aeij6ack78
430o$431o$430ob2o!

Can anyone figure out a rule for what lengths work for a given number of bounces, and for what the speeds of the adjustable families are?



This rule has a type of adjustability I have never seen before

Code: Select all

x = 12627, y = 3, rule = B2ck3acj4aejkr5cnr6e7e/S1e2cei3acenr4aky5aeijr6ac78
2ob2o3b5ob2o3b7ob2o3b8ob2o3b10ob2o3b20ob2o3b22ob2o3b23ob2o3b25ob2o3b
36ob2o3b27ob2o3b37ob2o3b39ob2o3b34ob2o3b43ob2o3b45ob2o3b28ob2o3b46ob2o
3b31ob2o3b48ob2o3b55ob2o3b57ob2o3b58ob2o3b54ob2o3b82ob2o3b83ob2o3b85ob
2o3b89ob2o3b91ob2o3b92ob2o3b52ob2o3b80ob2o3b69ob2o3b94ob2o3b70ob2o3b
65ob2o3b77ob2o3b76ob2o3b53ob2o3b66ob2o3b116ob2o3b117ob2o3b119ob2o3b78o
b2o3b71ob2o3b72ob2o3b120ob2o3b73ob2o3b74ob2o3b174ob2o3b175ob2o3b177ob
2o3b181ob2o3b183ob2o3b184ob2o3b172ob2o3b143ob2o3b129ob2o3b186ob2o3b
106ob2o3b103ob2o3b135ob2o3b158ob2o3b114ob2o3b159ob2o3b111ob2o3b126ob2o
3b154ob2o3b144ob2o3b205ob2o3b206ob2o3b148ob2o3b136ob2o3b239ob2o3b191ob
2o3b145ob2o3b151ob2o3b238ob2o3b162ob2o3b213ob2o3b222ob2o3b160ob2o3b
153ob2o3b226ob2o3b137ob2o3b157ob2o3b204ob2o3b197ob2o3b207ob2o3b194ob2o
3b215ob2o3b231ob2o3b216ob2o3b169ob2o3b201ob2o3b208ob2o3b217ob2o3b192ob
2o3b196ob2o3b230ob2o3b220ob2o$3o5b6o5b8o5b9o5b11o5b21o5b23o5b24o5b26o
5b37o5b28o5b38o5b40o5b35o5b44o5b46o5b29o5b47o5b32o5b49o5b56o5b58o5b59o
5b55o5b83o5b84o5b86o5b90o5b92o5b93o5b53o5b81o5b70o5b95o5b71o5b66o5b78o
5b77o5b54o5b67o5b117o5b118o5b120o5b79o5b72o5b73o5b121o5b74o5b75o5b175o
5b176o5b178o5b182o5b184o5b185o5b173o5b144o5b130o5b187o5b107o5b104o5b
136o5b159o5b115o5b160o5b112o5b127o5b155o5b145o5b206o5b207o5b149o5b137o
5b240o5b192o5b146o5b152o5b239o5b163o5b214o5b223o5b161o5b154o5b227o5b
138o5b158o5b205o5b198o5b208o5b195o5b216o5b232o5b217o5b170o5b202o5b209o
5b218o5b193o5b197o5b231o5b221o$2o6b5o6b7o6b8o6b10o6b20o6b22o6b23o6b25o
6b36o6b27o6b37o6b39o6b34o6b43o6b45o6b28o6b46o6b31o6b48o6b55o6b57o6b58o
6b54o6b82o6b83o6b85o6b89o6b91o6b92o6b52o6b80o6b69o6b94o6b70o6b65o6b77o
6b76o6b53o6b66o6b116o6b117o6b119o6b78o6b71o6b72o6b120o6b73o6b74o6b174o
6b175o6b177o6b181o6b183o6b184o6b172o6b143o6b129o6b186o6b106o6b103o6b
135o6b158o6b114o6b159o6b111o6b126o6b154o6b144o6b205o6b206o6b148o6b136o
6b239o6b191o6b145o6b151o6b238o6b162o6b213o6b222o6b160o6b153o6b226o6b
137o6b157o6b204o6b197o6b207o6b194o6b215o6b231o6b216o6b169o6b201o6b208o
6b217o6b192o6b196o6b230o6b220o![[ MAXGRIDSIZE 14 ]]

The main mechanics of these ships are 2 signals that are bouncing between the wall a p2 and eachother. When they touch they form a p2, and when one of the signals hits the p2 it destroys it and bounces the other way. Some specific positions will lead to different behavoir such as the ship breaking, the ship advancing, or new signals being formed. The overall behavior can be modeled just by the position of the p2.
Here is the rule for how the state of the pattern changes for a given length n with m being the distance to the closest edge, all patterns start at m=6

For odd n
a(0,1,2,4,(n-1)/2-3,(n-1)/2)=pattern breaks
a(3)=11
a(6)=21
a(7≤m≤(n-1)/2-4)=min(2*(m+1),n-2*(m+1)-1):
a(5,(n-1)/2-2,(n-1)/2-1)=6 pattern advances 1 cell

For even n
a(0,1,2,4,(n-1)/2-1,(n-1)/2)=pattern breaks
a(3)=11
a(6)=21
a(7≤m≤(n-1)/2-4)=min(2*(m+1),n-2*(m+1)-1)
a(5,(n-1)/2-3,(n-1)/2-2)=6 pattern advances 1 cell

I still have yet to fully map out the timing on each piece and whether the ship flips when it advances or stays on the same side, it seems not too complicated although a bit tedious. Can anyone think of a simpler way to represent the mechanics of this ship. Right now even with the timings for each reaction the best that can be done is just iterating the reaction rules until it a pattern reaches a p2 position it has reached before at which point it is an oscillator, it breaks, or it advances at which point it is a ship.

[AforAmpere]

Inspired by a question from NimbleRogue on the Discord, a constant population adjustable ship:

Code: Select all

x = 17, y = 4, rule = B2e3aijky4ait5ajnqy6k/S1c2-kn3-ceny4kwy5ein6an
2o$2o4b2o7b2o$8bo6b2o$6b2o!

As always with this type, there are adjustable slope ships, which are also constant population:

Code: Select all

x = 19, y = 38, rule = B2e3aijky4ait5ajnqy6k/S1c2-kn3-ceny4kwy5ein6an
15bo$b2o11bo2bo$b2o11bobobo$18bo$15bo2bo20$17bo$17bo$16b3o$3o$bo$bo5$
17b2o$2b2o5bo7b2o$2b2o5b3o$9bo!

[OogaBooga_]

c/20o

Code: Select all

x = 3, y = 29, rule = B2ck3-ei4-ez5ainqr6-en78/S2ci3ejn4eqrtz5acknr6-n78
2bo$o$obo$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$obo$o$2bo!

2c/65o in the same rule as the c/20o

Code: Select all

x = 3, y = 23, rule = B2ck3-ei4-ez5ainqr6-en78/S2ci3ejn4eqrtz5acknr6-n78
2bo$o$obo$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$obo$o$2bo!

Found out that the c/20o is the smallest (and fastest) of a family of adjustable ships of the form 2c/(6n+40), where n≥0

Code: Select all

#C The first 10 ships in the family
x = 60, y = 249, rule = B2ck3-ei4-ez5ainqr6-en78/S2ci3ejn4eqrtz5acknr6-n78
57bo$59bo$o56bobo$2bo56bo$obo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo54bobo$2bo56bo$2bo54bo$2bo$2bo$2bo$2bo54bo$2bo56bo$2bo54bobo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$obo56bo$2bo56bo$o58bo$59bo$59bo$59bo$o58bo$2bo56bo$obo56bo$2bo56bo$2bo54bobo$2bo56bo$2bo54bo$2bo$2bo$2bo$2bo54bo$2bo56bo$2bo54bobo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo54bobo$2bo56bo$2bo54bo$2bo$2bo$2bo$2bo54bo$2bo56bo$2bo54bobo$2bo56bo$obo56bo$2bo56bo$o58bo$59bo$59bo$59bo$o58bo$2bo56bo$obo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo54bobo$2bo56bo$2bo54bo$2bo$2bo$2bo$2bo54bo$2bo56bo$2bo54bobo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$obo56bo$2bo56bo$o58bo$59bo$59bo$59bo$o58bo$2bo56bo$obo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo54bobo$2bo56bo$2bo54bo$2bo$2bo$2bo$2bo54bo$2bo56bo$2bo54bobo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$2bo56bo$obo56bo$2bo56bo$o56bobo$59bo$57bo!

An adjustable ship that I found unintentionally (crossposted from unusual spaceships)

———————————————————————————————————————————————————————————————————————————————————————————

A rule with a diagonal ship that's adjustable in both orthogonal directions (both directions affect the ship equally, much like another ship posted earlier here).

Code: Select all

x = 62, y = 62, rule = B2c3acjr4an5inq6ac/S2ck3aikr4a5acij678
7bo$7bo13bo$8o13bo13bo$8o6b8o13bo12bo$8o6b8o6b8o12bo12bo$8o6b8o6b8o5b8o12bo$8o6b8o6b8o5b8o5b8o$8o6b8o6b8o5b8o5b8o$8o6b8o6b8o5b8o5b8o$8o6b8o6b8o5b8o5b8o4$7bo$7bo13bo$b7o13bo13bo$b7o7b7o13bo12bo$b7o7b7o7b7o12bo12bo$b7o7b7o7b7o6b7o12bo$b7o7b7o7b7o6b7o6b7o$b7o7b7o7b7o6b7o6b7o$b7o7b7o7b7o6b7o6b7o$b7o7b7o7b7o6b7o6b7o4$7bo$7bo13bo$2b6o13bo13bo$2b6o8b6o13bo12bo$2b6o8b6o8b6o12bo12bo$2b6o8b6o8b6o7b6o12bo$2b6o8b6o8b6o7b6o7b6o$2b6o8b6o8b6o7b6o7b6o$2b6o8b6o8b6o7b6o7b6o$2b6o8b6o8b6o7b6o7b6o4$7bo$7bo13bo$3b5o13bo13bo$3b5o9b5o13bo12bo$3b5o9b5o9b5o12bo12bo$3b5o9b5o9b5o8b5o12bo$3b5o9b5o9b5o8b5o8b5o$3b5o9b5o9b5o8b5o8b5o$3b5o9b5o9b5o8b5o8b5o$3b5o9b5o9b5o8b5o8b5o4$7bo$7bo13bo$4b4o13bo13bo$4b4o10b4o13bo12bo$4b4o10b4o10b4o12bo12bo$4b4o10b4o10b4o9b4o12bo$4b4o10b4o10b4o9b4o9b4o$4b4o10b4o10b4o9b4o9b4o$4b4o10b4o10b4o9b4o9b4o$4b4o10b4o10b4o9b4o9b4o!

This family of ships has speeds of the form c/2(a+b), a≥4, b≥4

EDIT:

In the same rulespace as the crossposted ships, there is a different rule that supports different adjustable spaceships (c/(6n+20), n≥4).

Code: Select all

x = 82, y = 277, rule = B2cik3-ei4-z5ainqr67e8/S2ci3ejn4eqrtwz5cknr678
bo79bo$2o78b2o$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo78b2o$bo79bo$bo$bo$bo$bo$bo$bo$bo$bo79bo$bo78b2o$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$2o79bo$bo79bo$81bo$81bo$81bo$81bo$81bo$81bo$81bo$bo79bo$2o79bo$bo79bo$bo79bo$bo79bo$bo78b2o$bo79bo$bo$bo$bo$bo$bo$bo$bo$bo79bo$bo78b2o$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo78b2o$bo79bo$bo$bo$bo$bo$2o$bo2$81bo$80b2o$81bo$81bo$81bo$81bo$bo79bo$2o79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo78b2o$bo79bo$bo$bo$bo$bo$bo$bo$bo$bo79bo$bo78b2o$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$2o79bo$bo79bo$81bo$81bo$81bo$81bo$81bo$81bo$81bo$bo79bo$2o79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo78b2o$bo79bo$bo$bo$bo$bo$bo$bo$bo$bo79bo$bo78b2o$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$bo79bo$2o79bo$bo79bo$81bo$81bo$81bo$81bo$81bo$81bo$81bo$81bo$81bo$81bo$80b2o$81bo!

[AforAmpere]

Here is some adjustable ships I found before.
○ (2n, 2n)c/(4n+4), n=[1,+Inf), B0 Version

Code: Select all

x = 43, y = 41, rule = B012-an3ijnqy4inqw5nry6an/S02ei3er4y5anr6ce7e
42bo$39bob2o2$40bo$38bobo$35bo$34b2o10$26bo$23bob2o2$24bo$22bobo2$18bo
$17b2o9$10bo$7bob2o2$8bo$6bobo3$bo$2o!

Inspired by kiho park's brilliant B0 ships, here is an example of arbitrarily close to C/2d ships without B0, (2n-2)c/4nd, n>=3:

Code: Select all

x = 16, y = 14, rule = B2a3ekry4akrtwyz5aijny6in7e/S2ai3cikqy4ijkqrwy5cej6ace
13bo$13bobo$13b2o$13b3o3$10bo$8bobo4$4o$2b2o$bobo!

EDIT, (2n-1)c/4nd, n>=3:

Code: Select all

x = 14, y = 13, rule = B2ak3ary4cknrtz5-ci6cin8/S2n3-ck4eijnr5jn6kn7c8
13bo$12b2o$11b3o3$8bo$6bobo4$2bo$b2o$3o!

[kiho park]

I FINALLY FOUND THIS!!!!!!
Edit : It's limit speed is LIGHT SPEED!!
B0, (8*n)/(8*n + 4), n>=1

Code: Select all

x = 28, y = 62, rule = B01c2kn3-cjr4-ceitz5ajny6in/S01c2kn3ace4aceqrw5jky6ac
o2b3ob3ob3ob3ob3ob3obo$b6o3bo3bo3bo3bo3bo$8bo3bo3bo3bo3bo10$o2b3ob3ob
3ob3ob3obo$b6o3bo3bo3bo3bo$8bo3bo3bo3bo10$o2b3ob3ob3ob3obo$b6o3bo3bo3b
o$8bo3bo3bo10$o2b3ob3ob3obo$b6o3bo3bo$8bo3bo10$o2b3ob3obo$b6o3bo$8bo
10$o2b3obo$b6o!

Edit : Yet another speed
B0, (8*n - 2)/(8*n + 4), n>=1

Code: Select all

x = 22, y = 50, rule = B01c2ikn3-cjk4-cirt5-jnq6i/S01c2-ei3ajnr4a5n6ac
b3ob3ob3ob3ob3obo$o3bo3bo3bo3bo3bo$6bo3bo3bo3bo10$b3ob3ob3ob3obo$o3bo
3bo3bo3bo$6bo3bo3bo10$b3ob3ob3obo$o3bo3bo3bo$6bo3bo10$b3ob3obo$o3bo3bo
$6bo10$b3obo$o3bo!

[AforAmpere]

It's limit speed is LIGHT SPEED!!

This is incredible! Would you mind describing a bit of the process of finding this? I saw your progress post in your personal thread, but I'm also not sure how that part was found. Was it LLS, or were there additional programs/techniques used?

[speedydelete]

I FINALLY FOUND THIS!!!!!!
Edit : It's limit speed is LIGHT SPEED!!
B0, (8*n)/(8*n + 4), n>=1

Wow, incredible! All we have to do is find universal constructors and we can prove all orthogonal speeds exist in B0...

[TheWayOfTheCon]

I FINALLY FOUND THIS!!!!!!
Edit : It's limit speed is LIGHT SPEED!!
B0, (8*n)/(8*n + 4), n>=1

I'm going to submit this discovery to the OCA news page but I just want to make sure its correctly summarized:

June 7: kiho park discovers a B0 isotropic non-totalistic rule with elementary adjustable spaceships of speeds up to c orthogonal.

EDIT: Nevermind, it seems someone else added it.

[kiho park]

This is incredible! Would you mind describing a bit of the process of finding this? I saw your progress post in your personal thread, but I'm also not sure how that part was found. Was it LLS, or were there additional programs/techniques used?

I once read a post from the 5S project. It said that finding fast spaceships such as 5c6o and 6c7o is equivalent to searching for diehards in 1D rules.
So I created a program that simulates a range 2 outer-totalistic 1D CA in which two rules are applied to each other, and I searched for adjustable 1D diehards.
As a result, I was able to discover three things: a pattern in which 2c/6 and P2 collide, a 3c4o fuse, and the 4c4o fuse that I used.
At the time, perhaps because of an issue with my computer, LLS was not producing correct results. After purchasing a new computer and equipping LLS with kissat, I was finally able to search for it successfully.
At first, I tried a design in which a signal crossed the entire spaceship while delaying it by one cell, but it resulted in failure after failure. Eventually, I was able to obtain a clean result only after making the signal delay the spaceship by two cells each time it hit the edge of the spaceship.

Wow, incredible! All we have to do is find universal constructors and we can prove all orthogonal speeds exist in B0...

As for that,
The existence of (2,6)c/6 is already known. Looking at the equivalent rule obtained by simulating the arrangement of cells at the front of this spaceship and how it changes across generations, it can be seen that, in addition to 2c6o, objects such as P2 also exist.

The Multispeed Design : Perpendicular version (Butterfly Design)

Code: Select all

# c3o Perpendicular Multispeed design
x = 216, y = 55, rule = B2cin3aenry4-aciz5-aekq6-en7e8/S02ek3-iqry4-ejny5ar6aek7e8
obo5bobo54bobo4bobo55bobo3bobo56bobo2bobo$obo7bo54bobo6bo55bobo5bo56bo
bo4bo$3o5b3o54b3o4b3o55b3o3b3o56b3o2b3o2$12b3o2b3o56b3o2b3o56b3o2b3o
56b3o2b3o$12bo4bobo56bo4bobo56bo4bobo56bo4bobo$12bobo2bobo56bobo2bobo
56bobo2bobo56bobo2bobo18$obo5bobo54bobo4bobo55bobo3bobo56bobo2bobo$obo
7bo54bobo6bo55bobo5bo56bobo4bo$3o5b3o54b3o4b3o55b3o3b3o56b3o2b3o4$14b
3o2b3o56b3o2b3o56b3o2b3o56b3o2b3o$14bo4bobo56bo4bobo56bo4bobo56bo4bobo
$14bobo2bobo56bobo2bobo56bobo2bobo56bobo2bobo12$obo5bobo54bobo4bobo55b
obo3bobo56bobo2bobo$obo7bo54bobo6bo55bobo5bo56bobo4bo$3o5b3o54b3o4b3o
55b3o3b3o56b3o2b3o6$16b3o2b3o56b3o2b3o56b3o2b3o56b3o2b3o$16bo4bobo56bo
4bobo56bo4bobo56bo4bobo$16bobo2bobo56bobo2bobo56bobo2bobo56bobo2bobo!

Two of them can pass through themselves.

Code: Select all

x = 212, y = 303, rule = B2cin3aenry4-aciz5-aekq6-en7e8/S02ek3-iqry4-ejny5ar6aek7e8
125bobo2bobo$125bo4bobo$125b3o2b3o112$3o8b3o$obo10bo$obo8bobo70$79bobo
8bobo$79bobo10bo$79b3o8b3o112$204b3o2b3o$204bo4bobo$204bobo2bobo!

2026/05/28 : (2*B, 2*B)/c(32 + 8*A + 4*B)
Diagonal version of above idea. All simplified speed (but not for all period) under c2d is possible.

Code: Select all

x = 263, y = 154, rule = B012ik3-jkqr4ijrw5qr6ac7c/S01c2eik3ajnqr4t5cy6ckn7e
16$21bo71bo71bo$21b2o70b2o70b2o$22b2o70b2o70b2o$25bo71bo71bo$25b2o11b
2o57b2o11b2o57b2o11b2o$25bobo9bobo57bobo9bobo57bobo9bobo$25b2o11b2o57b
2o11b2o57b2o11b2o$39bo$41b2o$42b2o70b2o$43bo71b2o70b2o$116bo71b2o$189b
o32$21bo71bo71bo$21b2o70b2o70b2o$22b2o70b2o70b2o$25bo71bo71bo$25b2o15b
2o53b2o15b2o53b2o15b2o$25bobo13bobo53bobo13bobo53bobo13bobo$25b2o15b2o
53b2o15b2o53b2o15b2o$43bo$45b2o$46b2o70b2o$47bo71b2o70b2o$120bo71b2o$
193bo32$21bo71bo71bo$21b2o70b2o70b2o$22b2o70b2o70b2o$25bo71bo71bo$25b
2o19b2o49b2o19b2o49b2o19b2o$25bobo17bobo49bobo17bobo49bobo17bobo$25b2o
19b2o49b2o19b2o49b2o19b2o$47bo$49b2o$50b2o70b2o$51bo71b2o70b2o$124bo
71b2o$197bo!

And, furthermore, as mentioned above, I think there is a possibility if one makes use of the "butterfly design" that I came up with long ago.

[AforAmpere]

The butterfly design but for non-B0 at C/2d, increasing the speed limit from kiho park's C/3d one in non-B0 INT:

Code: Select all

x = 20, y = 36, rule = B2ai3ackqr4-eiktw5q6-en7e8/S2aei3jry4jkr5-ceqy6cek8
bobo$ob2o$b3o4$6b2o2$6bo15$6b2o2$6bo7$17b3o$17b2o$17bobo$18bo!

Those cover 2nc/(24+4n+8m)d, n>=0, m>=0.

EDIT, an alternative way of getting all simplified speeds under C/14, I think this type of mechanism is new:

Code: Select all

x = 22, y = 3, rule = B2e3in4inr6ci/S01c2ce3-ikqr4r6i
obo3bo5bo5bo$7bo5bo5bobo$6bo5bo5bo!

Those cover all nc/(14n+4m)o, n>=1, m>=0.

EDIT 2, the diagonal butterfly one actually covers more speeds than I realized, as pointed out by iNoMed. Because the bouncing ships are p1, and the rule isn't B0, we get more freedom, and they actually cover nc/(20+2n+4m)d:

Code: Select all

x = 75, y = 43, rule = B2ai3ackqr4-eiktw5q6-en7e8/S2aei3jry4jkr5-ceqy6cek8
bo29bo29bo$obo27bobo27bobo$b2o28b2o28b2o$3o27b3o27b3o$7bo29bo29bo$5bo
2bo26bo2bo26bo2bo$5bo2bo26bo2bo26bo2bo$6bo29bo29bo$11b3o27bobo$11b2o
27bob2o28b3o$11bobo27b3o28b2o$12bo27bo31bobo$73bo18$3bo29bo29bo$3o27b
3o27b3o$2obo26b2obo26b2obo$obo27bobo27bobo$7bo29bo29bo$5bo2bo26bo2bo
26bo2bo$5bo2bo26bo2bo26bo2bo$6bo29bo29bo$11bobo$10bob2o28b3o27bobo$11b
3o28b2o27bob2o$10bo31bobo27b3o$43bo27bo!

[NimbleRogue]

I finally found an adjustable ship in INT where the period scales exponentially to the max length. In fact this rule has 2 ships with this property. These were all based on a small clean binary counter found by Ampere.
Their speeds are:
c/16⋅2^(2n)+8n+46 and c/96⋅2^(2n)+8n+47 where n>=1

Code: Select all

x = 20, y = 69, rule = B2cen3er4aceqt5-acer6-en78/S012-ac3ejnr4-ckqwy5acin6ak
16b4o$19bo$7b8o4bo$19bo$16b4o5$16b4o$19bo$5b10o4bo$19bo$16b4o5$16b4o$
19bo$3b12o4bo$19bo$16b4o5$16b4o$19bo$b14o4bo$19bo$16b4o6$16b4o$19bo$6b
9o4bo$19bo$16b4o5$16b4o$19bo$4b11o4bo$19bo$16b4o5$16b4o$19bo$2b13o4bo$
19bo$16b4o5$16b4o$19bo$15o4bo$19bo$16b4o!

Can anyone find any other "Exponential adjustables"?
Edit 1:
Many more exponential adjustables. These haven't been classified yet

Code: Select all

19, B2cen3ey4aerty5ciqy6aci7e8/S012-ac3-aiqy4-kqwy5aijkn6akn, 1, 0, 1760, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ey4aetwy5ijky6aci78/S01e2-ac3cejnr4-nwy5ain6ak, 1, 0, 15757, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cey4aetw5ciky6aci78/S012-ac3ejnr4-ceknwy5ain6ak, 2, 0, 15757, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cey4aceqtw5ceiky6-en78/S012-ac3ejknr4-cekqwy5aijn6ak, 2, 0, 15761, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
25, B2cen3cer4-cijnqz5iy6-en7e8/S012-ac3ejnr4-cknqwy5aein6ak, 1, 0, 5490, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
25, B2cen3cer4-cijnz5iy6-en7e8/S012-ac3ejnr4-cknqwy5aein6ak, 1, 0, 5489, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
22, B2cen3e4aekrtw5eijy6-e78/S012-ac3ejnr4-ceknwy5ain6akn, 1, 0, 7592, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ce4-cijnyz5eiy6aci7e8/S012-ac3ejnr4-knqwy5ain6ak, 2, 0, 15773, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cer4-ijnqyz5ceiny6-e78/S012-ac3ejnr4-ckqwy5aijn6ak, 1, 0, 4711, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ey4aektw5ijkqy6aci7e8/S012-ac3ejnr4-ekwy5aijn6ak, 1, 0, 18325, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cey4-ijnqz5eiqy6-en7e8/S012-ac3-aiqy4-cekqwy5acin6akn, 1, 0, 3113, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ey4-ijnryz5-ackr6-e7e8/S012-ac3ejnr4-kqwy5ain6aek, 1, 0, 13342, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3e4aeqty5ceiky6-en7e8/S012-ac3ejnqr4-cenqwy5-eqry6-ci, 1, 0, 6196, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ce4aceqty5eiky6-en7e8/S012-ac3ejnqr4-cewy5acijn6ak, 1, 0, 15779, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ey4aety5iy6-en78/S01e2-ac3-aciy4-enqwy5aijn6aek, 1, 0, 5318, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ce4acert5ciqy6-en78/S012-ac3ejnqr4-cenwy5-eqry6ak, 2, 0, 15768, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cer4aeqrty5ciqy6-en78/S012-ac3ejnqr4-cejnwy5acikn6aek, 1, 0, 6570, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ery4aektwy5ijy6aci78/S012-ac3-aiky4-eknwy5acijn6akn, 2, 0, 5506, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ce4acertw5eijky6aci7e8/S012-ac3-aciy4-ceqwy5aijkn6ak, 2, 0, 5886, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ey4-ijknyz5ijy6aci78/S012-ac3ejnqr4-enqwy5acin6akn, 1, 0, 13692, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ery4-ijknyz5ijy6aci78/S012-ac3-aciy4-enqwy5acin6akn, 1, 0, 14160, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
19, B2cen3ce4aeqtw5-acnr6aci7e8/S012-ac3-aciy4-cejqwy5acein6akn, 1, 0, 19694, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cery4aektw5ijky6aci7e8/S012-ac3-aciy4-cjqwy5aeijn6akn, 2, 0, 5566, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ey4aertwy5eijy6aci78/S012-ac3-aciy4-cenqwy5acein6ak, 1, 0, 5452, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ery4-ijknrz5ijqy6-e7e8/S012-ac3-aiky4-eknqwy5aikn6-ci, 1, 0, 4347, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3e4-ijnqyz5cijy6-ek7e8/S01e2-ac3-aiky4-cknqwy5-eqry6-ci, 1, 0, 5451, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ce4-ijnqz5ciy6-ek78/S012-ac3ejnqr4-knqwy5ain6-ci, 1, 0, 13617, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ce4-ijnz5ciy6-ek78/S012-ac3ejnqr4-knqwy5ain6-ci, 1, 0, 13611, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ce4acetw5iny6-e7e8/S012-ac3-aciy4-cknwy5ain6-ci, 1, 0, 15515, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3er4-ijknz5ijy6-e78/S01e2-ac3ejnqr4-cekqwy5aijkn6-ci, 1, 0, 5205, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ce4acetwy5ijkqy6-ek7e8/S012-ac3ejnqr4-ekqwy5acin6-ci, 1, 0, 15764, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3ce4aektwy5iy6-e7e8/S012-ac3ejnqr4-ekwy5ain6-ci, 1, 0, 5521, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cery4-ijnryz5ceiy6-ek7e8/S012-ac3ejnqr4-cknqwy5ain6-ci, 1, 0, 14627, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cey4aeqtwy5-anqr6-ek7e8/S012-ac3ejnqr4-knwy5aijn6-ci, 1, 0, 10783, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cery4aektw5ceiy6-ek7e8/S012-ac3-aciy4-cknwy5ain6-ci, 1, 0, 15686, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cey4aetwy5ijy6-en7e8/S01e2-ac3-aciy4-enqwy5aijn6-ci, 1, 0, 6301, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cey4aeqtwy5ijy6-en7e8/S01e2-ac3-aciy4-enqwy5aijn6-ci, 1, 0, 6300, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2cen3cey4-ijknz5ijy6-en7e8/S01e2-ac3-aciy4-enqwy5acijn6-ci, 1, 0, 7670, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2-ak3cer4aekrtw5cijy6-en7e8/S012-ac3ejnr4-enqwy5ain6ak, 2, 0, 8201, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
22, B2-ak3ce4aekrtw5eiy6-en7e8/S012-ac3ejnr4-eknqwy5aijn6ak, 1, 0, 2570, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
24, B2-ak3ery4-cijnrz5eiky6-en78/S012-ac3ejknr4-cenwy5aikn6aek, 1, 0, 3170, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2-ak3er4aeqt5eijy6-ek78/S012-ac3ejnqr4-nqwy5aikn6ak, 1, 0, 6197, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2-ak3ey4aekqt5eijqy6-en7e8/S012-ac3-aciy4-nqwy5-qry6ak, 2, 0, 4627, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2-ak3ey4aekqt5eijqy6-en7e8/S012-ac3-aciy4-nwy5-qry6ak, 2, 0, 8719, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2-ak3er4aetw5ceijy6aci78/S01e2-ac3ejnqr4-ceqwy5acijn6ak, 1, 0, 8228, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2-ak3er4aeqtw5ceijy6aci78/S01e2-ac3ejnqr4-ceqwy5acijn6ak, 1, 0, 8237, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2-ak3cer4-ijnqz5cijy6-ek78/S012-ac3-aiky4-cekwy5acijn6-ci, 2, 0, 8238, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2-ak3e4aektw5inqy6-ek7e8/S01e2-ac3-aiky4-ckqwy5aijn6-ci, 1, 0, 4134, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!
23, B2-ak3ce4-ijnryz5iy6aci7e8/S012-ac3-aciy4-eknqwy5-kqry6aek, 1, 0, 8230, b4o2$2o4b10o2$b4o16$b4o2$2o4b11o2$b4o16$b4o2$2o4b12o2$b4o16$b4o2$2o4b13o2$b4o16$b4o2$2o4b14o2$b4o16$b4o2$2o4b15o2$b4o16$b4o2$2o4b16o2$b4o16$b4o2$2o4b17o2$b4o16$b4o2$2o4b18o2$b4o16$b4o2$2o4b19o2$b4o16$b4o2$2o4b20o2$b4o16$b4o2$2o4b21o2$b4o16$b4o2$2o4b22o2$b4o16$b4o2$2o4b23o2$b4o16$b4o2$2o4b24o2$b4o16$b4o2$2o4b25o2$b4o16$b4o2$2o4b26o2$b4o!

This one has an interesting reaction that flips back and forth

Code: Select all

x = 25, y = 35, rule = B2-ak3er4aeqt5eijy6-ek78/S012-ac3ejnqr4-nqwy5aikn6ak
2b4o$2bo$3o4b6o$2bo$2b4o6$2b4o$2bo$3o4b10o$2bo$2b4o6$2b4o$2bo$3o4b14o$
2bo$2b4o6$2b4o$2bo$3o4b18o$2bo$2b4o!

[NimbleRogue]

I might make a thread for Phoenix rules later; As a teaser here is the first adjustable ship in a phoenix rule

The speeds are c/27+6nd

Code: Select all

x = 57, y = 17, rule = B2cek3-eky4-ekqrw5aejr6c/S
4bo19bo19bo$4bobo17bobo17bobo$4bobo17bobo17bobo$3b2obobo14b2obobo14b2o
bobo$4o2bobo11b4o2bobo11b4o2bobo$8bobo17bobo17bobo$b4o3bobo10b4o3bobo
10b4o3bobo$10bobo17bobo17bobo$3b4o3bobo10b4o3bobo10b4o3bobo$32bobo17bo
bo$5b4o16b4o3bobo10b4o3bobo$54bobo$7b2o18b4o16b4o3bobo2$29b2o18b4o2$
51b2o!

There is a c/17d and a smaller c/27d in the rule

Code: Select all

x = 28, y = 10, rule = B2cek3-eky4-ekqrw5aejr6c/S
5bo17bobo$3bobo15bo3bo$5bobo17bobo$bo2b2obo12bo4bobo$3b2o4bo14b2o$4o5b
o10b5o$9bo$2b2o5bo12b2o$8bo$4b4o!

[speedydelete]

All speeds less than or equal to c/7o are possible:

Code: Select all

x = 28, y = 5, rule = B2cei3ajqry4ajy5aij6a/S1e2i3aeqy4eit5ijq6aci8
6bo8bo5bo3bo$5bo10bo5bo2bo$25ob2o$5bo10bo5bo2bo$6bo8bo5bo3bo!

True-period c/7o:

Code: Select all

x = 50, y = 5, rule = B2cei3ajqry4ajy5aij6a/S1e2i3aeqy4eit5ijq6aci8
bo2bo$2bobo$4ob2o$2bobo$bo2bo!

The even periods require multiple signals, but are still possible, here's a true-period c/8o:

Code: Select all

x = 12, y = 5, rule = B2cei3ajqry4ajy5aij6a/S1e2i3aeqy4eit5ijq6aci8
bo4bo2bo$o6bobo$b8ob2o$o6bobo$bo4bo2bo!

The pass-through reactions were found by hand, the pull reaction was found by EPE, and the push reaction was found by LLS.

Edit: Fix typo

[speedydelete]

And an equivalent for diagonal ships, this covers all speeds less than or equal to c/7d:

Code: Select all

x = 24, y = 24, rule = B3aeijn4ajkq5an6e7c/S12cn3aik4cjqz5an6en8
o$bo$2bo$3bo$4bo$5b3o$5b2o$5bobo$8bo$9bobo$10b2o$9b3o$12bo$13bo$14bo$
15bobo$16b2o$15b3o$18bo$19bo2bo$20bo2bo$21bo$19bo$20bo!

True-period c/7d:

Code: Select all

x = 6, y = 6, rule = B3aeijn4ajkq5an6e7c/S12cn3aik4cjqz5an6en8
obo$b2obo$3o2bo$3bo$bo$2bo!

True-period c/8d:

Code: Select all

x = 11, y = 11, rule = B3aeijn4ajkq5an6e7c/S12cn3aik4cjqz5an6en8
3o$2o$obo$3bo$4bobo$5b2o$4b3o2bo$7bo2bo$8bo$6bo$7bo!

Both pass-through reactions and the pull reaction were found by hand, and the push reaction was found by LLS.

All the LLS searches for push reactions that allow for faster ships (for both orthogonal and diagonal) for the current rulespaces came up UNSAT. There could be one that works in a different rulespace, though.

Edit: Fix typo

[NimbleRogue]

And some for knightships using the original asymmetric design all found by me. Thanks to Ampere for analyzing and proving the bounds for these, as these ended up being a step up in complexity from the others.

All knightships with speeds ≤(2,1)c/12

Code: Select all

x = 27, y = 17, rule = B2cin3aej4cqrtwy5er6-cn7c8/S01e2-ai3cejnr4-ay5ijnqr6ik7c
24bo$24bo$24b3o$22b3o$20b3o$15bo2b3o$16b3o$14b3o$12b3o$10b3o$5bo2b3o$
6b3o2bo$4b3o$b2o$o2bo$obobo$2b2o!

For 3 signals and above this covers (2,1)nc/(12n+4m+2*mod(n,2)). If you choose n=2k, you get 2k/(24k+4m) = a/b -> m=kb/2a-6. Simply set k to some multiple of 2a and you get a valid m (as b/2a≥6). This means that all rationals ≤1/12 are covered

All unsimplified speeds are covered however, because each push and pull moves the ends by a displacement where the two directions are coprime in length and we can always space out the signals in groups to divide the period by any factor of the number of signals. There are an infinite number of solutions for any rational number that you can get by just multiplying the number of signals in a solution by some integer, and increasing m, so we can get any period multiple of a speed we find.


The current best covers all speeds ≤(2,1)c/10

Code: Select all

x = 28, y = 16, rule = B2cin3-cein4ceiq5kqy6-k/S01e2-ai3ejnqr4-cey5-aciy6-kn7e8
25bo$23bobobo$23b3o$21b3o$19b3o$17b3o2bo$15b3o$11bob3o$11b3o$9b3o$7b3o
$3bob3o2bo$b5o$o4bo$2b3o$3b2o!

For 3 signals and above this covers (2,1)nc/(10n+4m), n≥3, m≥0, and n/(10n+4m) giving you all unsimplified speeds ≤1/10


Here is a push reaction that works at RT9 which would improve the bound with a good enough backend but I am not finding any

Code: Select all

x = 15, y = 9, rule = B2cek3ajkry4-aciwz5jqy6ikn7e8/S01e2ikn3-kqy4-aciy5-ciy6cik78
12bo$12bo$12b3o$8bob3o$8b3o$6b3o$bo2b3o$2b3o$3o!