A Bouncer which approaches to lightspeed but can't reach.
Here is 3 State INT Rule with FASTEST small adjustable ships.
Sadly, This is not 2 State INT Rule. But, I think there is some possibility for 2 State rule.
Approaches to lightspeed but can't reach it.
2n/(2+2n), n >= 2
Code: Select all
x = 10, y = 50, rule = SAS00
B2AB$4B6$8.AB$B8AB$9B6$7.AB$B7AB$8B6$6.AB$B6AB$7B6$5.AB$B5AB$6B6$4.AB
$B4AB$5B6$3.AB$B3AB$4B!
@RULE SAS00
@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect
var a={0,1,2}
var b={0,1,2}
var c={0,1,2}
var d={0,1,2}
var e={0,1,2}
var f={0,1,2}
var g={0,1,2}
var h={0,1,2}
var i={0,1,2}
# Format: C,N,NE,E,SE,S,SW,W,NW,C'
0,0,0,0,1,2,0,0,0,2
2,0,0,1,2,2,0,0,0,2
0,0,0,0,1,1,2,0,0,1
1,0,0,1,2,2,2,2,0,2
0,0,0,1,0,1,1,0,0,1
1,0,1,0,2,2,2,1,0,2
1,0,0,1,2,0,1,0,0,1
0,1,1,2,0,2,2,1,0,2
0,0,0,0,1,1,1,0,0,1
2,1,1,2,0,0,2,0,1,2
1,0,0,1,2,2,2,1,0,2
1,0,0,2,2,2,0,1,0,1
2,1,2,2,0,0,2,0,1,2
2,0,0,0,0,2,1,1,0,2
2,2,0,0,0,0,2,1,1,2
0,2,0,0,0,0,0,2,1,2
1,0,1,1,2,2,2,1,0,2
0,0,0,1,1,1,1,0,0,1
1,0,0,2,2,1,1,0,0,1
1,0,2,2,2,0,2,1,0,1
0,1,2,2,2,2,0,2,1,2
2,2,0,0,0,2,0,1,0,2
2,2,0,0,0,2,2,0,1,2
0,0,0,0,2,1,0,1,0,1
1,0,0,2,2,2,2,0,1,2
a,b,c,d,e,f,g,h,i,0
@COLORS
0 0 0 0
1 255 0 0
2 0 255 0
After I changed my computer bran-new, My LLS became can handle photons and tachyons.
2026/05/27 : I finally found most promising failed examples
The 4c4d signal shifts whole pattern an 1 cell back. And, sometimes "kick-back" reaction also appeared when I LLS searching it.
Code: Select all
# 2c2o extensible spaceship and 4c4d shifting reaction
x = 60, y = 5, rule = B012-ac3-a4-cir5-ejq6aei7e/S012ckn3-ey4jknqwz5knqy6aci7e
b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob4o$o3bo3bo3bo3bo3bo3bo3bo3bo3bo3b
o3bo3b2ob4ob3o$49b4o2bo3bo$2bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo4bo$53b
o3bo!
Code: Select all
x = 36, y = 3, rule = B01c2eik3-aknr4-eknwy5ay6ai/S01c2cek3cir4aenqtwy5n6ac
ob3ob3ob3ob3ob3ob3ob2o$bo3bo3bo3bo3bo3bo5b3ob3obo$25bo4bo3bo!
This is similar to first two examples but, 4c4d fuse reaction delays 2 cells back.
Code: Select all
x = 48, y = 4, rule = B01c2en3-aenr4aeiqrtz5acejk6-ac7e/S12ack3acejq4aejrtz5jq6ac
ob3ob3ob3ob3ob3ob3ob3ob3ob3o2bo$bo3bo3bo3bo3bo3bo3bo3bo3bo3bobo$37b2ob
2ob3obo$39bo2bo3bo!
A few years ago, Someone discovered
(2,6)c/6 spaceship. And, The alternative 1D rule that supports (2,6)c/6 tachyon also can have (0,2)c/2 spaceship.
According to
this post, If there is 1D diehard reaction on front line of pattern's edge, (n-1)c/n is possible. And, There is 1D adjustable diehard in that rule. (Look closer front line of below pattern. You can see all cell in front line dies at gen 44.)
Code: Select all
x = 21, y = 1, rule = B01e2ce3-aeqr4ejknrz5enqry6-ei7e8/S1e2ack3ejkqy4-ackq5-any6-ai7e
2o14bob3o!
So, It means there are some possibilities to the near-lightspeed SAS in 2 state B0 rulespace. But, I can't even trying to search both (0,2)c/2 and (2,6)c/6 because of my LLS is still can't find any tachyons.
※ Bouncer : Can SAS break the speed limit of 1 < (|x| + |y|)/P <= 1.5?? Use c2d and 3c4d wave as traveling media?
c2d wave ship with 2c2o signal on it : No example yet
2c4d wave ship with (1,3)c/4 signal on it : No example yet
2c4d wave ship with 2c2o signal on it : No example yet
2c4d wave ship with 4c4o signal on it : No example yet
3c4d wave ship with (2,4)c/4 signal on it : No example yet
Two c2d or 2c4d ships and 2c2o ship between them : No example yet
The Multispeed Design : By switching the speed.
The traditional Bouncer shifts outside spaceship for every collision. And, I came up with new idea switching outside spaceship's property instead of shifting it's place. Then I discovered
all orthogonal speed under c2o,
all diagonal speed under c3o And all B0 diagonal speed under c2d.
All diagonal speed under 3c4d project
Following rule have 3c4d extensible spaceship and 4c4d signal on it. If the 4c4d signal can overtake 3c4d head and control it, It means It's possible.
Code: Select all
x = 41, y = 41, rule = B012ekn3-eijr4aqrw5jk6aci7c/S01c2-c3ciq4jknwy5acekq6-an7
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbooobbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbooobbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbobbbobbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbboobobbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbooobobbobbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbobbboooobbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbooooobbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbooooooobbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbooooooobooobbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbooooooobbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbooooooobbbobbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbooooooobbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbooooooobbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbooooooobbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbooooooobbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbooooooobbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbooooooobbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbooooooobbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbooooooobbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbooooooobbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbooooooobbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbboooobobbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbooboobbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbooobbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb!
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$197bo!
2026/05/31 : When if use (0,2)c/3 and (1,2)c/3?
I used c3o and c3d in above example. It can be more faster if use (0,Y)c/P and (X,Y)c/P spaceship.
For example, X = 1, Y = 1 and P = 2 for all speed under c2o. X = 1, Y = 2 and P = 3 for all speed under 2c3o.
If X = 2, Y = 6 and P = 6. It means ALL SPEED UNDER LIGHTSPEED IS POSSIBLE!! -As you know there are already (2,6)c/6 spaceship-.
Also, It can be applied to diagonal if use (t,t)c/P and (t-s,t+s)c/P spaceship.
Edit : All orthogonal speeds under lightspeed.
2*A/(12 + 2*A + 2*B), A = [0,+Inf), B = [0,+Inf) (Discovered in 23:32 2023-03-21)
Code: Select all
x = 272, y = 68, rule = SAS02
3A14.3A109.A2.BA27.A2.BA27.A2.BA27.A2.BA27.A2.BA$A.A14.A.A69.2A37.A.A
.2A26.A.A.2A26.A.A.2A26.A.A.2A26.A.A.2A$.A16.A70.AB37.3A29.3A29.3A29.
3A29.3A3$145.3A28.3A28.3A28.3A28.3A$98.3A37.2A5.A.A22.2A4.A.A23.2A3.A
.A24.2A2.A.A25.2A.A.A$95.2A.A.A37.AB6.A23.AB5.A24.AB4.A25.AB3.A26.AB
2.A$95.AB2.A8$129.A2.BA27.A2.BA27.A2.BA27.A2.BA27.A2.BA$128.A.A.2A26.
A.A.2A26.A.A.2A26.A.A.2A26.A.A.2A$128.3A29.3A29.3A29.3A29.3A2$144.3A
28.3A28.3A28.3A28.3A$137.2A5.A.A22.2A4.A.A23.2A3.A.A24.2A2.A.A25.2A.A
.A$137.AB6.A23.AB5.A24.AB4.A25.AB3.A26.AB2.A10$129.A2.BA27.A2.BA27.A
2.BA27.A2.BA27.A2.BA$128.A.A.2A26.A.A.2A26.A.A.2A26.A.A.2A26.A.A.2A$
128.3A29.3A29.3A29.3A29.3A$143.3A28.3A28.3A28.3A28.3A$136.2A5.A.A22.
2A4.A.A23.2A3.A.A24.2A2.A.A25.2A.A.A$136.AB6.A23.AB5.A24.AB4.A25.AB3.
A26.AB2.A11$129.A2.BA27.A2.BA27.A2.BA27.A2.BA27.A2.BA$128.A.A.2A26.A.
A.2A26.A.A.2A26.A.A.2A26.A.A.2A$128.3A11.3A15.3A10.3A16.3A9.3A17.3A8.
3A18.3A7.3A$135.2A5.A.A22.2A4.A.A23.2A3.A.A24.2A2.A.A25.2A.A.A$135.AB
6.A23.AB5.A24.AB4.A25.AB3.A26.AB2.A12$129.A2.BA27.A2.BA27.A2.BA27.A2.
BA27.A2.BA$128.A.A.2A7.3A16.A.A.2A6.3A17.A.A.2A5.3A18.A.A.2A4.3A19.A.
A.2A3.3A$128.3A3.2A5.A.A16.3A3.2A4.A.A17.3A3.2A3.A.A18.3A3.2A2.A.A19.
3A3.2A.A.A$134.AB6.A23.AB5.A24.AB4.A25.AB3.A26.AB2.A!
@RULE SAS02
@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect
var a={0,1,2}
var b={0,1,2}
var c={0,1,2}
var d={0,1,2}
var e={0,1,2}
var f={0,1,2}
var g={0,1,2}
var h={0,1,2}
var i={0,1,2}
# Format: C,N,NE,E,SE,S,SW,W,NW,C'
# c1d
0,0,0,0,2,0,0,0,0,2
0,0,0,0,1,2,0,0,0,1
2,0,0,1,1,1,0,0,0,1
0,0,0,0,0,1,2,0,0,0
0,0,0,0,0,0,1,0,0,0
0,0,0,0,0,0,1,1,0,0
# c1o
0,0,0,0,0,1,0,0,0,1
0,0,0,1,0,1,0,0,0,1
1,0,0,0,1,0,1,0,0,0
1,0,1,0,1,1,0,0,0,1
0,1,0,1,1,1,1,1,0,1
0,1,1,0,0,0,0,0,1,0
# reaction A
0,0,0,0,1,2,0,2,1,2
2,0,0,1,1,1,0,0,2,1
2,0,0,0,0,1,2,1,0,1
# reaction B
0,0,2,1,0,0,1,1,0,1
0,0,0,0,2,0,1,0,0,1
0,0,0,2,0,1,0,1,0,2
2,0,0,1,1,0,1,0,0,2
0,2,1,1,0,1,1,1,0,2
1,0,0,1,2,0,1,0,0,1
2,1,1,2,2,0,1,0,1,1
1,0,0,0,0,1,1,2,2,2
0,0,0,0,0,1,2,2,1,1
2,2,0,1,1,1,0,0,2,1
0,0,2,1,0,0,0,0,1,0
1,0,2,0,0,0,0,1,1,1
0,2,2,2,1,0,0,1,0,0
1,0,0,1,2,2,0,1,0,1
1,0,0,0,0,2,2,1,0,0
2,1,0,0,1,2,0,2,1,1
1,1,1,2,1,0,0,0,0,1
0,1,2,1,0,0,0,0,0,1
2,1,1,1,0,1,0,1,1,1
1,2,1,0,0,0,0,0,1,0
1,1,0,1,1,0,1,2,1,1
0,1,1,1,0,0,0,1,2,1
# reaction A Up
0,0,0,0,2,0,0,0,2,1
1,1,0,1,1,1,0,1,1,1
1,1,1,1,1,0,0,0,0,1
0,0,0,0,0,1,1,1,0,2
1,0,0,0,0,1,1,1,0,1
1,1,1,1,1,2,0,0,0,1
a,b,c,d,e,f,g,h,i,0
@COLORS
0 0 0 0
1 255 0 0
2 0 255 0
I also came up with a good idea which can make SAS have speed range of Max(|x|,|y|)/P < 1/2.
I'll post it here when I find properly working one.
Coming soon : Worm style adjustable spaceship (2026/05/27)
Someone already posted
This cool rule have a good example of adjustable spaceship which I have designed. It is technically same as "c3o Perpendicular Multispeed design".
My Multispeed design is switching component spaceship's direction to 180 degrees. And his design turn it's head by 90 degrees when chasing signal collides with it.
After I read his post, I decided to find an example which works in 2 state range 1 moore INT rule.
