Slowest one cell spaceships of each state count

[AforAmpere]

This will be a challenge to find the slowest 1-cell spaceship in a non-symmetric rule of any number of states. For 2 states, it is obviously c, whether orthogonal or diagonal, as it cannot move in any direction without using a B1e or B1c transition, and so has to move at c:

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x = 1, y = 1, rule = MAPGAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

However, this is not true for higher state rules, as this preliminary example shows, with three states, acheiving C/16:

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@RULE SlowestOneCell3StateCurrent

@TABLE

n_states:3
neighborhood:Moore
symmetries:none

var a={0,1,2}

0,0,0,0,0,1,0,0,0,2
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,1,2,0,1
0,0,0,0,0,0,0,2,1,1
0,0,0,0,0,0,1,0,1,2
0,0,0,0,0,2,0,1,0,2
0,2,0,0,0,0,0,1,0,2
0,1,2,2,2,1,2,1,2,2
2,0,0,1,2,1,0,0,0,0
1,2,1,2,1,2,0,0,0,0
2,1,2,1,0,0,0,0,0,0
2,0,0,0,0,2,2,1,0,0
2,2,0,0,0,2,1,2,1,0
2,2,0,0,0,0,0,1,2,0
2,1,2,2,2,1,2,1,2,2
1,2,2,2,0,0,0,2,1,0
2,0,0,0,0,0,0,0,0,1
0,0,0,2,0,0,0,0,0,1
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,2
0,0,0,0,1,1,0,0,0,2
0,0,0,0,0,1,1,0,0,2
1,2,0,2,0,2,2,1,2,2
2,2,0,2,0,2,2,1,2,1
2,0,0,2,2,1,0,0,0,0
2,0,0,0,2,2,1,2,0,0
2,0,0,0,0,0,2,2,2,0
2,2,2,0,0,0,0,2,1,0
2,1,2,2,0,0,0,0,0,0
1,2,2,2,2,2,0,0,0,0
1,0,0,2,2,2,1,2,0,0
0,0,0,0,0,2,2,2,0,2
0,2,0,0,0,0,0,2,2,2
2,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,0,0,1,0

The slowest found of each state count will be held here. Entries should be submitted only with the condition that the spaceship the rule is designed for is one celled in one phase, and the state of the cell in that phase is state 1. The above two rules follow this condition, so when one state 1 cell is placed, it will follow the evolution of the entry spaceship. No direction is required, just a speed.

Records:

2-state: C

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MAPGAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

3-state: C/36

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@RULE slowshiptry
@TABLE
n_states: 3
neighborhood:Moore
symmetries:none
1,0,0,0,0,0,0,0,0,1
0,0,0,0,0,0,0,1,0,2
2,0,0,0,0,0,0,1,0,1
1,0,0,1,0,0,0,0,0,2
0,0,0,0,2,1,2,0,0,1
0,0,0,1,1,2,0,0,0,2
0,0,0,2,2,0,0,0,0,1
1,0,0,2,2,0,0,0,0,0
0,1,2,2,0,0,0,0,0,1
0,0,0,2,2,1,0,0,0,2
2,0,0,2,2,1,0,0,0,1
1,2,2,2,0,0,0,0,0,2
1,0,0,2,2,2,0,0,0,0
2,0,2,2,0,0,0,0,0,0
2,2,1,1,0,0,0,2,0,0
2,0,0,1,1,0,0,0,0,0
1,1,0,1,0,0,0,0,2,2
0,0,0,0,1,1,2,1,0,2
1,0,0,2,1,2,0,0,0,0
2,0,0,0,1,1,2,0,0,0
0,0,0,0,1,1,1,2,0,2
2,0,0,2,1,1,2,0,0,0
2,0,0,2,1,1,1,0,0,0
0,0,0,0,1,1,1,2,0,2
0,0,0,0,2,1,1,2,0,2
1,0,0,0,0,0,0,1,2,0
0,0,0,0,2,0,1,2,0,2
0,0,0,2,0,0,0,1,2,2
0,0,0,0,0,2,2,2,0,2
2,0,0,2,2,1,0,0,0,0
2,2,0,2,0,0,0,1,2,1
2,0,0,0,0,0,0,2,2,0
2,0,0,2,0,1,1,0,0,0
0,0,0,2,0,1,1,0,0,2
1,0,2,0,0,0,0,1,0,0
2,0,0,0,0,0,1,0,0,0
0,0,0,2,0,1,2,0,0,2
1,2,0,0,0,0,0,2,0,0
2,0,0,0,0,0,2,0,0,0
2,0,2,0,0,0,0,0,0,1

4-state: C/917636

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@RULE MinSpeed4s-AFP-9-12-17
@TABLE
n_states:4
neighborhood:Moore
symmetries:none
0100000002
0200000003
0001000002
0002000003
2001200303
3002000002
2100030023
3200000002
2200000001
3100000000
1200000000
2000000000
3000300000
3000000030
0020030003
2300003000
0030030003
3300000000
0300000302
2300000303
3033000000
0313000023
3313030020
0233000023
0223000023
0223000033
0223000003
0323000003
3002330001
1002330002
1002333202
2002333101
3233000311
2003333101
2001133203
3311000322
2311000323
2003233203
3001123202
2001133303
3311000332
3001123302
2311000333
3001123302
3332000322
2311000333
3002323202
2323000323
2003233303
3332000332
2323000333
3002323302
2003230000
0313030023
3313230020
3032000000
3023000000
2002333000
3001133000
1003313000
1133000303
3011000000
3001333001
1000033100
3100000310
3113000000
0200020001
0100000303
0021330002
2021330000
3100000320
1200033200

[muzik]

Couldn't you just make a cell age as in Generations, but as it reaches its last stage, instead of just dying outright it births a state-1 cell to the right of it?

[blah]

Couldn't you just make a cell age as in Generations, but as it reaches its last stage, instead of just dying outright it births a state-1 cell to the right of it?

Yeah, but that's probably not optimal in most cases. See the example he actually posted, of a 3-state rule in which a single cell travels more slowly than the 3-state implementation of your idea.

Edit: Maybe your idea is still useful to establish an upper bound on the lowest possible speed for a given number of states.

[BlinkerSpawn]

This looks like a neat variation on the busy beaver problem.
EDIT: c/550 diagonal, 3 ON states:

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@RULE BB3b

@TABLE
n_states:4
neighborhood:Moore
symmetries:none
var c1={1,3}
var c2=c1
var c3=c2
var c4=c3
var c5=c4
var c6=c5
var c7=c6
var c8=c7
var C1={0,1,3}
var C2=C1
var C3=C2
var C4=C3
var C5=C4
var C6=C5
var C7=C6
var C8=C7
#open up
1,0,0,0,0,0,0,0,0,2
3,0,0,0,0,0,0,0,0,2
2,0,0,0,0,0,0,0,0,3
0,2,0,0,0,0,0,0,0,2
0,0,2,0,0,0,0,0,0,3
0,0,0,2,0,0,0,0,0,2
0,0,0,0,2,0,0,0,0,3
0,0,0,0,0,2,0,0,0,2
0,0,0,0,0,0,2,0,0,3
0,0,0,0,0,0,0,2,0,2
0,0,0,0,0,0,0,0,2,3
0,3,2,0,0,0,0,0,0,3
0,2,3,0,0,0,0,0,3,3
0,3,0,0,0,0,0,0,2,3
0,0,0,3,2,0,0,0,0,3
0,0,3,2,3,0,0,0,0,3
0,0,2,3,0,0,0,0,0,3
0,0,0,0,0,3,2,0,0,3
0,0,0,0,3,2,3,0,0,3
0,0,0,0,2,3,0,0,0,3
0,0,0,0,0,0,0,3,2,3
0,0,0,0,0,0,3,2,3,3
0,0,0,0,0,0,2,3,0,3
2,3,2,3,2,3,0,0,0,3
2,0,0,3,2,3,2,3,0,3
2,3,0,0,0,3,2,3,2,3
2,3,2,3,0,0,0,3,2,3
#count or decay
1,1,1,1,1,0,0,0,0,0
1,1,1,1,0,0,0,0,0,0
1,0,1,1,1,0,0,0,0,0
1,1,1,1,0,0,0,0,1,0
1,1,1,0,0,0,0,0,1,0
1,1,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,1,0
1,0,0,0,1,1,0,0,0,0
1,0,0,1,0,0,0,0,0,0
1,0,0,1,1,0,0,0,0,0
3,0,0,0,0,c1,c2,c3,c4,1
1,0,0,0,0,c1,c2,c3,c4,3
3,1,0,0,0,C1,C2,C3,C4,1
1,1,0,0,0,C1,C2,C3,C4,3
3,0,0,0,1,C1,C2,C3,C4,1
1,0,0,0,1,C1,C2,C3,C4,3
3,1,0,1,1,C1,C2,C3,C4,1
1,1,0,1,1,C1,C2,C3,C4,3
3,1,1,1,1,C1,C2,C3,C4,1
1,1,1,1,1,C1,C2,C3,C4,3
3,1,1,1,0,C1,C2,C3,C4,1
1,1,1,1,0,C1,C2,C3,C4,3
3,1,1,0,0,C1,C2,C3,C4,1
1,1,1,0,0,C1,C2,C3,C4,3
3,0,0,1,1,C1,C2,C3,C4,1
1,0,0,1,1,C1,C2,C3,C4,3
3,0,1,1,1,C1,C2,C3,C4,1
1,0,1,1,1,C1,C2,C3,C4,3
#decay
3,3,0,3,3,0,0,3,3,2
2,3,0,3,3,0,0,3,3,1
3,0,0,0,3,2,3,3,0,0
3,0,0,0,0,3,0,2,3,0
3,3,0,0,0,0,0,0,2,0
3,3,3,2,0,0,0,0,0,0
3,0,0,3,2,3,0,0,0,0
3,0,1,0,0,0,0,0,0,0

Extensible to higher state numbers as well, but would likely require non-trivial changes.

[dvgrn]

Yikes. No limit on the number of lines in the rule table, only on the number of states? The lower bound on the busy beaver Σ(N) function for increasing N goes like

4
6
13
4098
3.5×10^18267
10^10^10^10^18705352

I'm not sure the Single-Cell Spaceship Slowness function will take off quite as vertically as that, but when the exponents get big enough it can be kind of hard to tell the difference...! Come to think of it, rule tables would seem to have some resemblance to two-dimensional Turing machines -- for all I know, the function could even go up faster than Σ.

EDIT: Here's a problem that's probably about to show up: the rule table file for the slowest possible spaceship will start taking up terabytes of space, while the number of states is still in the single digits. Can I suggest a modification of the contest conditions? The rule table should fit in a

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 block in a forum post -- not an attached ZIP file or anything like that, just the plain quoted text in a single message.

[toroidalet]

c/36:

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x = 1, y = 1, rule = slowshiptry
A!

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@RULE slowshiptry
@TABLE
n_states: 3
neighborhood:Moore
symmetries:none
1,0,0,0,0,0,0,0,0,1
0,0,0,0,0,0,0,1,0,2
2,0,0,0,0,0,0,1,0,1
1,0,0,1,0,0,0,0,0,2
0,0,0,0,2,1,2,0,0,1
0,0,0,1,1,2,0,0,0,2
0,0,0,2,2,0,0,0,0,1
1,0,0,2,2,0,0,0,0,0
0,1,2,2,0,0,0,0,0,1
0,0,0,2,2,1,0,0,0,2
2,0,0,2,2,1,0,0,0,1
1,2,2,2,0,0,0,0,0,2
1,0,0,2,2,2,0,0,0,0
2,0,2,2,0,0,0,0,0,0
2,2,1,1,0,0,0,2,0,0
2,0,0,1,1,0,0,0,0,0
1,1,0,1,0,0,0,0,2,2
0,0,0,0,1,1,2,1,0,2
1,0,0,2,1,2,0,0,0,0
2,0,0,0,1,1,2,0,0,0
0,0,0,0,1,1,1,2,0,2
2,0,0,2,1,1,2,0,0,0
2,0,0,2,1,1,1,0,0,0
0,0,0,0,1,1,1,2,0,2
0,0,0,0,2,1,1,2,0,2
1,0,0,0,0,0,0,1,2,0
0,0,0,0,2,0,1,2,0,2
0,0,0,2,0,0,0,1,2,2
0,0,0,0,0,2,2,2,0,2
2,0,0,2,2,1,0,0,0,0
2,2,0,2,0,0,0,1,2,1
2,0,0,0,0,0,0,2,2,0
2,0,0,2,0,1,1,0,0,0
0,0,0,2,0,1,1,0,0,2
1,0,2,0,0,0,0,1,0,0
2,0,0,0,0,0,1,0,0,0
0,0,0,2,0,1,2,0,0,2
1,2,0,0,0,0,0,2,0,0
2,0,0,0,0,0,2,0,0,0
2,0,2,0,0,0,0,0,0,1

[AforAmpere]

Edited, what is the number of states where a computer that counts to any arbitrarily high number and then resets to one cell is possible? I feel like it is probably 50 states or less.

[toroidalet]

What is the number of states where a computer that counts to any arbitrarily high number and then resets to one cell is possible?

Should be possible in ≤15 states to make a ship with a period on the order of double or maybe triple exponential, based on the double-binary counter ship posted here (by me, shameless self-promo). I would make this, except that the vodka is good, but the meat is rotten.

[praosylen]

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@RULE MinSpeed4s-AFP-9-17-17
@TABLE
n_states:4
neighborhood:Moore
symmetries:none
0100000002
0200000003
0001000002
0002000003
2001200303
3002000002
2100030023
3200000002
2200000001
3100000000
1200000000
2000000000
3000300000
3000000030
0020030003
2300003000
0030030003
3300000000
0300000302
2300000303
3033000000
0313000023
3313030020
0233000023
0223000023
0223000033
0223000003
0323000003
3002330001
1002330002
1002333202
2002333101
3233000311
2003333101
2001133203
3311000322
2311000323
2003233203
3001123202
2001133303
3311000332
3001123302
2311000333
3001123302
3332000322
2311000333
3002323202
2323000323
2003233303
3332000332
2323000333
3002323302
2003230000
0313030023
3313230020
3032000000
3023000000
2002333000
3001133000
1003313000
1133000303
3011000000
3001333001
1000033100
3100000310
3113000000
0200020001
0100000303
0021330002
2021330000
3100000320
1200033200

c/917636:

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x = 1, y = 1, rule = MinSpeed4s-AFP-9-17-17
A!

I'm sure there are plenty of trivial improvements that could be made, as well as nontrivial ones such as adding another binary counter.

EDIT: Fixed date.

[gameoflifemaniac]

Tried to make a 1-cell 2-state c/4 spaceship, and I got this:

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@RULE MyEntry
@TABLE
n_states:2
neighborhood:Moore
symmetries:none

0,0,0,0,0,1,0,0,0,1
0,0,0,0,0,0,1,1,0,1
0,1,0,0,0,0,0,1,1,1
1,0,0,1,1,1,0,0,0,0
1,0,0,0,0,1,1,1,0,0
1,1,0,0,0,0,0,1,1,1
1,1,1,1,0,0,0,0,0,0

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x = 1, y = 1, rule = MyEntry
o!

[fluffykitty]

Please check your rule.

[fluffykitty]

c/2596148429267413814265248164610160 in 3 states. Also, I completely forgot that this thread existed until someone linked it in a thread someone linked to in the small long lived methuselahs thread.

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@RULE 3S1CShip2
startup: 108
main: sum(3,110)2^n=2^111-8
ending: 12
total: 2^111+112=2596148429267413814265248164610160
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
0,0,0,0,0,2,1,2,0,2
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
#downward stop
0,1,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,2,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,2,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,2,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2
2,0,0,0,0,0,0,1,1,0
1,1,0,0,0,2,2,0,0,2
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,0
1,2,0,0,0,2,2,0,0,2
0,2,1,1,2,2,0,0,2,2
#1,1,0,0,0,2,2,0,2,1
2,2,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,2,0
1,0,0,0,0,0,0,2,0,2
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
#leftward counting
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
1,0,2,2,0,0,0,1,0,2
0,0,0,2,2,2,1,0,0,2
2,0,0,0,2,2,1,0,0,0
2,2,0,2,0,0,0,1,0,1
1,0,2,2,0,0,0,2,0,2
2,0,0,0,1,2,1,0,0,0
2,2,0,1,0,0,0,1,0,1
0,0,0,2,2,2,0,0,0,2
2,0,0,0,1,1,0,0,0,0
2,0,0,1,0,2,0,0,0,0
2,2,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,2,0,2
1,0,0,2,0,0,2,2,0,2
1,0,2,2,0,0,2,2,0,2
#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0
2,0,0,0,0,0,0,0,0,1
#diagonal mode
#2,0,0,0,2,0,0,0,0,0
#2,0,1,0,0,0,0,0,2,0
#0,0,0,1,0,2,0,2,0,1

necrodoublepost ftw
Edit: c/131661808029361064474122541992202249544316172470474290896938957889657411706431738059855987100606116738608709863898114516322696806682779725395040361126073989754846342223650752839934282507553095228819445591564242224229100999549808158043220482537489286899542806927109262299798576702052364647531326323060875437512721666750074735365806697524459192563914773873444570420147733289826848369892651509013842153766576752759546709772991670483710813378588223114875800405103605361303657861719088971021114521028156816509308794659625756698728308129465992649969171244954433589856461308546917926791439305402526271547340075851639933262085702464422986758336147589425826676630311810520418347644992379850195840502843574915602319663 in 3 states. Can you get 3 counters in 3 states?

Code: Select all

@RULE 3S1CShip5
TODO
startup: 2346
main: sum(3,2348)2^n=2^2349-8
ending: 13
total: 2^2349+2351=131661808029361064474122541992202249544316172470474290896938957889657411706431738059855987100606116738608709863898114516322696806682779725395040361126073989754846342223650752839934282507553095228819445591564242224229100999549808158043220482537489286899542806927109262299798576702052364647531326323060875437512721666750074735365806697524459192563914773873444570420147733289826848369892651509013842153766576752759546709772991670483710813378588223114875800405103605361303657861719088971021114521028156816509308794659625756698728308129465992649969171244954433589856461308546917926791439305402526271547340075851639933262085702464422986758336147589425826676630311810520418347644992379850195840502843574915602319663
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
0,0,0,0,0,2,1,2,0,2
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
#downward stop
0,1,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2
2,0,0,0,0,0,0,1,1,0
1,1,0,0,0,2,2,0,0,2
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,0
1,2,0,0,0,2,2,0,0,2
0,1,1,1,2,2,0,0,2,2
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
#leftward counting
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
1,0,2,2,0,0,0,1,0,2
0,0,0,2,2,2,1,0,0,2
2,0,0,0,2,2,1,0,0,0
2,2,0,2,0,0,0,1,0,1
1,0,2,2,0,0,0,2,0,2
2,0,0,0,1,2,1,0,0,0
2,2,0,1,0,0,0,1,0,1
0,0,0,2,2,2,0,0,0,2
2,0,0,0,1,1,0,0,0,0
2,0,0,1,0,2,0,0,0,0
2,2,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,2,0,2
1,0,0,2,0,0,2,2,0,2
1,0,2,2,0,0,2,2,0,2
#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0
2,0,0,0,0,0,0,0,0,1
#diagonal mode
#2,0,0,0,2,0,0,0,0,0
#2,0,1,0,0,0,0,0,2,0
#0,0,0,1,0,2,0,2,0,1
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,0,0,0,0,0,1,1,2,0
2,0,0,1,2,0,0,2,0,1
2,2,2,1,0,0,0,0,0,1
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1

[Moosey]

Is it possible to do 4 or five states where the counter counts using counters, e.g.
Not states, counted numbers

Code: Select all

0 0 0 0 0 counter->
0 0 0 0 1
0 0 0 0 2
0 0 0 0 3
...
0 0 0 1 0
0 0 0 1 1
0 0 0 1 2
...
0 0 0 2 0
...
...
0 0 1 0 0
0 0 1 0 1
0 0 1 0 2
...
0 0 1 1 0
...
0 0 1 2 0
...
...
...
0 1 0 0 0
etc.

How long would it go?
How many states to make it so that the counter tapes get progressively longer?

That would be really slow!
On a related note, could the ships in the said rule be adjustable?

Sorry to sorta go off on a tangent.

[toroidalet]

Significantly slower (I'm not sure what the period is, but the second counter counts up to about 6,900):

Code: Select all

@RULE 3S1CShip7
#7 because I previously made a version 6 and also this rule is somewhat different
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
0,0,0,0,0,2,1,2,0,2
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
#downward stop
0,1,0,0,0,0,2,1,0,1
1,0,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
2,2,1,1,0,0,0,0,0,0
1,1,0,0,0,0,0,2,2,0
0,0,0,2,2,1,2,1,1,1
1,0,0,0,2,1,2,1,1,2
2,1,2,1,0,0,0,0,0,0
1,2,0,2,0,0,0,2,1,0
0,0,0,0,0,2,1,1,0,2
1,1,0,2,1,2,0,0,1,0
2,0,0,0,2,1,2,1,1,0
2,0,1,0,0,0,0,1,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
1,1,1,0,0,2,2,0,0,2
1,1,0,0,0,0,2,1,1,0
0,0,2,0,0,0,1,2,2,1
0,0,0,0,0,1,1,1,1,1
0,0,2,0,0,0,2,1,1,1
0,2,0,0,0,1,2,2,1,1
0,0,2,0,0,0,2,2,2,1
1,1,0,1,0,1,0,0,1,2
1,1,0,0,0,0,2,2,2,0
1,1,0,0,0,0,1,2,2,0
1,0,0,0,0,0,2,2,1,0
1,0,0,0,0,0,1,2,1,0
1,1,0,0,0,0,1,1,1,0
0,0,2,0,0,0,1,1,1,1
0,0,0,0,0,0,2,0,2,1
1,0,0,0,0,2,0,0,1,0
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2
2,0,0,0,0,0,0,1,1,0
1,1,0,0,0,2,2,0,0,2
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,0
1,2,0,0,0,2,2,0,0,2
0,1,1,1,2,2,0,0,2,2
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
2,1,1,0,0,0,0,0,2,0
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,1,0,0,0
#leftward counting
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
1,0,2,2,0,0,0,1,0,2
0,0,0,2,2,2,1,0,0,2
2,0,0,0,2,2,1,0,0,0
2,2,0,2,0,0,0,1,0,1
1,0,2,2,0,0,0,2,0,2
2,0,0,0,1,2,1,0,0,0
2,2,0,1,0,0,0,1,0,1
0,0,0,2,2,2,0,0,0,2
2,0,0,0,1,1,0,0,0,0
2,0,0,1,0,2,0,0,0,0
2,2,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,2,0,2
1,0,0,2,0,0,2,2,0,2
1,0,2,2,0,0,2,2,0,2
#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0
2,0,0,0,0,0,0,0,0,1
#diagonal mode
#2,0,0,0,2,0,0,0,0,0
#2,0,1,0,0,0,0,0,2,0
#0,0,0,1,0,2,0,2,0,1
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,0,0,0,0,0,1,1,2,0
2,0,0,1,2,0,0,2,0,1
2,2,2,1,0,0,0,0,0,1
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1

I had made a variant of the slowshiptry rule with a c/54 ship, but that doesn't seem useful anymore.

Is it possible to do 4 or five states where the counter counts using counters...

So it would have a sequence of counters and every time one counter overflowed, it would trigger the next one to count and when the very last counter overflows, it would destroy itself? That might work, except it might need a few more states for signals.

[fluffykitty]

I made a rule with tetrationally slow ships (~c/2^^n with 2n cells) at http://www.conwaylife.com/forums/viewto ... =25#p51354. Also, 3S1CShips7 has a small bug that is fixed here:

Code: Select all

@RULE 3S1CShip8
v6 and v7 made by toroidalet
startup: 6908
main: sum(3,6910)2^n=2^6911-8
ending: 13
total: 2^6911+6913=26199924135232771946302945082142267646361287611183858888105878141097146284516799831042207935664233039650479000253912904922771642475731623570814064416253781364092711339053059999903025978136729323217679386289259716419683670948646023812141184875681945563968577497179990209595449685176614744961594950626560211884531284197640394761093553905046063780027895153209787942001752179924270127515264970630023873812492980939002822141152564625446373219448429758099463080183236186289644573331878107376094245464350507388846551751046612070714565610178006262325931767558598663756603524710091836568086585567457582719555198482702777497152917647713931772397794446480673474453561715398402565647895798977733825391494685454766789557545473602733743489446098894582747379919590022524327668286045820662926856507795043034908992104472345005832428884147960277965274231868039010559321290713143465608035562427335152773965238234364115181780266120198067562665325786292427327285082253794788586031222880339518555791075364838339105682822212623973098802249679263152169631485280007941546320088715920833952965887911686467922942093278225469934289248985421166049533594930296131436406782844461227172597419523940735285524817830265186717280715381153340934435524413089365663132951826300964878165876115877456321519871137927184515404511244296109196015310844309425916538601758601506755054623439329923395989582441201949702784143957477436389201828161767915088756130899725645032475916297263635572338097104291727119796586891454172270804516130061996391584953195213962055999127981606862469614528570944490481961815733359163745933237148318698949933861294045259868727519925870307847766277701373806698228034652816172832635092274619498470510299902864195522028303384354963284200397613571516894351225452609490085477998496433453738629933293500194584668382708191550532193329097472001535189222239048638243327986932257122929771989683230924125732348809919922259131496658284595708970604039562910688418658511076045962717614689204677807638527786100521285127133676423571868395252424476812075884746012485749210828645724603893058548869805107256798685960961
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
0,0,0,0,0,2,1,2,0,2
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
#downward stop
0,1,0,0,0,0,2,1,0,1
1,0,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
2,2,1,1,0,0,0,0,0,0
1,1,0,0,0,0,0,2,2,0
0,0,0,2,2,1,2,1,1,1
1,0,0,0,2,1,2,1,1,2
2,1,2,1,0,0,0,0,0,0
1,2,0,2,0,0,0,2,1,0
0,0,0,0,0,2,1,1,0,2
1,1,0,2,1,2,0,0,1,0
2,0,0,0,2,1,2,1,1,0
2,0,1,0,0,0,0,1,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
1,1,1,0,0,2,2,0,0,2
1,1,0,0,0,0,2,1,1,0
0,0,2,0,0,0,1,2,2,1
0,0,0,0,0,1,1,1,1,1
0,0,2,0,0,0,2,1,1,1
0,2,0,0,0,1,2,2,1,1
0,0,2,0,0,0,2,2,2,1
1,1,0,1,0,1,0,0,1,2
1,1,0,0,0,0,2,2,2,0
1,1,0,0,0,0,1,2,2,0
1,0,0,0,0,0,2,2,1,0
1,0,0,0,0,0,1,2,1,0
1,1,0,0,0,0,1,1,1,0
0,0,2,0,0,0,1,1,1,1
0,0,0,0,0,0,2,0,2,1
1,0,0,0,0,2,0,0,1,0
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2
2,0,0,0,0,0,0,1,1,0
1,1,0,0,0,2,2,0,0,2
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,0
1,2,0,0,0,2,2,0,0,2
0,1,1,1,2,2,0,0,2,2
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
2,1,1,0,0,0,0,0,2,0
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,1,0,0,0
#leftward counting
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
1,0,2,2,0,0,0,1,0,2
0,0,0,2,2,2,1,0,0,2
2,0,0,0,2,2,1,0,0,0
2,2,0,2,0,0,0,1,0,1
1,0,2,2,0,0,0,2,0,2
2,0,0,0,1,2,1,0,0,0
2,2,0,1,0,0,0,1,0,1
0,0,0,2,2,2,0,0,0,2
2,0,0,0,1,1,0,0,0,0
2,0,0,1,0,2,0,0,0,0
2,2,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,2,0,2
1,0,0,2,0,0,2,2,0,2
1,0,2,2,0,0,2,2,0,2
#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0
2,0,0,0,0,0,0,0,0,1
#diagonal mode
#2,0,0,0,2,0,0,0,0,0
#2,0,1,0,0,0,0,0,2,0
#0,0,0,1,0,2,0,2,0,1
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,0,0,0,0,0,1,1,2,0
2,0,0,1,2,0,0,2,0,1
2,2,2,1,0,0,0,0,0,1
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1
#bugfix
1,0,0,0,1,1,2,1,0,0

[Moosey]

...

Is it possible to do 4 or five states where the counter counts using counters...

So it would have a sequence of counters and every time one counter overflowed, it would trigger the next one to count and when the very last counter overflows, it would destroy itself? That might work, except it might need a few more states for signals.

Yes, that’s what I mean, a tetrationally slow 1-cell ship

[gameoflifemaniac]

For two states it could theoretically be c/2. If the whole universe fills up and the one dot disappears, only one cell next to the gap may survive and the rest dies. It can't be done in Golly because it doesn't support B0 properly for rule tables.

[CoolCreeper39]

c/2596148429267413814265248164610160 in 3 states. Also, I completely forgot that this thread existed until someone linked it in a thread someone linked to in the small long lived methuselahs thread.

Code: Select all

@RULE 3S1CShip2
startup: 108
main: sum(3,110)2^n=2^111-8
ending: 12
total: 2^111+112=2596148429267413814265248164610160
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
0,0,0,0,0,2,1,2,0,2
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
#downward stop
0,1,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,2,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,2,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,2,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2
2,0,0,0,0,0,0,1,1,0
1,1,0,0,0,2,2,0,0,2
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,0
1,2,0,0,0,2,2,0,0,2
0,2,1,1,2,2,0,0,2,2
#1,1,0,0,0,2,2,0,2,1
2,2,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,2,0
1,0,0,0,0,0,0,2,0,2
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
#leftward counting
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
1,0,2,2,0,0,0,1,0,2
0,0,0,2,2,2,1,0,0,2
2,0,0,0,2,2,1,0,0,0
2,2,0,2,0,0,0,1,0,1
1,0,2,2,0,0,0,2,0,2
2,0,0,0,1,2,1,0,0,0
2,2,0,1,0,0,0,1,0,1
0,0,0,2,2,2,0,0,0,2
2,0,0,0,1,1,0,0,0,0
2,0,0,1,0,2,0,0,0,0
2,2,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,2,0,2
1,0,0,2,0,0,2,2,0,2
1,0,2,2,0,0,2,2,0,2
#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0
2,0,0,0,0,0,0,0,0,1
#diagonal mode
#2,0,0,0,2,0,0,0,0,0
#2,0,1,0,0,0,0,0,2,0
#0,0,0,1,0,2,0,2,0,1

necrodoublepost ftw
Edit: c/131661808029361064474122541992202249544316172470474290896938957889657411706431738059855987100606116738608709863898114516322696806682779725395040361126073989754846342223650752839934282507553095228819445591564242224229100999549808158043220482537489286899542806927109262299798576702052364647531326323060875437512721666750074735365806697524459192563914773873444570420147733289826848369892651509013842153766576752759546709772991670483710813378588223114875800405103605361303657861719088971021114521028156816509308794659625756698728308129465992649969171244954433589856461308546917926791439305402526271547340075851639933262085702464422986758336147589425826676630311810520418347644992379850195840502843574915602319663 in 3 states. Can you get 3 counters in 3 states?

Code: Select all

@RULE 3S1CShip5
TODO
startup: 2346
main: sum(3,2348)2^n=2^2349-8
ending: 13
total: 2^2349+2351=131661808029361064474122541992202249544316172470474290896938957889657411706431738059855987100606116738608709863898114516322696806682779725395040361126073989754846342223650752839934282507553095228819445591564242224229100999549808158043220482537489286899542806927109262299798576702052364647531326323060875437512721666750074735365806697524459192563914773873444570420147733289826848369892651509013842153766576752759546709772991670483710813378588223114875800405103605361303657861719088971021114521028156816509308794659625756698728308129465992649969171244954433589856461308546917926791439305402526271547340075851639933262085702464422986758336147589425826676630311810520418347644992379850195840502843574915602319663
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
0,0,0,0,0,2,1,2,0,2
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
#downward stop
0,1,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2
2,0,0,0,0,0,0,1,1,0
1,1,0,0,0,2,2,0,0,2
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,0
1,2,0,0,0,2,2,0,0,2
0,1,1,1,2,2,0,0,2,2
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
#leftward counting
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
1,0,2,2,0,0,0,1,0,2
0,0,0,2,2,2,1,0,0,2
2,0,0,0,2,2,1,0,0,0
2,2,0,2,0,0,0,1,0,1
1,0,2,2,0,0,0,2,0,2
2,0,0,0,1,2,1,0,0,0
2,2,0,1,0,0,0,1,0,1
0,0,0,2,2,2,0,0,0,2
2,0,0,0,1,1,0,0,0,0
2,0,0,1,0,2,0,0,0,0
2,2,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,2,0,2
1,0,0,2,0,0,2,2,0,2
1,0,2,2,0,0,2,2,0,2
#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0
2,0,0,0,0,0,0,0,0,1
#diagonal mode
#2,0,0,0,2,0,0,0,0,0
#2,0,1,0,0,0,0,0,2,0
#0,0,0,1,0,2,0,2,0,1
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,0,0,0,0,0,1,1,2,0
2,0,0,1,2,0,0,2,0,1
2,2,2,1,0,0,0,0,0,1
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1

How did you run the entire thing? Golly slows down for me at about 8^7 steps

[AforAmpere]

How did you run the entire thing? Golly slows down for me at about 8^7 steps

Nobody did. The period is estimated based on how the ship works. You can calculate the period because it does the same type of thing over and over (the binary counting).

[gameoflifemaniac]

I have found a c/2 in 2 states!!!

Code: Select all

x = 1, y = 1, rule = MAP//////////////////////////////////////////4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABA
o!

I knew this could be made, but always failed to do it. I mentioned about it earlier:

For two states it could theoretically be c/2. If the whole universe fills up and the one dot disappears, only one cell next to the gap may survive and the rest dies. It can't be done in Golly because it doesn't support B0 properly for rule tables.

but no one cared.

[blah]

I have found a c/2 in 2 states!!!

Code: Select all

x = 1, y = 1, rule = MAP//////////////////////////////////////////4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABA
o!

Optimised to C/4.

Code: Select all

@RULE 2Sslow
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
2,1,1,1,1,1,1,1,1,2
1,1,1,1,1,1,1,2,1,1
1,2,1,1,1,1,1,1,1,1
2,1,2,2,2,2,2,1,2,2
1,2,1,1,2,2,2,2,2,1
1,1,2,2,2,2,2,1,2,1
1,a,b,c,d,e,f,g,h,2
2,a,b,c,d,e,f,g,h,1

Code: Select all

x = 20, y = 20, rule = 2Sslow
20A$20A$20A$20A$20A$20A$20A$20A$20A$9AB10A$20A$20A$20A$20A$20A$20A$
20A$20A$20A$20A!

I don't care enough to convert this to a MAP. Anyway, your approach has much more potential, I think. I believe with enough effort you could absolutely make a much, much slower 1-cell 2-state ship. It's trivial to prove that it must have an even period.

[gameoflifemaniac]

I don't care enough to convert this to a MAP.

I tried to do it, but doesn't work.

Code: Select all

x = 1, y = 1, rule = MAPAAB//4AA//8AAP//AAD//4AA//8AAP//AAD//wAA//8AAP//AAD//wAB//4AAP//AAD//wEA//8AAP//AAD//w
o!

[blah]

I just created a script to do the conversion automatically.

Code: Select all

local g = golly()

dead_state = tonumber(g.getstring("Enter state for dead cells, or h for help."))

if dead_state==nil then
	g.warn([[automap.lua - blah 2020

This script generates a MAP rulestring for the current rule, where 2 states are considered and all others are ignored. Useful, primarily, if you want to design a 2-state rule with B0 using RuleLoader.

The script maps the provided 2 states from the current rule onto the 2 states of the generated MAP rule. For example, running this script with B3/S23 as the current rule and entering 0, then 1, will generate a MAP conversion of B3/S23. Entering 1 then 0 will generate its inverse.

This requires that a universe of only cells with one of the two provided states will never produce a third state. Otherwise, the script will produce an error.]],false)
	g.exit()
end

live_state = tonumber(g.getstring("And the one for live cells."))

g.addlayer()
g.select({-1,-1,5,5}) -- used to clear edges, so explosions won't evolve

rule_string = "MAP"
base64_digs='ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'
bit6buf = 0 -- number in which the 6 bits of a base64 digit are built up

for neigh = 0, 515 do -- 515 instead of 511, since 512 is not a multiple of 6
                      -- the bits beyond 511 simply don't matter
	bits = {}
	for bit = 0, 8 do
		if neigh/(2^bit) % 2 < 1 then
			bits[bit] = dead_state
		else
			bits[bit] = live_state
		end
	end
	-- write new state out
	g.setcell(2,2,bits[0])
	g.setcell(1,2,bits[1])
	g.setcell(0,2,bits[2])
	g.setcell(2,1,bits[3])
	g.setcell(1,1,bits[4])
	g.setcell(0,1,bits[5])
	g.setcell(2,0,bits[6])
	g.setcell(1,0,bits[7])
	g.setcell(0,0,bits[8])
	-- test what it produces
	g.step()
	new_cell = g.getcell(1,1)
	g.clear(0)
	-- convert new cell to binary value
	if new_cell == live_state then
		new_cell = 1
	elseif new_cell == dead_state then
		new_cell = 0
	else
		g.dellayer()
		g.error("Attempt to convert non-2-state subrule.")
		g.exit()
	end
	bit6buf = bit6buf*2 + new_cell
	if neigh%6 == 5 then -- add new base64 digit
		rule_string = rule_string .. base64_digs:sub(bit6buf+1,bit6buf+1)
		bit6buf = 0
	end
end

g.dellayer()

g.warn(rule_string)

With my rule, fed the parameters 1 and 2, it produces this rule:

Code: Select all

x = 1, y = 1, rule = MAP//+AAH//AAD//wAA//8AAH//AAD//wAA//8AAP//AAD//wAA//8AAP/+AAH//wAA//8AAP7/AAD//wAA//8AAP
o!

Were you trying to do it manually?

[gameoflifemaniac]

Were you trying to do it manually?

Yes.

[gameoflifemaniac]

Found C/8:

Code: Select all

@RULE slowship2statetest
@TABLE
n_states:3
neighborhood:Moore
symmetries:none

var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a

1,2,1,1,1,2,2,2,2,1
1,2,2,2,2,1,2,2,2,1
1,1,2,2,2,2,2,2,2,1

2,2,2,2,2,2,2,1,2,2
2,2,2,2,2,1,1,2,2,2
2,1,2,2,2,2,2,2,1,2
2,1,1,1,1,1,2,2,2,2

1,a,b,c,d,e,f,g,h,2
2,a,b,c,d,e,f,g,h,1

Code: Select all

x = 39, y = 29, rule = slowship2statetest
39A$39A$39A$39A$39A$39A$39A$39A$39A$39A$39A$39A$39A$39A$2AB36A$39A$
39A$39A$39A$39A$39A$39A$39A$39A$39A$39A$39A$39A$39A!

Code: Select all

x = 1, y = 1, rule = MAP//8AAP//AAD//wAA//8AAf//AAD//wAA//8AAP//AAD//wAA//8IAP//AAD//gAA//8AAP3/AAD//wAB//sAQP
o!

EDIT: C/12:

Code: Select all

@RULE slowship2statetest2
@TABLE
n_states:3
neighborhood:Moore
symmetries:none

var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a

2,2,2,2,2,2,2,1,2,2
2,2,1,2,2,1,1,1,1,2

1,1,1,1,2,2,1,1,1,1
1,2,1,1,1,1,1,1,2,1
1,1,1,1,1,2,1,2,1,1
1,2,2,1,1,2,2,2,2,1
1,2,2,2,2,1,2,2,2,1

1,a,b,c,d,e,f,g,h,2
2,a,b,c,d,e,f,g,h,1

Code: Select all

x = 85, y = 73, rule = slowship2statetest2
85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$
85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$
85A$85A$85A$17AB67A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$
85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$85A$
85A$85A$85A$85A$85A$85A!

Code: Select all

x = 1, y = 1, rule = MAP7/8AAN//AAD//wAA//8AAP//AED//wAA//8AAP//AAD//wAA//8AAP//AAD//wAAf/8AAP//AAD//wAB/fsAAO
o!

By the way, can someone help me find the slowest ship?