Miscellaneous Discoveries in Other Cellular Automata

[Saka]

A cooler version of the t ship

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x = 3, y = 2, rule = B2ci3aik4w6ck/S012an3-jnry4-acenz5enqr7c
bo$3o!

[Hdjensofjfnen]

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x = 4, y = 3, rule = B3-n4kq/S237
2bo$b3o$2obo!

EDIT: It's an 8c/56.

EDIT: Unrelated:

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x = 29, y = 8, rule = B3-n4kq6in7c/S234e7c
b3o21b3o$bobo21bobo$o3bo19bo3bo$bobo21bobo$b3o21b3o3$20b3o!

EDIT: Same rule:

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x = 55, y = 16, rule = B3-n4kq6in7c/S234e7c
51bo$50bobo$49b2ob2o$49bo3bo$6b2o2$6bo2bo10b2o31b2o$7b2o11b2o31b2o$7b
2o6$2o$2o!

[gmc_nxtman]

9c/72 diagonal:

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x = 5, y = 4, rule = B2ikn3aijn/S23-i4q
2bo$bobo$o3bo$4o!

EDIT: Rule has a 1-tick glider advancer:

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x = 21, y = 7, rule = B2in3/S2-c3
2bo$2o$b2o2$3bo15bo$2b2o14b2o$2bobo13bobo!

EDIT2: More miscellaneous stuff in another rule (p6 flipper, c/4 diagonal ship and wickstretcher, 9c/80 diagonal):

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x = 55, y = 8, rule = B3-cn/S234q
2bo14b2o14b2ob2o14b3o$2ob2o11bo15bo4bo14bo$17b2o14b2obo15bo$2ob2o13b2o
14b2o17b2o$bobo2$bobo$2bo!

[Hdjensofjfnen]

How long does this take to stabilize?

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x = 18, y = 11, rule = B36/S23
2b3o$bo2bo$o3bo$o2bo$3o2$15b3o$14bo2bo$13bo3bo$13bo2bo$13b3o!

[Saka]

That was unexpected.

Code: Select all

x = 7, y = 3, rule = B2in3-q4cint5cjk6cik/S2ace3-jqr4cejqrw5n6a7e8
o4b2o$2o3b2o$o!

EDIT:
Unfortunately unextendable (try saying that 3 times fast):

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x = 3, y = 6, rule = B2-ae3ajnqr4-cjkny5-aijr6ain78/S012-ak3aijkr4-acjtz5ejkqy6-ek7
o$bo$2bo$2bo$bo$o!

[muzik]

All speeds for 2c/4n , where n > 3, in a familiar rule:

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x = 47, y = 19, rule = B2c3ae4ai56c_S2-kn3-enq4
6bo15bo15bo2$b3o2bo2b3o5b3o2bo2b3o5b3o2bo2b3o$2bo7bo7bo7bo7bo7bo$2bo7b
o7bo7bo7bo7bo$2bo7bo7bo7bo7bo7bo$bobo5bobo6bo7bo7bo7bo$2bo7bo6bobo5bob
o6bo7bo$18bo7bo6bobo5bobo$34bo7bo5$3o3bobob3o3b3o3bobob3o3b3o3bob3ob3o
$2bo3bobo3bo5bo3bobobo7bo3bo3bobobo$3o2bo2bob3o3b3o2bo2bob3o3b3o2bo2b
3obobo$o3bo3bobo5bo3bo3bobobo3bo3bo3bo3bobo$3obo3bob3o3b3obo3bob3o3b3o
bo3b3ob3o!

Based on the fact that this exists:
http://catagolue.appspot.com/object/xq1 ... 2-kn3-enq4


Now we just need to find adjustables that move at 2c/odd, and we've proved that as well.

[wildmyron]

Adjustable speed diagonal ship: 2c/(12n+2) for n>3

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x = 28, y = 30, rule = B2cek3cky4-anwy5-ny6-ak78/S123aeik4-aiqrw5-n6-ak78
27bo$27bo4$22b2o$24bo3$20b2o2$16bo$16bo3$12b2o$14bo3$10b2o3$5bo$5bo2$
2b2o$4bo3$2o!

works in: B2cek4ejt5aj6c/S123a5i - B2cek3cky4-anwy5-ny6-ak78/S123aeik4-aiqrw5-n6-ak78

[praosylen]

Adjustable speed diagonal ship: 2c/(12n+2) for n>3

Code: Select all

x = 28, y = 30, rule = B2cek3cky4-anwy5-ny6-ak78/S123aeik4-aiqrw5-n6-ak78
27bo$27bo4$22b2o$24bo3$20b2o2$16bo$16bo3$12b2o$14bo3$10b2o3$5bo$5bo2$
2b2o$4bo3$2o!

works in: B2cek4ejt5aj6c/S123a5i - B2cek3cky4-anwy5-ny6-ak78/S123aeik4-aiqrw5-n6-ak78

Congratulations! The 2 full-diagonal translation is interesting, too — it disallows true-period ships, but allows odd-denominator reduced speeds.

[Rhombic]

Congratulations! The 2 full-diagonal translation is interesting, too — it disallows true-period ships, but allows odd-denominator reduced speeds.

Very impressed, wildmyron! It seems that muzik's idea wasn't far-fetched at all!
These spaceships allow things that can't really be described with other normal spaceships, like crossing through:

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x = 63, y = 49, rule = B2cek4ejt5aj6c/S123a5i
5bo$5bo2$2b2o$4bo3$2o9$62bo$62bo4$57b2o$59bo26$32b2o!

Should we consider these spaceships elementary?

[muzik]

They're elementary and engineerable at the same time. I'm kind of torn as to their classification.

[wildmyron]

Here's another example, this time with the c/4 version of the tiny diagonal ship.

Adjustable speed diagonal ship: c/8n for n>1

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x = 28, y = 27, rule = B2cen4i6a/S12aen3r4a5c
27bo$27bo4$22bo$23bo$23bo$20b2o2$16bo$16bo3$12bo$13bo$13bo$10b2o3$5bo$
5bo2$2bo$3bo$3bo$2o!

works in B2cen4i6a/S12aen3r4a5c - B2-ak3ck4-ry5-q678/S12-k3acekr456-k78

Thank you for the congrats. And thank you Rhombic for your version of the searchRules script - it's particularly useful for this kind of search.

[muzik]

The answer is probably no for small searchable patterns, but could adjustable-slope spaceships exist?

It looks like the rule AforAmpere made uses two different types of cell to move the stationary cells at each side, with one moving the edges orthogonally and the other diagonally, and these can be mixed and matched to give a desired slope.

[BlinkerSpawn]

The answer is probably no for small searchable patterns, but could adjustable-slope spaceships exist?

It looks like the rule AforAmpere made uses two different types of cell to move the stationary cells at each side, with one moving the edges orthogonally and the other diagonally, and these can be mixed and matched to give a desired slope.

Possibly, if this other post of his in the same thread is anything to go on.

[wildmyron]

Adjustable speed orthogonal ship: 2c/4n for n>12

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x = 3, y = 55, rule = B2cek3n4eijwy5j6i/S02e3ny4n6c
bo4$bo$bo2$obo5$o8$bo4$bo$bo2$obo6$o7$bo4$bo$bo2$obo7$o!

works in B2cek3n4eijwy5j6i/S02e3ny4n6c - B2cek3cn4-knrt5-cy6-c78/S02e3ajny4-aci5-j678

This one travels perpendicular to the direction of the small ship - I was actually thinking it would travel parallel to it. I think it's likely we could find one based on this idea:

• Small ship with very low period (p1 or p2)
• works with S0
• supports two interactions with dots:
  • push + reflection reaction with dot on one row
  • pull + reflection with dot on a different row

Edit:

Also found this 4c/29 orthogonal back rake which can be converted to an adjustable size 4c/29 ship while running a similar search

Code: Select all

x = 37, y = 25, rule = B2cek3aer4i5k7e/S01c3y4iz5k8
34b2o$27bo4b2o2bo$29bo3bobo$27bo4b2o2bo$34b2o6$34b2o$20bo6bo4b2o2bo$
29bo3bobo$27bo4b2o2bo$34b2o6$34b2o$o26bo4b2o2bo$29bo3bobo$27bo4b2o2bo$
34b2o!

[Saka]

Konghrachuleshuns again to wildmyron!

A rulesrc result:

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x = 7, y = 3, rule = B2e3inq4aej5k6k/S1c23aeiqy4-cirw5ceiy6an
2o$bo3b2o$2o3b2o!

[Rhombic]

Rulesrc t+block xq178, diagonal

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x = 6, y = 3, rule = B3-k4nt5q6ce/S02ack3-cjk4knrtwy5ry6ek8
o$2o2b2o$o3b2o!

[wildmyron]

Here are several more examples of adjustable speed spaceships using the same mechanism as the one above:

Orthogonal 2c/4n for n>4

Code: Select all

x = 3, y = 49, rule = B2e3-ceny4ain6k/S01c2cek3ijnq4an
o2$bo$obo3$bo14$o3$bo$obo3$bo13$o4$bo$obo3$bo!

works in B2e3-ceny4ain6k/S01c2cek3ijnq4an - B2ein3-eny4-r5-in678/S01c2-a3-aer4-ijr5-in6-c78

Orthogonal 2c/(4n+2) for n>4

Code: Select all

x = 3, y = 51, rule = B2-ak3ejny4kz/S01c2ae3r5k
o2$bo$obo5$bo12$o3$bo$obo5$bo11$o4$bo$obo5$bo!

works in B2-ak3ejny4kz/S01c2ae3r5k - B2-ak3ejkny4-ajnr5-acik678/S01c2aei3kqry4-ajr5-ry6-k78

Orthogonal 2c/4n for n>6

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x = 5, y = 49, rule = B2ik3ai4ae5ay6i/S01e2ck4r5aq6k
bo2$2bo$o3bo3$2bo14$bo3$2bo$o3bo3$2bo13$bo4$2bo$o3bo3$2bo!

works in B2ik3ai4ae5ay6i/S01e2ck4r5aq6k - B2ikn3aiknr4-ir5-ci678/S01e2ckn3-aijr4-aeinw5-ceir6-a78

[muzik]

First one seems to be explosive, depressingly enough.

I should probably create a thread for discussion of these rules.

[Saka]

c/28d

Code: Select all

x = 6, y = 3, rule = B2ek3ciy4aeqtw5-ciny6aik/S01c2-in4q5aceiq6-in7c
2o3bo$bo$2o!

2c/96

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x = 8, y = 3, rule = B2ek3aeir4-acint5aejkq6i7/S01c2-in3ceijk4qrtw5ejy6ekn7e
2o5bo$bo$2o!

c/8

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x = 4, y = 3, rule = B2cen3ae4eikqz5ceir6ek/S03kqr4qr5c7c
o2bo2$o!

[praosylen]

A minor result to report: In the 8-cell extended von Neumann neighborhood, all non-exploding outer-totalistic rules that can contain spaceships must necessarily have B2 and neither of B01. I created rule tables for B2/S and B2/S0 and determined that both are explosive, and so it seems unlikely that any of these rules is non-exploding and still supports spaceships. NOTE: This says nothing about isotropic non-totalistic rules or even radius-dependent totalistic rules.

For reference, here are the rule tables:

Code: Select all

@RULE B2SEN8
@TABLE
n_states:33
neighborhood:vonNeumann
symmetries:none
var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32}
var aa=a
var ab=a
var ac=a
var ad=a
var lon={18,20,22,24,26,28,30,32}
var loff={17,19,21,23,25,27,29,31}
var nlon={2,4,6,8,10,12,14,16}
var nloff={0,3,5,7,9,11,13,15}
var ron={6,8,14,16,22,24,30,32}
var roff={5,7,13,15,21,23,29,31}
var nron={2,4,10,12,18,20,26,28}
var nroff={0,3,9,11,17,19,25,27}
var uon={4,8,12,16,20,24,28,32}
var uoff={3,7,11,15,19,23,27,31}
var nuon={2,6,10,14,18,22,26,30}
var nuoff={0,5,9,13,17,21,25,29}
var don={10,12,14,16,26,28,30,32}
var doff={9,11,13,15,25,27,29,31}
var ndon={2,4,6,8,18,20,22,24}
var ndoff={0,3,5,7,17,19,21,23}
var off={loff,nloff}
var on={lon,nlon}
0,0,0,0,0,0
1,0,0,0,0,2
0,1,0,0,0,3
1,1,0,0,0,4
0,0,1,0,0,5
1,0,1,0,0,6
0,1,1,0,0,7
1,1,1,0,0,8
0,0,0,1,0,9
1,0,0,1,0,10
0,1,0,1,0,11
1,1,0,1,0,12
0,0,1,1,0,13
1,0,1,1,0,14
0,1,1,1,0,15
1,1,1,1,0,16
0,0,0,0,1,17
1,0,0,0,1,18
0,1,0,0,1,19
1,1,0,0,1,20
0,0,1,0,1,21
1,0,1,0,1,22
0,1,1,0,1,23
1,1,1,0,1,24
0,0,0,1,1,25
1,0,0,1,1,26
0,1,0,1,1,27
1,1,0,1,1,28
0,0,1,1,1,29
1,0,1,1,1,30
0,1,1,1,1,31
1,1,1,1,1,32
off,nuoff,nroff,ndoff,lon,1
off,nuoff,nroff,doff,loff,1
off,nuoff,nroff,ndon,loff,1
off,nuoff,roff,ndoff,loff,1
off,nuoff,nron,ndoff,loff,1
off,uoff,nroff,ndoff,loff,1
off,nuon,nroff,ndoff,loff,1
off,nuoff,nroff,doff,nlon,1
off,nuoff,nroff,ndon,nlon,1
off,nuoff,roff,ndoff,nlon,1
off,nuoff,nron,ndoff,nlon,1
off,uoff,nroff,ndoff,nlon,1
off,nuon,nroff,ndoff,nlon,1
off,nuoff,nroff,don,nloff,1
off,nuoff,roff,doff,nloff,1
off,nuoff,nron,doff,nloff,1
off,uoff,nroff,doff,nloff,1
off,nuon,nroff,doff,nloff,1
off,nuoff,roff,ndon,nloff,1
off,nuoff,nron,ndon,nloff,1
off,uoff,nroff,ndon,nloff,1
off,nuon,nroff,ndon,nloff,1
off,nuoff,ron,ndoff,nloff,1
off,uoff,roff,ndoff,nloff,1
off,nuon,roff,ndoff,nloff,1
off,uoff,nron,ndoff,nloff,1
off,nuon,nron,ndoff,nloff,1
off,uon,nroff,ndoff,nloff,1
a,aa,ab,ac,ad,0
@COLORS
0 30 30 30
1 225 225 225
2 100 100 100
3 100 100 100
4 100 100 100
5 100 100 100
6 100 100 100
7 100 100 100
8 100 100 100
9 100 100 100
10 100 100 100
11 100 100 100
12 100 100 100
13 100 100 100
14 100 100 100
15 100 100 100
16 100 100 100
17 100 100 100
18 100 100 100
19 100 100 100
20 100 100 100
21 100 100 100
22 100 100 100
23 100 100 100
24 100 100 100
25 100 100 100
26 100 100 100
27 100 100 100
28 100 100 100
29 100 100 100
30 100 100 100
31 100 100 100
32 100 100 100

Code: Select all

@RULE B2S0EN8
@TABLE
n_states:33
neighborhood:vonNeumann
symmetries:none
var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32}
var aa=a
var ab=a
var ac=a
var ad=a
var lon={18,20,22,24,26,28,30,32}
var loff={17,19,21,23,25,27,29,31}
var nlon={2,4,6,8,10,12,14,16}
var nloff={0,3,5,7,9,11,13,15}
var ron={6,8,14,16,22,24,30,32}
var roff={5,7,13,15,21,23,29,31}
var nron={2,4,10,12,18,20,26,28}
var nroff={0,3,9,11,17,19,25,27}
var uon={4,8,12,16,20,24,28,32}
var uoff={3,7,11,15,19,23,27,31}
var nuon={2,6,10,14,18,22,26,30}
var nuoff={0,5,9,13,17,21,25,29}
var don={10,12,14,16,26,28,30,32}
var doff={9,11,13,15,25,27,29,31}
var ndon={2,4,6,8,18,20,22,24}
var ndoff={0,3,5,7,17,19,21,23}
var off={loff,nloff}
var on={lon,nlon}
0,0,0,0,0,0
1,0,0,0,0,2
0,1,0,0,0,3
1,1,0,0,0,4
0,0,1,0,0,5
1,0,1,0,0,6
0,1,1,0,0,7
1,1,1,0,0,8
0,0,0,1,0,9
1,0,0,1,0,10
0,1,0,1,0,11
1,1,0,1,0,12
0,0,1,1,0,13
1,0,1,1,0,14
0,1,1,1,0,15
1,1,1,1,0,16
0,0,0,0,1,17
1,0,0,0,1,18
0,1,0,0,1,19
1,1,0,0,1,20
0,0,1,0,1,21
1,0,1,0,1,22
0,1,1,0,1,23
1,1,1,0,1,24
0,0,0,1,1,25
1,0,0,1,1,26
0,1,0,1,1,27
1,1,0,1,1,28
0,0,1,1,1,29
1,0,1,1,1,30
0,1,1,1,1,31
1,1,1,1,1,32
off,nuoff,nroff,ndoff,lon,1
off,nuoff,nroff,doff,loff,1
off,nuoff,nroff,ndon,loff,1
off,nuoff,roff,ndoff,loff,1
off,nuoff,nron,ndoff,loff,1
off,uoff,nroff,ndoff,loff,1
off,nuon,nroff,ndoff,loff,1
off,nuoff,nroff,doff,nlon,1
off,nuoff,nroff,ndon,nlon,1
off,nuoff,roff,ndoff,nlon,1
off,nuoff,nron,ndoff,nlon,1
off,uoff,nroff,ndoff,nlon,1
off,nuon,nroff,ndoff,nlon,1
off,nuoff,nroff,don,nloff,1
off,nuoff,roff,doff,nloff,1
off,nuoff,nron,doff,nloff,1
off,uoff,nroff,doff,nloff,1
off,nuon,nroff,doff,nloff,1
off,nuoff,roff,ndon,nloff,1
off,nuoff,nron,ndon,nloff,1
off,uoff,nroff,ndon,nloff,1
off,nuon,nroff,ndon,nloff,1
off,nuoff,ron,ndoff,nloff,1
off,uoff,roff,ndoff,nloff,1
off,nuon,roff,ndoff,nloff,1
off,uoff,nron,ndoff,nloff,1
off,nuon,nron,ndoff,nloff,1
off,uon,nroff,ndoff,nloff,1
on,nuoff,nroff,ndoff,nloff,1
a,aa,ab,ac,ad,0
@COLORS
0 30 30 30
1 225 225 225
2 100 100 100
3 100 100 100
4 100 100 100
5 100 100 100
6 100 100 100
7 100 100 100
8 100 100 100
9 100 100 100
10 100 100 100
11 100 100 100
12 100 100 100
13 100 100 100
14 100 100 100
15 100 100 100
16 100 100 100
17 100 100 100
18 100 100 100
19 100 100 100
20 100 100 100
21 100 100 100
22 100 100 100
23 100 100 100
24 100 100 100
25 100 100 100
26 100 100 100
27 100 100 100
28 100 100 100
29 100 100 100
30 100 100 100
31 100 100 100
32 100 100 100

This p6 is the most interesting thing I've found in either rule:

Code: Select all

x = 6, y = 5, rule = B2SEN8
3.A2$2A2.2A2$2.A!

[Hdjensofjfnen]

c/28d

Code: Select all

x = 6, y = 3, rule = B2ek3ciy4aeqtw5-ciny6aik/S01c2-in4q5aceiq6-in7c
2o3bo$bo$2o!

2c/96

Code: Select all

x = 8, y = 3, rule = B2ek3aeir4-acint5aejkq6i7/S01c2-in3ceijk4qrtw5ejy6ekn7e
2o5bo$bo$2o!

c/8

Code: Select all

x = 4, y = 3, rule = B2cen3ae4eikqz5ceir6ek/S03kqr4qr5c7c
o2bo2$o!

Think I like the first one the most.

[toroidalet]

In the 8-cell extended von Neumann neighborhood, all non-exploding outer-totalistic rules that can contain spaceships must necessarily have B2 and neither of B01.

What's the neighborhood for the 8-cell extended von Neumann neighborhood? Is it the cross-shape neighborhood that I exhaustively enumerated, thinking it was the extended von Neumann neighborhood?
This rake is great, but the rule is explosive:

Code: Select all

x = 2, y = 3, rule = B2i3-y5e6ci/S2-i3-e
o$2o$o!

Code: Select all

x = 4, y = 3, rule = B2i3-y5e6ci/S2-i3-e
2o$ob2o$2bo!

[praosylen]

What's the neighborhood for the 8-cell extended von Neumann neighborhood? Is it the cross-shape neighborhood that I exhaustively enumerated, thinking it was the extended von Neumann neighborhood?

Yes. I don't know that what I called it is the correct term, though. I would say it does classify as an extended von Neumann neighborhood, although it's not the canonical way of extending it.

[M. I. Wright]

P92 HWSS gun in Rhombic's Omnipotens rule:

Code: Select all

x = 31, y = 16, rule = Omnipotens
14.2A$6.2B5.A.A$5.B.B5.A$4.B8.3A$3.B25.B$3.2B23.B.B$29.B$2B11.3A$2B
11.A$13.A.A$14.2A$9.2B$9.2B$2.B$2.B$2.B!

Could be bumped down to p46 with some way to edgeshoot the bi-blocks from the left (w/o the leftmost state-2 block)

[BlinkerSpawn]

P92 HWSS gun in Rhombic's Omnipotens rule:

Code: Select all

x = 31, y = 16, rule = Omnipotens
14.2A$6.2B5.A.A$5.B.B5.A$4.B8.3A$3.B25.B$3.2B23.B.B$29.B$2B11.3A$2B
11.A$13.A.A$14.2A$9.2B$9.2B$2.B$2.B$2.B!

Could be bumped down to p46 with some way to edgeshoot the bi-blocks from the left (w/o the leftmost state-2 block)

A tad more leftward clearance, but it's still not enough to, say, construct the bi-block trivially with gliders.

Code: Select all

x = 31, y = 16, rule = Omnipotens
14.2A$5.B.B5.A.A$4.B.2B5.A$4.B8.3A$3.2B24.B$28.B.B$29.B$2B11.3A$2B11.
A$13.A.A$14.2A$9.2B$9.2B2$2.2B$2.2B!