ConwayLife.com

Posted: **January 30th, 2018, 3:38 pm**

Rhombic wrote:After a couple hours, 269 iterRulesrc results for a D2_+1 4-cell search:

The c/32 rule has 3 ships:

x = 4, y = 19, rule = B2cek4aiqrw5ry/S01c2ikn3-acqy4-ekqw5jry
3bo$o$3bo6$b2o$o$obo6$obo$2o$obo!

I may APGsearch

Posted: **January 31st, 2018, 2:09 am**

Naturally-occured butterfly still-life

Code: Select all

x = 7, y = 9, rule = B3-ce/S2-i35ce6ce
b2o$o2bobo$bo2bobo$2b4o$bo$2b4o$bo2bobo$o2bobo$b2o!

Posted: **January 31st, 2018, 4:09 am**

Hutton32 rule has self-replicator.

Code: Select all

x = 105, y = 99, rule = Hutton32
104.J$104.J$103.LpA$LO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO3KOKO5KO4K
2O4K5OKOKJ$4IM5IM5IM5IM5IM5IM5IM5IMIM3IM5IM5IM5IM5IM5IM5IM5IM5IM2IPJ$
P5KO5KO3KOK9O75KOKJ$5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM
5IMILJ$L3KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO3KJ$IM5IM
5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IPJ$LKO5KO5KO5KO5KO5KO
5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KJ$3IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5I
M5IM5IM5IM5IM5IM5IM3ILJ$P2KO2K3O3K3OKO2KOKO2KO5KO5KO5KO5KO5KO5KO5KO5K
O5KO5KO5KO5KO5KOKJ$IMI9M5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM
ILJ$L3KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO3KJ$IM5IM5IM
5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IPJ$LKO5KO5KO5KO5KO5KO5KO
5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KJ$3IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5I
M5IM5IM5IM5IM5IM3ILJ$P5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5K
O5KOKJ$2IMIM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5I5MI5MI5MI5MI5MI3MPJ$LOKOK
OK5OK5OK5OK5OK5OK5OK5OK5OK5OK5OK5OK5OK5OK5OK5OK5OKOJ$5MIMIMIMI5MIMIMI
MI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMLJ$P3OKOK
OKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5O
KOKOJ$MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI
5MIMIMIMI5MIMIMIMLJ$LOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK
5OKOKOKOK5OKOKOKOK5OKOKOKOK5OJ$MIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMI
MI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI3MPJ$L4KO5KO5KO5KO5KO5KO5KO5KOK
OKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOKOJ$M5IM5IM5IM5IM5IM5IM5IM5I
M5IM5IM5IM5IM5IM5IM5IM5IM5IMLJ$L2KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO
5KO5KO5KO5KO5KO4KJ$2IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5I
M4ILJ$LO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KOJ$4IM5IM5I
M5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM2ILJ$L4KO5KO5KO5KO5KO5KO5K
O5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO2KJ$M5IM5IM5IM5IM5IM2IMI5MI5MI5MI5MI5M
I5MI5MI5MI5MI5MI5MI2MPJ$PKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OK5OK5OK5OK
5OK5OK5OK5OK5OK5OK2OJ$I5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI
5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIPJ$P2OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKO
K5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKJ$2MIMIMIMI5MIMIMIMI5MIMI
MIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIPJ$PK5OKOKOKO
K5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKOKOKOK5OKJ$
IMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI5MIMIMIMI
5MIMIMIMI2MPJ$L3KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KOKOKOKOK5OKOK
OKOK2OJ$IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IPJ$LKO5KO
5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KJ$3IM5IM5IM5IM5IM5IM5I
M5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM3ILJ$P5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5K
O5KO5KO5KO5KO5KO5KOKJ$5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5I
M5IMILJ$LO2KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO3KJ$5MI
5MI5MI5MI5MI5MI5MI5MI5MI5MI5MI5MI5MI5MI5MI5MI5MIMPJ$L2K5OKO4K5OKO4K5O
KO4K5OKO4K5OKO4K5OKO4K5OKO4K2O4K2O4K2O4K2O4KJ$IMI5M4IMI5M4IMI5M4IMI5M
4IMI5M4IMI5M4IMI5M4IMI5M4IMI5M4IMIMPJ$LK5OKO4K5OKO4K5OKO4K5OKO4K5OKO
4K5OKO4K5OKO4K5OKO4K5OKO4K3OJ$2IMI5M4IMI5M4IMI5M4IMI5M4IMI5M4IMI5M4IM
I5M4IMI5M4IMI5M4IMIPJ$L5OKO4K5OKO4K5OKO4K5OKO4K5OKO4K5OKO4K5OKO4K5OKO
4K5OKO4K4OJ$3IMI5M4IMI5M4IMI5M4IMI4M5IM5IM5IM5IM5IM5IM5IM5IM5IM5IMILJ
$L3KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO3KJ$IM5IM5IM5IM
5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IPJ$LKO5KO5KO5KO5KO5KO5KO5KO
5KO5KO5KO5KO5KO5KO5KO5KO5KO5KJ$3IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5I
M5IM5IM5IM5IM3ILJ$P5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5K
OKJ$5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IMILJ$L5OK5OK5OK
5OK5OK5OK5OK5OK5OK5OK5OK5OK5OK5OKO2KO5KO5KO3KJ$5MI5MI5MIMIMIMI5MI5MI
5MI5MIMIMIMIM5IM5IM5IM5IM5IM5IM5IM5IMLJ$P4OK5OK5OK5OKO2KO5KO5KO5KO5KO
5KO5KO5KO5KO5KO5KO5KO5KO4KJ$I5MI2M4I3M3I2M4I2M4I2M4I2M4I2M4I2M4I2M4I
2M4IMI5M4IMI5M4I2M4I2M4IMIPJ$L4KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO
5KO5KO5KOKOKOK3OJ$M5IM5IM5IM5IM5IM2IMI5MI5MI5MI5MI5MIMI4MI4MI4M5IM5IM
5IM4ILJ$P2OK5OK5OK5OK5OK5OK5OKOKOKO3K3OKOKOKOK5OK5OK5OK5OK5OKO2KO5KO
5KOJ$2MIMIMI7MI5MI5MI5MI5MIMIMI3M5IM5IM5IM5IM5IM5IM5IM5IM5IM3ILJ$PK4O
KOK5OK5OK5OK5OK5OKO2KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KOKJ$3MI8MI5MI5MI5M
I5MI5MI5MIMI8MI5MI5MI5MI5MIMI4M5IM5IMILJ$L3KO5KO5KO5KO5KO5KO5KO5KO5KO
5KO5KO5KO5KO5KO5KO5KO5KO3KJ$IM2IMI5MI5MI5MI5MI5MIMIMIMI3M3IMIMIMI5MI
5MI5MI5MI5MI5MI5MIMIMIMIMLJ$L2KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KOKOKO
KOK5O2K2OKO2K2OKO2K2OKO2K2OJ$2IM5IM5IM5IM5IM5IM5IM5IM5IM2IMI5MI5MI5MI
5MI5MIMI4MI4MI6MPJ$LO5KO5KO5KO5KOKOKOKOK8OKO4K2O4K2O4K5OKOK5OK5OK5OK
5OK5OK5OKOJ$4IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM2IMI4MPJ$
POK5OK5OKOKOKOK5OK5OK5OK5OK5OK5OK5OKOKOKO3K3OKOKOKO3K3O4K5OKO4K2OKJ$
3MI5MI5MIMIMIMIM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM2ILJ$P4OK5OK8O
K4OK4OK4OKOK5O3K5OKOKOK5OKO2KO5KO5KO5KO5KO5KO5KO2KJ$I5MI5MI5MI5MIMI5M
4IMI5M4IMI5M4IMI4M5IM5IM5IM5IM5IM5IM3ILJ$PO3K5OKOKOK5OKO2KO5KO5KO5KO
5KO5KO5KO5KO5KO5KO5KO5KO5KO5KOKJ$3MI2M4IMIMIMI2M4IMIMIMI5MI5MI5MI5MI
5MI5MI5MIMIMIMI5MI5MI5MI3M3IM2ILJ$L4KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO
5KO5KO5KO5KO5KO5KO2KJ$M2IMI5MIMIMI5M3I2M4I2M4I3M3I5MI2M4I2M4I3M3I5MI
5MI5MI5MI5MIMI4MIMPJ$L4KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO5KO3K3OK
5O2K2OKO2KJ$M5IM5IM5IM5IM2IMI5MIMIMI4M4IMI8MIMI5M4IMI8MIMI5M4IMI5M4IM
PJ$L2KO5KO5KO5KO5KO5KO5KO5KO5KO5K2OKOK2OK5OK5OKOKOKOK5OKOKOKOK5O3KOJ$
2IM5IM5IM5IM5IM5IM5IM5IM5IM5IM2IMI5MIMIMI7MI2M4IMI4MIMIMI5MIMPJ$LO5KO
5KO5KO5K3OKOK4OK2O2KOKOKOKOKO4K5OKO4K5OKOK5O3K3OK5OKOKOK4OKO4KJ$4IM5I
M5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM2IMI5MIMIMIPJ$PO2KOKOK5OK5OK
5OK5OKOKOKO4K2O4K2OK5OK5OK5OK5OK5OK5OK5OK5OK6OJ$5IM5IM5IM5IM5IM5IM5IM
5IM5IM5IM5IM5IM5IM5IM5IM5IM5IMILJ$PKOK3OKOK3OKOK3OKOK3OKOK3OKOK3OKOK
3OKOK3OKOK3OKOK3OKOK3OKOK3OKOK3OKOK3OKOK4OKOKOK5OKOJ$2MIMI3MIMI2M5IM
5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IM5IMLJ$L3KO5KO5KO5KO5KO5KO5KO5K
O5KO5KO5KO5KO5KO5KO5KOKO2KO5KO4KJ$IM5IM5IM5IMIM3IM77ILJ$L103KJ$103ILJ
$L103KJ$104IJ!

Posted: **February 2nd, 2018, 12:59 am**

Photon in B1e rule without b2c or b3i:

Code: Select all

x = 3, y = 3, rule = B1e3-n5q/S1e2-ek3-n
2o$2bo$b2o!

Posted: **February 2nd, 2018, 7:13 am**

Majestas32 wrote:Photon in B1e rule without b2c or b3i:
Code: Select all
x = 3, y = 3, rule = B1e3-n5q/S1e2-ek3-n
2o$2bo$b2o!

Another:

Code: Select all

x = 4, y = 3, rule = B1e3-i5q/S1e2-ek3-n
3o$3bo$2b2o!

EDIT: And another:

Code: Select all

x = 3, y = 3, rule = B1e3a/S3i4a6c
2o$3o$2o!

Might be known.

Posted: **February 2nd, 2018, 8:03 am**

Some really lovely finds by LLS in otherwise boring rules that are so non-explosive that one would assume they do not support spaceships:

Code: Select all

x = 10, y = 10, rule = B2ik3-cjny6-i/S2-n3aeikn4ckqtz5-acy
3bo4b2o$2bobo2bobo$5bo2b2o$2bo2bo3bo$bo3bo$bobob5o$4bo3bo$ob2obo$o2bob
2o$2bobo!

I'd consider this a soupship since it looks like some kind of random soup in every phase.
EDIT: another ship in a particularly stable rule

Code: Select all

x = 7, y = 6, rule = B3aeiqy4-knqtw6ek/S2-en3-ejkr4yz5-knq
3b2o$6bo$b3ob2o$o5bo$4b2o$3b2o!

Posted: **February 2nd, 2018, 9:10 am**

LLS is really fun.
3c/5o

Code: Select all

x = 5, y = 7, rule = B1e2cin3aciqr4ackqy5einr6n78/S01e2-en4acekrz5-ejkr6acn7e
3b2o$4bo2$4bo2$o$2o!

(2,3)c/5

Code: Select all

x = 4, y = 8, rule = B2ac3a4r5ijq6ekn7/S02ai3acekn4aejkqrw5ajn6ein7c
bo$o3$3bo2$3bo$b3o!

Is there a way to force B1e?

EDIT(s):
4c/5o

Code: Select all

x = 4, y = 4, rule = B2-kn3kry4actwy5aenqr6in7c/S01e2ce3-aci4-aeinq5ijy6i78
4o$bo$3bo$3bo!

2c/5d

Code: Select all

x = 7, y = 6, rule = B2-ei3ac4ikqry5iqy6cik7c/S02aen3ckny4-aejqz5cejkr6eik7e
3bo$bobo2bo$o$4bo2$5bo!

3c/5o in a rule without S012

Code: Select all

x = 4, y = 6, rule = B2-en3cer4acjnrwy5-ej6-ak7e8/S3cij4cjtwyz5-acn6-k7c8
2bo2$bobo2$2obo$2bo!

Random small c/5o

Code: Select all

x = 3, y = 4, rule = B34-nty5-ejnq67/S3-cey4-iz5-iny6-ac7c8
2o$b2o$2bo$obo!

Weird wide c/2 in a B2a rule

Code: Select all

x = 4, y = 11, rule = B2ain4-jknwz5e6cei7/S3-ky4-aeqt5cin6-an8
2bo$2b2o$obo$b2o$2b2o$b2o$4o$2bo$2bo$2b2o$2bo!

Another wide c/2 in a rule w/o b2a

Code: Select all

x = 5, y = 13, rule = B2cek4ejyz5cenqy6-i7/S3-er4-aeint5-ack6-ck7c8
2bo$3bo$b2obo$b2o$bobo$b2o2$2bo$b2o$bo$2obo$2bo$bo!

Unrelated to LLS but I found this weird thing that makes a nonspinski at the bottom part

Code: Select all

x = 16, y = 40, rule = B2ain4-jknwz5e6cei7/S3-ky4-aeqt5cin6-an8
6bobo$4bob2obobobobo$2bo2b5obobobo$o35$8bo$8bo!

Posted: **February 2nd, 2018, 1:24 pm**

To force B1e, do -r pB1e-c2-a345678/S012345678

Or pB1e-c2c-a3i45678/S012345678 for relativistic (non-lightspeed) ships

Posted: **February 2nd, 2018, 3:56 pm**

If I want to force B3, do I have to type out B3aceijknqry?

Posted: **February 2nd, 2018, 4:04 pm**

BlinkerSpawn wrote:If I want to force B3, do I have to type out B3aceijknqry?

Apparently, yes.

Posted: **February 2nd, 2018, 4:05 pm**

Posted: **February 2nd, 2018, 9:33 pm**

Searching for (2,1)c/2 up to 11x11 seemed to turn up nothing? Does one exist?

EDIT, (3,2)c/4!:

Code: Select all

x = 2, y = 3, rule = B02aei3-enq4nrz5ijnqr6aek7c/S1c2-an3-ajqy4iknqrty5ijk6ak
bo$2o$2o!

Posted: **February 3rd, 2018, 1:37 am**

AforAmpere wrote:Searching for (2,1)c/2 up to 11x11 seemed to turn up nothing? Does one exist?

I suspect not. I tried up to 32x32, and still nothing.

I'm starting to suspect that any rule that supports expansion at that speed and period is likely explosive, but I haven't managed to prove that yet.

AforAmpere wrote:(3,2)c/4!:
Code: Select all
x = 2, y = 3, rule = B02aei3-enq4nrz5ijnqr6aek7c/S1c2-an3-ajqy4iknqrty5ijk6ak
bo$2o$2o!

Here's a smaller one:

Code: Select all

x = 2, y = 3, rule = B02-ce3-r4aeikr5-ciry6cek7e/S02-c4aijr5i6a
2o$o$bo!

And an even smaller one yet:

Code: Select all

x = 2, y = 3, rule = B01e2i3aqr4qt5ej6aei7/S1e2e4iny5enr6cn7e
o2$2o!

EDIT: OK, I think I have a proof that (2,1)/c2 is impossible. Specifically, I have this LLS search pattern:

Code: Select all

0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'
0'  0   0   0   0   0   0   0   0'  0'  0   0   0   0   0   0   0   0'
0'  0   1   b1  c1  d1  e1  f1  *'  *'  i1  j1  k1  l1  1   0   0   0'
y2' z2  a2  b2  c2  d2  e2  f2  *'  *'  i2  j2  k2  l2  m2  n2  o2  p2'
y3' z3  a3  b3  c3  d3  e3  f3  *'  *'  i3  j3  k3  l3  m3  n3  o3  p3'
y4' z4  a4  b4  c4  d4  e4  f4  *'  *'  i4  j4  k4  l4  m4  n4  o4  p4'
y5' z4  a5  b5  c5  d5  e5  f5  *'  *'  i5  j5  k5  l5  m5  n5  o5  p5'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
y8' z8  a8  b8  c8  d8  e8  f8  *'  *'  i8  j8  k8  l8  m8  n8  o8  p8'
y9' z9  a9  b9  c9  d9  e9  f9  *'  *'  i9  j9  k9  l9  m9  n9  o9  p9'
0'  0   1   b0  c0  d0  e0  f0  *'  *'  i0  j0  k0  l0  1   0   0   0'
0'  0   0   0   0   0   0   0   0'  0'  0   0   0   0   0   0   0   0'
0'  0   0   0   0   0   0   0   0'  0'  0   0   0   0   0   0   0   0'
0'  0   0   0   0   0   0   0   0'  0'  0   0   0   0   0   0   0   0'
0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'

1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'
1'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   1   1'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
1'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   1   1'
1'  1   1   1   1   1   1   1   1'  1'  1   1   1   1   1   1   1   1'
1'  1   1   1   1   1   1   1   1'  1'  1   1   1   1   1   1   1   1'
1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'

0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'
0'  0   0   0   0   0   0   0   0'  0'  0   0   0   0   0   0   0   0'
0'  0   0   0   0   0   0   0   0'  0'  0   0   0   0   0   0   0   0'
0'  0   0   0   0   0   0   0   0'  0'  0   0   0   0   0   0   0   0'
0'  0   0   1   b1  c1  d1  e1  *'  *'  h1  i1  j1  k1  l1  1   0   0'
x2' y2  z2  a2  b2  c2  d2  e2  *'  *'  h2  i2  j2  k2  l2  m2  n2  o2'
x3' y3  z3  a3  b3  c3  d3  e3  *'  *'  h3  i3  j3  k3  l3  m3  n3  o3'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
x6' y6  z6  a6  b6  c6  d6  e6  *'  *'  h6  i6  j6  k6  l6  m6  n6  o6'
x7' y7  z7  a7  b7  c7  d7  e7  *'  *'  h7  i7  j7  k7  l7  m7  n7  o7'
x8' y8  z8  a8  b8  c8  d8  e8  *'  *'  h8  i8  j8  k8  l8  m8  n8  o8'
x9' y9  z9  a9  b9  c9  d9  e9  *'  *'  h9  i9  j9  k9  l9  m9  n9  o9'
0'  0   0   1   b0  c0  d0  e0  *'  *'  h0  i0  j0  k0  l0  1   0   0'
0'  0   0   0   0   0   0   0   0'  0'  0   0   0   0   0   0   0   0'
0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'

The search pattern above actually consists of four independent quadrants, separated in each generation by two rows and two columns of "don't care" cells that can take any value and don't have to obey the CA rule. So we're effectively looking for a single rule that can support the evolution of each of these independent quadrants under the given constraints.

The top left quadrant of the first generation contains a single live cell, with all dead cells on the rows above it and on the same row to the left of it. It should be fairly evident that any pattern with a finite, non-zero number of live cells always contains a matching subpattern. (Just let the marked live cell be the leftmost live cell on the topmost non-empty row.)

The other three quadrants are the same, but mirrored horizontally and/or vertically; the last generation is the same as the first, but with the cells in each quadrant shifted two spaces right and one down. The generation in between just consists of unknown cell states, except on the edges where we know some of the cells must be live (since all their ancestors are dead, and since we're looking for a B0 rule).

Running this input through LLS with the rule string pB0c12345678/S01234567 gives the following output:

Code: Select all

~/git/logic-life-search$ nice ./lls -r pB0c12345678/S01234567 hyperknight.txt

Getting search pattern...
Done

Preprocessing...
Done

Number of undetermined cells: 466
Number of variables: 505
Number of clauses: 175286

Active width: 18
Active height: 13
Active duration: 3

Solving...
Done

Time taken: 7.03316807747 seconds

Unsatisfiable

In effect, this proves that there is no isotropic CA rule where the ends of the top/bottom row of any pattern could both advance, retreat and move sideways at (2,1)c/2. Which proves that there cannot be any spaceship with that period and speed.

Ps. I suspect the search pattern above is actually bigger than necessary, and that some of the rows and/or columns could probably be removed, and some named cells replaced by asterisks, while still leaving the pattern unsatisfiable. If sufficiently thus reduced, one might even be able to extract a short human-readable proof of why no isotropic rule can support (2,1)c/2 spaceships from it.

EDIT 2: Here's a simplified version of the search pattern above that's still unsatisfiable:

Code: Select all

0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'
0'  0   0   0   0   0   0   0'  0'  0'  0   0   0   0   0   0   0   0'
0'  0   1   b1  c1  d1  e1  *'  *'  *'  i1  j1  k1  l1  1   0   0   0'
*'  z2  a2  b2  c2  d2  e2  *'  *'  *'  i2  j2  k2  l2  m2  n2  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  z9  a9  b9  c9  d9  e9  *'  *'  *'  i9  j9  k9  l9  m9  n9  *'  *'
0'  0   1   b0  c0  d0  e0  *'  *'  *'  i0  j0  k0  l0  1   0   0   0'
0'  0   0   0   0   0   0   0'  0'  0'  0   0   0   0   0   0   0   0'
0'  0   0   0   0   0   0   0'  0'  0'  0   0   0   0   0   0   0   0'
0'  0   0   0   0   0   0   0'  0'  0'  0   0   0   0   0   0   0   0'
0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'

1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'
1'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   1'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   *'
1'  *   *   *   *   *   *   *   *'  *'  *   *   *   *   *   *   *   1'
1'  1   1   1   1   1   1   1   1'  1'  1   1   1   1   1   1   1   1'
1'  1   1   1   1   1   1   1   1'  1'  1   1   1   1   1   1   1   1'
1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'  1'

0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'
0'  0   0   0   0   0   0   0   0'  0'  0'  0   0   0   0   0   0   0'
0'  0   0   0   0   0   0   0   0'  0'  0'  0   0   0   0   0   0   0'
0'  0   0   0   0   0   0   0   0'  0'  0'  0   0   0   0   0   0   0'
0'  0   0   1   b1  c1  d1  e1  *'  *'  *'  i1  j1  k1  l1  1   0   0'
*'  *'  z2  a2  b2  c2  d2  e2  *'  *'  *'  i2  j2  k2  l2  m2  n2  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'  *'
*'  *'  z9  a9  b9  c9  d9  e9  *'  *'  *'  i9  j9  k9  l9  m9  n9  *'
0'  0   0   1   b0  c0  d0  e0  *'  *'  *'  i0  j0  k0  l0  1   0   0'
0'  0   0   0   0   0   0   0   0'  0'  0'  0   0   0   0   0   0   0'
0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'  0'

Posted: **February 3rd, 2018, 3:51 am**

All in B1e:
c/2o

Code: Select all

x = 4, y = 7, rule = B1e2cik3-eijn4arwyz6i7e8/S2-kn3jknr4jnrt5ejn6c7e8
2o$o$o2bo$bo$3bo$o$2o!

c/3o

Code: Select all

x = 6, y = 4, rule = B1e2cn3-ijr4-cekry5-aijy6aen78/S01e2akn3-einr4ajnq5akr6a7
3b2o$b3obo$o4bo$obo!

c/4o

Code: Select all

x = 6, y = 5, rule = B1e2cn3acenr4acnyz5-ajkq6aik8/S12ac3kqry4aenq5cejqy6ein7c
bobo$5bo$o2bobo$2o$3b2o!

EDIT(s)++:
c/5o is where it starts to get strange?

Code: Select all

x = 9, y = 8, rule = B1e2k3iknr4jry5ijkry6-kn7/S012-ek3aeiy4aetwz5eiqy6ekn
7b2o$5bob2o2$5bo3$obo$2o!

I guess (c/6o)

Code: Select all

x = 9, y = 7, rule = B1e2k3-aekq4acint5jnq6eik7e8/S01e2a3-aejn4-ceijn5acj6ek
7b2o$2o6bo$o$4bo2$5bo$4b2o!

Let's see if I have to adjust force_at_most for c/7o...

Nope! Still 10!
Surprisingly normal c/7o

Code: Select all

x = 6, y = 4, rule = B1e2-ac3-acry4crtwyz5ry6cek7c8/S12ack3-acjr4jkqrtyz5aeijn6ace7
2b4o$3b3o$o$2o!

Now changing force_at_most to 20...

Really weird c/2d

Code: Select all

x = 8, y = 5, rule = B1e2-ak3eknq4-einqw5-ckqy6ckn7/S1e2in3-acjn4-aijr5ceikr6ae7e8
8o$4b2obo$2ob3obo$6bo$4b2o!

another

Code: Select all

x = 14, y = 9, rule = B1e2ci3ajnqr4acrwyz5eikn6ikn7e8/S02ikn3-acny4-ejkny5ejkqy6-ae7
3b7o2b2o$3b2o3b2o2b2o$3b5o4bo$3b3o3bob3o$5o$2o2b2o4bo$3o2b2o2bo$3b3o$
6b2o!

c/3d

Code: Select all

x = 7, y = 6, rule = B1e2ek3iq4ceiktwy5ijkq6-in7c8/S1e2-cn3cjkn4iknqt5-nqry6i7e8
2b2o2$o2bob2o$obo3bo$3bobo$2b4o!

c/4d that LLS found that doesn't look like a B1e ship.

Code: Select all

x = 5, y = 5, rule = B1e2-ac3ciknq4cek5cky6cin7c/S1e2cik3acir4aijnrz5iy6-ci8
2ob2o$2ob2o$3bo$4o$2o!

Funny weird 4c/5o

Code: Select all

x = 4, y = 8, rule = B1e2cn3inr4aijqtz5-ceiy6-en7c8/S01c2-e3aceiy4ktwyz5-acy6kn
2obo$o2bo$2b2o$2b2o$2b2o$2b2o$o2bo$2obo!

(2,1)c/6

Code: Select all

x = 4, y = 4, rule = B1e2cen3cq4aiknqr5-aei6an7e8/S01e2-e3ceijq4aceknyz5ck6-e78
4o$2o$3bo$obo!

3c/5o

Code: Select all

x = 3, y = 6, rule = B1e2ik3-jr4-cqwz5-acnr6-c7e8/S01c2ac3acijq4-jrwy5-cei6cen7
b2o$2bo$obo$obo$2bo$b2o!

B2a:
(1,3)c/5

Code: Select all

x = 4, y = 5, rule = B2-e3ckqry4cijqtw5ikqr6-kn/S12kn3jkq4aiwz5ijkny6akn
bo$bo$3bo$b3o$4o!

c/5o

Code: Select all

x = 6, y = 5, rule = B2ain3acn4einrtw5acqry6cen78/S1e3aknry4aeqrt5cy6ck7c8
3o2bo2$3bobo$2bobo$2bo2bo!

Posted: **February 3rd, 2018, 11:31 am**

9c/10 B0:

Code: Select all

x = 5, y = 8, rule = B012ekn3-ackn4-nry5cjknq6ckn/S01e2-a3acjnq4-eijrz5-eqr6-cn7e
2bo$bobo$2b3o$2bobo$b4o$ob2o$bobo$2bo!

EDIT, 4 cells:

Code: Select all

x = 2, y = 7, rule = B01c2ce3-ky4aceikyz5-ainq6i7e/S01c2-i3aeiy4inq5aej6ac
o2$bo2$bo2$o!

Posted: **February 3rd, 2018, 10:08 pm**

It appears that the statement that rules with S0123 cannot have spaceships is false.
Other than AbhpzTa's counterexample, I found more.
2c/3o

Code: Select all

x = 5, y = 7, rule = B1e2c3-ajkq4ceiqwz5ejr6ci7/S01234ciqr5-acnr6i
2b2o2$o3bo$o3bo$2bobo2$3b2o!

3c/5o

Code: Select all

x = 4, y = 6, rule = B1e2cen3-aqr4acnty5anry6k8/S01234ntz5ceknr6cei7e8
2b2o2$o2bo$ob2o$bo$2b2o!

c/2o

Code: Select all

x = 4, y = 3, rule = B1e2-an3cenq4-ai5aq6eik8/S01234ez5aery6ce
ob2o$3bo$ob2o!

Code: Select all

x = 4, y = 6, rule = B1e2cn3-ain4-rtyz5-aiqr6cek8/S01234jkntyz5aceiq6akn8
2b2o$bo$ob2o$ob2o$bo$2b2o!

2c/5o

Code: Select all

x = 8, y = 5, rule = B2cei3ceknq4aeinqz5-ajkq6aen7e8/S01234-acert5nr6ci8
6bo$7bo$2bobobo$o6bo$2o4bo!

c/3o (No B1e)

Code: Select all

x = 4, y = 6, rule = B2-a3cnqry4-y5cjqy6-a78/S01234entwz5cknqr6-kn7e
2bo$3bo$2b2o$2o$b3o$2bo!

c/4o

Code: Select all

x = 6, y = 5, rule = B1e2cin3-aiky4ejn5-aiqr6cn7c/S01234nqrty5-ejy6-ac7c
bobo$o$obo2bo$b2o$4b2o!

c/5o

Code: Select all

x = 5, y = 6, rule = B1e2cik3-aijk4ijnwyz5-ci6-a/S01234cijkqwy5-ac6ein
2b2o2$4bo$o2b2o$obo$b2o!

===Diagonal===
c/3d

Code: Select all

x = 6, y = 6, rule = B1e2cen3cqy4-ekwz5-aey6ckn78/S01234ceikqyz5ceiky6ace
2b2obo$bo$obo2bo$o2$obo!

c/4d

Code: Select all

x = 5, y = 5, rule = B1e2ckn3-akqr4-acery5-cnq6cek7e8/S01234ceknz5ikqry6-ak7e8
3b2o2$2o2bo$obobo$b2o!

c/5d

Code: Select all

x = 4, y = 6, rule = B2-ai3cejky4-ajkwz5-y678/S01234ceikntz5eijry6-kn
2b2o$3bo$o$2b2o$ob2o$o!

==Oblique===
(2,1)c/5

Code: Select all

x = 4, y = 5, rule = B1e2cn3ce4acektwy5aknr6-in7e8/S01234-anqz5aeknq6-in
b2o$o2bo$2o$o2bo$2o!

(2,1)c/6

Code: Select all

x = 5, y = 4, rule = B2ekn3cikqy4eijnqrw5-cjqr6-ek7c8/S01234ciwz5iq6k7e
2bobo$3b2o$5o$2bo!

(3,1)c/6

Code: Select all

x = 3, y = 6, rule = B1e2ci3ceinr4ijkrtwy5aikq/S01234ikqrty5jqr6c7e
b2o$obo$obo$obo2$2o!

(2,3)c/6 with a nice phase at gen 4

Code: Select all

x = 5, y = 5, rule = B1e2cei3ejqy4cinqtw5-ceir6a7c/S01234erw5cej6cik
3b2o2$ob3o$b2o$obo!

Posted: **February 4th, 2018, 12:06 am**

Saka wrote:It appears that the statement that rules with S0123 cannot have spaceships is false.

It was only ever true for entirely outer-totalistic rules anyway (in particular, for rules without B2a or B3a, which, if outer-totalistic, excludes all non-B0 rules with spaceships).

Posted: **February 4th, 2018, 2:19 am**

Can someone make this a rule with a sub c/2 spacefiller? I'd love to see a dynamic where a pond makes a spacefiller that eventually gets destroyed by the simple c/2 photon in this rule

Code: Select all

x = 4, y = 24, rule = B2e3i4qrw5ac6ekn7e/S1c2-ai3-eik4acw5ak7e8
o$bo$2o8$o$bo$o8$b2o$o2bo$o2bo$b2o!

Posted: **February 4th, 2018, 3:44 am**

A for awesome wrote:
Saka wrote:It appears that the statement that rules with S0123 cannot have spaceships is false.
It was only ever true for entirely outer-totalistic rules anyway (in particular, for rules without B2a or B3a, which, if outer-totalistic, excludes all non-B0 rules with spaceships).

Correct me if I'm wrong, but isn't B3a alone also insufficient for a rule to have spaceships (at least one of B2a, B2e or B3i would also be required)?

Posted: **February 4th, 2018, 11:22 am**

Posted: **February 4th, 2018, 12:47 pm**

77topaz wrote:Correct me if I'm wrong, but isn't B3a alone also insufficient for a rule to have spaceships (at least one of B2a, B2e or B3i would also be required)?

But none of those would be allowed in totalistic rules, since B2a would disallow the whole B2, and B3a would disallow B3. B1e wouldn't work since B1c explodes in all directions, so the statement still stands strong.

Posted: **February 4th, 2018, 4:14 pm**

danny wrote:
77topaz wrote:Correct me if I'm wrong, but isn't B3a alone also insufficient for a rule to have spaceships (at least one of B2a, B2e or B3i would also be required)?
But none of those would be allowed in totalistic rules, since B2a would disallow the whole B2, and B3a would disallow B3. B1e wouldn't work since B1c explodes in all directions, so the statement still stands strong.

Oh, I see, an outer-totalistic rule with B3a would automatically also have B3i, so an outer-totalistic rule with B3a (or, more simply, a B3 rule) would be able to have spaceships. It's just that the original phrasing of your statement (outer-totalistic rules without B2a or B3a, which are designations used for non-totalistic rules) confused me because of its contradictory nature.

Posted: **February 4th, 2018, 8:59 pm**

a simple replicator, a relative of the b-heptomino:

Code: Select all

x = 5, y = 4, rule = B34cj8/S235e6c8
2bo$b3o$o2b2o$2o!

Posted: **February 4th, 2018, 11:25 pm**

googleplex wrote:a simple replicator, a relative of the b-heptomino:
Code: Select all
x = 5, y = 4, rule = B34cj8/S235e6c8
2bo$b3o$o2b2o$2o!

What is 4c/8 (or 8c/16) spaceship?

Posted: **February 4th, 2018, 11:38 pm**

Ruler Sequence replicator from Platoon. Discovered a while ago, but a post in the copypaste thread reminded me of it.

Code: Select all

x = 3, y = 2, rule = B2cek3i/S12-ak
bo$obo!

ConwayLife.com

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Re: Miscellaneous Discoveries in Other Cellular Automata

Re: Miscellaneous Discoveries in Other Cellular Automata

Re: Miscellaneous Discoveries in Other Cellular Automata

Re: Miscellaneous Discoveries in Other Cellular Automata

Re: Miscellaneous Discoveries in Other Cellular Automata

Re: Miscellaneous Discoveries in Other Cellular Automata

Re: Miscellaneous Discoveries in Other Cellular Automata

Re: Miscellaneous Discoveries in Other Cellular Automata

Re: Miscellaneous Discoveries in Other Cellular Automata

Re: Miscellaneous Discoveries in Other Cellular Automata

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