## Partitioned Cellular Automata

For discussion of other cellular automata.
bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Three new ships have been found.

This c/394 diagonal ship:

Code: Select all

``````x = 5, y = 4, rule = PCA_4
A3.H2\$H.A\$.B.D!
``````
this 4c/1318 orthogonal ship:

Code: Select all

``````x = 4, y = 5, rule = PCA_4
3.D\$D\$.F.D2\$.B!
``````
and the c/50 record breaking diagonal ship posted by Gustone above.

Small ships with 32 different speeds have now been found in rule PCA_4.

The list of ships in this thread's introduction and the associated archive have been updated.

Brian Prentice

Hdjensofjfnen
Posts: 1476
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Partitioned Cellular Automata

bprentice wrote:Three new ships have been found.
You missed my 7c/13589 orthogonal ship, which I think is new.
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

``````x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o\$6bo\$o3b3o\$2o\$bo!
``````

AforAmpere
Posts: 1079
Joined: July 1st, 2016, 3:58 pm

### Re: Partitioned Cellular Automata

C/27 orthogonal:

Code: Select all

``````x = 3, y = 2, rule = PCA_4
F.C\$.E!
``````
2c/244 orthogonal:

Code: Select all

``````x = 3, y = 2, rule = PCA_4
A.O\$.D!
``````
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

testitemqlstudop
Posts: 1323
Joined: July 21st, 2016, 11:45 am
Location: in catagolue
Contact:

### Re: Partitioned Cellular Automata

Current diagonal ships:

Code: Select all

``````x = 772, y = 12, rule = PCA_4
633.B89.A3.H\$632.H48.A.H\$582.A48.A91.H.A\$221.B321.A35.A.D.H50.D44.H
44.B.D42.A.I\$.L220.A109.B54.B60.I.B43.D47.B37.D50.D.H46.D.D\$B46.F96.A
32.A153.B.D52.C.B58.D47.I47.B35.H101.H87.A.I\$.H42.D33.A.B22.D72.J41.A
.H.D70.H.D36.B54.D.D56.A3.D93.H\$H44.D.D58.B37.I.D30.B116.F.D34.A.D52.
H62.B43.A.D47.F\$78.C.C24.D39.D30.L43.D44.F.B27.A\$104.D.D388.B\$263.H\$
266.A!
``````
Current orthogonal ships:

Code: Select all

``````x = 8, y = 378, rule = PCA_4
.H2\$3.A\$A3.L2\$4.H21\$2.L\$.E22\$.B2\$.H\$2.D.J\$5.D16\$4.B\$3.B\$2.A\$3.F\$2.D
28\$5.A\$4.I\$3.H2\$3.H14\$3.B.B\$2.A.H.I19\$3.D.B2\$5.D\$4.D.D25\$2.B.B\$5.D\$4.
J2\$2.D22\$4.H2\$4.J\$5.D2\$3.H.D30\$3.A\$4.A.I\$5.H20\$3.D.D\$4.F2\$2.H22\$5.F.D
\$4.H2\$2.D\$5.H16\$5.A\$2.F.J29\$6.D\$3.D\$4.F.D2\$4.B26\$2.F.C\$3.E20\$A.O\$.D!
``````

AforAmpere
Posts: 1079
Joined: July 1st, 2016, 3:58 pm

### Re: Partitioned Cellular Automata

6c/1900 diagonal:

Code: Select all

``````x = 3, y = 3, rule = PCA_4
2.C\$.C\$L!
``````
C/81 orthogonal:

Code: Select all

``````x = 2, y = 3, rule = PCA_4
.J\$L\$.I!
``````
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

AforAmpere

I will add your new ships to the list and archive tomorrow.

Hdjensofjfnen

Your ship is included, it has a period of 7c/13549.

Brian Prentice

Gustone
Posts: 598
Joined: March 6th, 2019, 2:26 am

### Re: Partitioned Cellular Automata

Code: Select all

``````x = 4, y = 6, rule = PCA_4
2.F\$.D.D\$.A.B2\$3.B\$H!
``````
My favourite oscillator of all time

Code: Select all

``````x = 15, y = 13, rule = B3/S23
7bo2\$3b2o5b2o\$b2o4bo4b2o\$5b2ob2o\$bobo7bobo\$bo2bobobobo2bo\$5obobob5o\$o
4bo3bo4bo\$b3obobobob3o\$3bob2obo2bo\$8bobo\$8b2o!
``````

Hdjensofjfnen
Posts: 1476
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Partitioned Cellular Automata

p1812 RRO:

Code: Select all

``````x = 4, y = 3, rule = PCA_4
A.B\$3.B\$2.F!
``````
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

``````x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o\$6bo\$o3b3o\$2o\$bo!
``````

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

The Square Cell version of PCA is here:

http://bprentice.webenet.net/PCA/PCA.zip

A dialog can be used to display and change the rule table allowing exploration of other rule variants. Patterns are rotated correctly which makes pattern editing easier.

The paper here:

http://bprentice.webenet.net/PCA/16%20S ... tomata.pdf

shows how to construct logic gates in rule PCA_1. Those of you who are interested in such matters might enjoy constructing some computing machines.

Can guns be implemented in PCA?

Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Two PCA_2 oscillators with periods 501 and 2004:

Code: Select all

``````x = 77, y = 32, rule = PCA_2
15.AB43.AB\$15.HD43.HD2\$13.I\$14.I9\$28.C44.C\$27.C44.C\$AB28.AB13.AB28.
AB\$HD28.HD13.HD28.HD\$4.L\$3.L9\$17.F\$18.F2\$15.AB43.AB\$15.HD43.HD!
``````
Two more with periods 489 and 1956.

Code: Select all

``````x = 73, y = 30, rule = PCA_2
14.AB41.AB\$14.HD41.HD2\$12.I\$13.I8\$26.C42.C\$25.C42.C\$AB26.AB13.AB26.
AB\$HD26.HD13.HD26.HD\$4.L\$3.L8\$16.F\$17.F2\$14.AB41.AB\$14.HD41.HD!
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Another Golly rule tree:

Code: Select all

``````  /* Put your state count, neighbor count, and function here */
final static int numStates = 16;
final static int numNeighbors = 4;
private int rule[] = {0,4,8,3,1,10,6,11,2,9,5,13,12,14,7,15};

/* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */
/* order for five neighbors is n, w, e, s, c */
int f(int[] a)
{
int s = 0;
if ((a[3] & 4) > 0)
s = s | 1;
if ((a[1] & 8) > 0)
s = s | 2;
if ((a[0] & 1) > 0)
s = s | 4;
if ((a[2] & 2) > 0)
s = s | 8;
return rule[s];
}
``````

Code: Select all

``````@RULE PCA_5
@TREE
num_states=16
num_neighbors=4
num_nodes=31
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
2 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
2 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 4
3 2 2 5 5 2 2 5 5 2 2 5 5 2 2 5 5
1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
2 7 7 7 7 8 8 8 8 7 7 7 7 8 8 8 8
1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
1 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
2 10 10 10 10 11 11 11 11 10 10 10 10 11 11 11 11
3 9 9 12 12 9 9 12 12 9 9 12 12 9 9 12 12
4 6 6 6 6 6 6 6 6 13 13 13 13 13 13 13 13
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 15 15 15 15 16 16 16 16 15 15 15 15 16 16 16 16
1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
1 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
2 18 18 18 18 19 19 19 19 18 18 18 18 19 19 19 19
3 17 17 20 20 17 17 20 20 17 17 20 20 17 17 20 20
1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
1 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
2 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 23
1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
1 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
2 25 25 25 25 26 26 26 26 25 25 25 25 26 26 26 26
3 24 24 27 27 24 24 27 27 24 24 27 27 24 24 27 27
4 21 21 21 21 21 21 21 21 28 28 28 28 28 28 28 28
5 14 29 14 29 14 29 14 29 14 29 14 29 14 29 14 29
``````
This one is model 2 described in:

http://bprentice.webenet.net/PCA/16%20S ... tomata.pdf

which like rule PCA_1 (model 1) is proved to be computation-universal.

The rule is not symmetric but is omniperiodic. The first five oscillators:

Code: Select all

``````x = 48, y = 9, rule = PCA_5
I5.IC2.IC4.IC3.IC4.IC4.IC4.IC5.IC\$.F4.LF.BLF4.LF2.BLF4.LF3.BLF4.LF4.
BLF\$7.A9.A10.A11.A\$10.D\$6.ICH.IC9.D\$6.LF2.LF4.ICH2.IC10.D\$16.LF3.LF
4.ICH3.IC11.D\$27.LF4.LF4.ICH4.IC\$39.LF5.LF!
``````
Brian Prentice
Last edited by bprentice on October 2nd, 2019, 4:32 pm, edited 1 time in total.

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Four more PCA_3 patterns.

Two new diagonal ships with periods 3c/642 and c/2188:

Code: Select all

``````x = 5, y = 3, rule = PCA_3
3.H\$D3.D\$.B.E!
``````

Code: Select all

``````x = 5, y = 4, rule = PCA_3
3.A\$H\$.H.D\$2.A.D!
``````
The archive at:

http://bprentice.webenet.net/PCA/PCA_3%20Ships.zip

now contains ships with these speeds:

Code: Select all

``````c/11   S008.sqc
c/12   DS001.sqc
2c/28  S003.sqc
c/15   S007.sqc
2c/44  S002.sqc
2c/48  S004.sqc
3c/149 S005.sqc
c/61   S009.sqc
2c/124 S006.sqc
c/158  DS003.sqc
2c/368 S001.sqc
c/242  DS002.sqc
3c/642 DS004.sqc
c/2188 DS005.sqc
``````
Two oscillator sets, the first set has periods 28 40 52 64 ...

Code: Select all

``````x = 38, y = 3, rule = PCA_3
A7.A9.A11.A\$HC6.HCHC6.HCHCHC6.HCHCHCHC\$LB6.LBLB6.LBLBLB6.LBLBLBLB!
``````
and the second set has periods 1272 1316 1360 1404 ...

Code: Select all

``````x = 79, y = 19, rule = PCA_3
HA.C7.HA5.HA.C9.HA5.HA.C11.HA5.HA.C13.HA\$DB2.B6.DB5.DB2.B8.DB5.DB2.
B10.DB5.DB2.B12.DB\$3.B17.B19.B21.B\$10.D.F17.D.F19.D.F21.D.F\$11.D19.
D21.D23.D4\$.A\$I.A\$9.H9.A\$HA6.H2.HA5.I.A\$DB7.L.DB16.H9.A\$18.HA8.H2.H
A5.I.A\$18.DB9.L.DB18.H9.A\$38.HA10.H2.HA5.I.A\$38.DB11.L.DB20.H\$60.HA
12.H2.HA\$60.DB13.L.DB!
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Continuing the exploration of rule PCA_3, some symmetrical patterns generate ships constructed of dominoes:

Code: Select all

``````x = 31, y = 32, rule = PCA_3
15.A\$14.B2A\$13.A2B2A\$12.B2A2B2A\$11.A2B2A2B2A\$10.B2A2B2A2B2A\$9.A2B2A
2B2A2B2A\$8.B2A2B2A2B2A2B2A\$7.A2B2A2B2A2B2A2B2A\$6.B2A2B2A2B2A2B2A2B2A
\$5.A2B2A2B2A2B2A2B2A2B2A\$4.B2A2B2A2B2A2B2A2B2A2B2A\$3.A2B2A2B2A2B2A2B
2A2B2A2B2A\$2.B2A2B2A2B2A2B2A2B2A2B2A2B2A\$.A2B2A2B2A2B2A2B2A2B2A2B2A
2B2A\$B2A2B2A2B2A2B2A2B2A2B2A2B2A2B2A\$2B2A2B2A2B2A2B2A2B2A2B2A2B2A2B
A\$.2B2A2B2A2B2A2B2A2B2A2B2A2B2AB\$2.2B2A2B2A2B2A2B2A2B2A2B2A2BA\$3.2B
2A2B2A2B2A2B2A2B2A2B2AB\$4.2B2A2B2A2B2A2B2A2B2A2BA\$5.2B2A2B2A2B2A2B2A
2B2AB\$6.2B2A2B2A2B2A2B2A2BA\$7.2B2A2B2A2B2A2B2AB\$8.2B2A2B2A2B2A2BA\$9.
2B2A2B2A2B2AB\$10.2B2A2B2A2BA\$11.2B2A2B2AB\$12.2B2A2BA\$13.2B2AB\$14.2B
A\$15.B!
``````
An example of a diagonal ship with a new speed of c/178 showing the ship together with a domino version:

Code: Select all

``````x = 26, y = 3, rule = PCA_3
H21.2H\$.A21.2A\$2.K21.2K!
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Another PCA rule:

Code: Select all

``````  /* Put your state count, neighbor count, and function here */
final static int numStates = 16;
final static int numNeighbors = 4;
private int rule[] = {0,2,4,3,8,10,6,14,1,9,5,7,12,11,13,15};

/* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */
/* order for five neighbors is n, w, e, s, c */
int f(int[] a)
{
int s = 0;
if ((a[3] & 4) > 0)
s = s | 1;
if ((a[1] & 8) > 0)
s = s | 2;
if ((a[0] & 1) > 0)
s = s | 4;
if ((a[2] & 2) > 0)
s = s | 8;
return rule[s];
}
``````

Code: Select all

``````@RULE PCA_6
@TREE
num_states=16
num_neighbors=4
num_nodes=31
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 0 0 0 0 1 1 1 1 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 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
2 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 4
3 2 2 5 5 2 2 5 5 2 2 5 5 2 2 5 5
1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
2 7 7 7 7 8 8 8 8 7 7 7 7 8 8 8 8
1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
2 10 10 10 10 11 11 11 11 10 10 10 10 11 11 11 11
3 9 9 12 12 9 9 12 12 9 9 12 12 9 9 12 12
4 6 6 6 6 6 6 6 6 13 13 13 13 13 13 13 13
1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 15 15 15 15 16 16 16 16 15 15 15 15 16 16 16 16
1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
1 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
2 18 18 18 18 19 19 19 19 18 18 18 18 19 19 19 19
3 17 17 20 20 17 17 20 20 17 17 20 20 17 17 20 20
1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
1 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
2 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 23
1 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
1 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
2 25 25 25 25 26 26 26 26 25 25 25 25 26 26 26 26
3 24 24 27 27 24 24 27 27 24 24 27 27 24 24 27 27
4 21 21 21 21 21 21 21 21 28 28 28 28 28 28 28 28
5 14 29 14 29 14 29 14 29 14 29 14 29 14 29 14 29
``````
Two oscillator sets:

Code: Select all

``````x = 112, y = 22, rule = PCA_6
102.B\$69.B\$38.B64.D\$9.B60.D30.HD\$39.D28.HD\$10.D26.HD\$8.HD4\$.A11.AB14.
A13.AB14.A15.AB14.A17.AB\$2.AB10.AH14.AB12.AH14.AB14.AH14.AB16.AH\$H27.
H29.H31.H\$6.A.B25.A.B27.A.B29.A.B\$5.A.B25.A.B27.A.B29.A.B3\$7.HD\$7.D
B27.HD\$36.DB29.HD\$67.DB31.HD\$100.DB!
``````
Periods 188, 236, 284, 332.

Code: Select all

``````x = 90, y = 69, rule = PCA_6
O34.6O34.11O17\$2O33.7O33.12O17\$3O32.8O32.13O17\$4O31.9O31.14O17\$5O30.
10O30.15O!
``````
Periods:

Code: Select all

``````1     4
2     4
3    28
4    28
5   280
6    40
7   520
8    52
9   832
10   64
11 1216
12   76
13 1672
14   88
15 2200
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Consider these four PCA_6 oscillators:

Code: Select all

``````x = 11, y = 74, rule = PCA_6
.B.B\$D.D.D23\$.B.B.B\$D.D.D.D23\$.B.B.B.B\$D.D.D.D.D23\$.B.B.B.B.B\$D.D.D
.D.D.D!
``````
They have periods of 408, 16300, 534012 and 5147120.

Now consider this pattern:

Code: Select all

``````x = 61, y = 2, rule = PCA_6
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B\$D.D.D.
D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D!
``````
It is presumably also an oscillator, but it is far beyond Golly's ability to calculate its period. It is however, fascinating to observe its evolution.

Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Some more PCA_6 oscillator sets:

Code: Select all

``````x = 69, y = 10, rule = PCA_6
68.J2\$46.J19.J2\$24.J19.J19.J2\$2.J19.J19.J19.J2\$B.B17.B.B17.B.B17.B.
B\$.D19.D19.D19.D!
``````

Code: Select all

``````x = 66, y = 6, rule = PCA_6
65.J\$44.J19.J\$23.J19.J19.J\$2.J19.J19.J19.J\$.A19.A19.A19.A\$J19.J19.J
19.J!
``````
Each of these sets has periods 40, 56, 72, 88 ...

c/61 orthogonal ship shuttle set:

Code: Select all

``````x = 12, y = 33, rule = PCA_6
AB5.AB\$HD.A.H.HD\$4.I8\$AB6.AB\$HD.A.H2.HD\$4.I8\$AB7.AB\$HD.A.H3.HD\$4.I8\$
AB8.AB\$HD.A.H4.HD\$4.I!
``````
Periods 218, 340, 462, 584 ...

c/12 diagonal ship shuttle set:

Code: Select all

``````x = 66, y = 9, rule = PCA_6
AB17.AB17.AB17.AB\$HD17.HD17.HD17.HD\$2.H\$.H.D18.H\$2.D.AB15.H.D18.H\$4.
HD16.D.AB15.H.D18.H\$24.HD16.D.AB15.H.D\$44.HD16.D.AB\$64.HD!
``````
Periods 232, 256, 280, 304 ...

Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Try patterns like this:

Code: Select all

``````x = 23, y = 22, rule = PCA_4:T150,150
12.A5.G\$2.I2.M\$8.E2.A\$16.N\$10.G6.MF\$11.M2.K\$D15.EF4.O\$10.E\$2.G5.D2.
K.F7.E\$5.I7.D\$I.M11.F7.A\$ME.J9.A\$.B\$.D5.M5.I4.F\$6.E\$7.J3.N\$21.J\$A\$17.
G3.I\$5.O7.I\$15.F\$.I17.B!
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Using the technique shown in the post above, five more PCA_4 ships have been found. This brings the total to 41 PCA_4 ships with different speeds.

Two diagonal ships with speeds of c/1214 and c/2126:

Code: Select all

``````x = 5, y = 4, rule = PCA_4
3.I\$2.D.J2\$A!
``````

Code: Select all

``````x = 4, y = 5, rule = PCA_4
3.H3\$C.D\$3.E!
``````
and three orthogonal ships with speeds of 5c/4195, 5c/8409 and c/237:

Code: Select all

``````x = 4, y = 6, rule = PCA_4
A.I2\$2.C3\$3.H!
``````

Code: Select all

``````x = 6, y = 6, rule = PCA_4
5.H\$2.A\$.A.L3\$H!
``````

Code: Select all

``````x = 4, y = 3, rule = PCA_4
3.L\$J\$.C!
``````
The list of ships in this thread's introduction and the associated archive have been updated.

Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Another PCA_6 oscillator set:

Code: Select all

``````x = 14, y = 53, rule = PCA_6
.A\$A.B\$.A3.D\$4.DHD\$3.D.D.D12\$.A\$A.B\$.A3.D.D\$4.DHDHD\$3.D.D.D.D12\$.A\$
A.B\$.A3.D.D.D\$4.DHDHDHD\$3.D.D.D.D.D12\$.A\$A.B\$.A3.D.D.D.D\$4.DHDHDHDH
D\$3.D.D.D.D.D.D!
``````
These have periods of 120, 172, 224 and 276.

A larger one with a period of 900:

Code: Select all

``````x = 38, y = 5, rule = PCA_6
.A\$A.B\$.A3.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D\$4.DHDHDHDHDHDHDHDHDHDHDH
DHDHDHDHDHD\$3.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D!
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

A new PCA rule:

Code: Select all

``````  /* Put your state count, neighbor count, and function here */
final static int numStates = 16;
final static int numNeighbors = 4;
private int rule[] = {0,2,4,12,8,5,9,14,1,6,10,7,3,11,13,15};

/* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */
/* order for five neighbors is n, w, e, s, c */
int f(int[] a)
{
int s = 0;
if ((a[3] & 4) > 0)
s = s | 1;
if ((a[1] & 8) > 0)
s = s | 2;
if ((a[0] & 1) > 0)
s = s | 4;
if ((a[2] & 2) > 0)
s = s | 8;
return rule[s];
}
``````

Code: Select all

``````@RULE PCA_7
@TREE
num_states=16
num_neighbors=4
num_nodes=31
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 0 0 0 0 1 1 1 1 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 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 4
3 2 2 5 5 2 2 5 5 2 2 5 5 2 2 5 5
1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
2 7 7 7 7 8 8 8 8 7 7 7 7 8 8 8 8
1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
2 10 10 10 10 11 11 11 11 10 10 10 10 11 11 11 11
3 9 9 12 12 9 9 12 12 9 9 12 12 9 9 12 12
4 6 6 6 6 6 6 6 6 13 13 13 13 13 13 13 13
1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
2 15 15 15 15 16 16 16 16 15 15 15 15 16 16 16 16
1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
1 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
2 18 18 18 18 19 19 19 19 18 18 18 18 19 19 19 19
3 17 17 20 20 17 17 20 20 17 17 20 20 17 17 20 20
1 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
1 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
2 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 23
1 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
1 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
2 25 25 25 25 26 26 26 26 25 25 25 25 26 26 26 26
3 24 24 27 27 24 24 27 27 24 24 27 27 24 24 27 27
4 21 21 21 21 21 21 21 21 28 28 28 28 28 28 28 28
5 14 29 14 29 14 29 14 29 14 29 14 29 14 29 14 29
``````
A 2c/3908 diagonal ship:

Code: Select all

``````x = 6, y = 3, rule = PCA_7
H\$.A.D.B\$2.H.B!
``````
A nice period 67292 rotating oscillator:

Code: Select all

``````x = 5, y = 4, rule = PCA_7
A3.D\$.H\$4.J\$3.H!
``````
and a reflector demonstration:

Code: Select all

``````x = 24, y = 29, rule = PCA_7:T150,150
23.H3\$10.A2\$B2\$14.A5\$19.B5\$6.A4\$B5.D\$.L.B6\$19.D!
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

An archive for rule PCA_7 patterns is here:

http://bprentice.webenet.net/PCA/PCA_7%20Ships.zip

This archive currently contains ships with 62 different speeds. They are tabulated below:

Code: Select all

``````Diagonal Ships

2c/3908  DS001.rle
c/1270   DS002.rle
3c/682   DS002.rle
c/190    DS004.rle
2c/194   DS005.rle
2c/2208  DS006.rle
2c/172   DS007.rle
c/102    DS008.rle
7c/3394  DS009.rle
4c/2096  DS010.rle
2c/300   DS011.rle
c/316    DS012.rle
c/278    DS013.rle
2c/2040  DS014.rle
2c/272   DS015.rle
4c/3760  DS016.rle
c/774    DS017.rle
c/1818   DS018.rle
c/400    DS019.rle
c/94     DS020.rle
2c/576   DS021.rle
c/104    DS022.rle
c/326    DS023.rle
c/50     DS024.rle
c/1662   DS025.rle
2c/128   DS026.rle
c/5458   DS027.rle
3c/6190  DS028.rle
c/546    DS029.rle
c/2076   DS030.rle
c/58     DS031.rle
2c/1508  DS032.rle
c/3110   DS033.rle
2c/1252  DS034.rle
c/240    DS035.rle
2c/2012  DS036.rle
2c/92    DS037.rle
3c/6534  DS038.rle

Orthogonal Ships

2c/180   S001.rle
2c/516   S002.rle
c/83     S003.rle
2c/1656  S004.rle
c/113    S005.rle
c/27     S006.rle
c/81     S007.rle
4c/258   S008.rle
4c/690   S009.rle
6c/3548  S010.rle
3c/1413  S011.rle
c/415    S012.rle
6c/2492  S013.rle
c/2465   S014.rle
4c/5618  S015.rle
2c/848   S016.rle
2c/608   S017.rle
10c/8120 S018.rle
6c/3094  S019.rle
4c/76    S020.rle
c/2989   S021.rle
10c/6252 S022.rle
5c/3015  S023.rle
2c/1468  S024.rle

Rotating Oscillators

67292    O001.rle
9644     O002.rle
8160     O003.rle
5972     O004.rle
8320     O005.rle
20420    O006.rle
38464    O007.rle
16908    O008.rle
91596    O009.rle
``````

The archive and this post will be updated when more objects are found.

Brian Prentice
Last edited by bprentice on October 7th, 2019, 6:33 pm, edited 6 times in total.

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

A better reflector demonstration:

Code: Select all

``````x = 141, y = 146, rule = PCA_7:T150,150
115.A\$75.D2\$81.H3\$119.H8\$20.A57.B\$35.B\$30.A2\$22.A39.H50.A\$112.A2\$112.
C\$129.H6\$70.H2\$70.D\$61.A\$64.B\$75.D\$97.B2\$92.B2\$74.A\$47.B62.H26.B\$138.
H\$137.C3\$22.A\$75.B2\$120.B\$121.B3\$81.A2\$116.A\$123.A\$108.A\$78.D2\$82.D
12.A\$13.A126.A\$76.A28.H3\$29.B\$10.D2\$4.A2\$24.A45.B\$17.H47.D.H5\$60.D34.
A\$47.B\$56.H19.D\$57.D31.H5\$24.H63.D8.D\$100.H2\$53.D2\$35.B100.H3\$119.B3\$
31.H53.A3\$78.B2\$88.H2\$44.B4\$60.D3\$H2\$21.A\$54.B3\$99.H\$56.A7.B7.B7\$39.D
\$86.A\$12.H5\$94.H17\$124.H!
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Rule PCA_8

Code: Select all

``````  /* Put your state count, neighbor count, and function here */
final static int numStates = 16;
final static int numNeighbors = 4;
private int rule[] = {0,2,4,12,8,10,9,14,1,6,5,7,3,11,13,15};

/* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */
/* order for five neighbors is n, w, e, s, c */
int f(int[] a)
{
int s = 0;
if ((a[3] & 4) > 0)
s = s | 1;
if ((a[1] & 8) > 0)
s = s | 2;
if ((a[0] & 1) > 0)
s = s | 4;
if ((a[2] & 2) > 0)
s = s | 8;
return rule[s];
}
``````

Code: Select all

``````@RULE PCA_8
@TREE
num_states=16
num_neighbors=4
num_nodes=31
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 0 0 0 0 1 1 1 1 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 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 4
3 2 2 5 5 2 2 5 5 2 2 5 5 2 2 5 5
1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
2 7 7 7 7 8 8 8 8 7 7 7 7 8 8 8 8
1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
2 10 10 10 10 11 11 11 11 10 10 10 10 11 11 11 11
3 9 9 12 12 9 9 12 12 9 9 12 12 9 9 12 12
4 6 6 6 6 6 6 6 6 13 13 13 13 13 13 13 13
1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 15 15 15 15 16 16 16 16 15 15 15 15 16 16 16 16
1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
1 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
2 18 18 18 18 19 19 19 19 18 18 18 18 19 19 19 19
3 17 17 20 20 17 17 20 20 17 17 20 20 17 17 20 20
1 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
1 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
2 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 23
1 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
1 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
2 25 25 25 25 26 26 26 26 25 25 25 25 26 26 26 26
3 24 24 27 27 24 24 27 27 24 24 27 27 24 24 27 27
4 21 21 21 21 21 21 21 21 28 28 28 28 28 28 28 28
5 14 29 14 29 14 29 14 29 14 29 14 29 14 29 14 29
``````
An oscillator set:

Code: Select all

``````x = 219, y = 16, rule = PCA_8
217.BA\$217.HD\$186.BA29.BA\$186.HD29.HD\$155.BA29.BA29.BA\$155.HD29.HD29.
HD\$124.BA29.BA29.BA29.BA\$124.HD29.HD29.HD29.HD\$93.BA29.BA29.BA29.BA
29.BA\$93.HD29.HD29.HD29.HD29.HD\$62.BA29.BA29.BA29.BA29.BA29.BA\$62.H
D29.HD29.HD29.HD29.HD29.HD\$31.BA29.BA29.BA29.BA29.BA29.BA29.BA\$31.H
D29.HD29.HD29.HD29.HD29.HD29.HD\$BA29.BA29.BA29.BA29.BA29.BA29.BA29.
BA\$HD29.HD29.HD29.HD29.HD29.HD29.HD29.HD!
``````
with periods:

Code: Select all

``````       16
104
1136
12376
4464
552828
1480252
210067136
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

A nice period 408 oscillator:

Code: Select all

``````x = 119, y = 119, rule = PCA_7
84.I\$83.I\$82.I\$81.I\$80.I\$79.I\$78.I\$77.I\$76.I\$75.I\$74.I\$73.I\$72.I\$71.
I\$70.I\$69.I\$68.I\$67.I\$66.I\$65.I\$64.I\$63.I\$62.I\$61.I\$60.I\$59.I\$58.I\$
57.I\$56.I\$55.I\$54.I\$53.I\$52.I\$51.I\$50.I\$49.I\$48.I\$L46.I\$.L44.I22.C\$
2.L42.I24.C\$3.L40.I26.C\$4.L38.I28.C\$5.L36.I30.C\$6.L34.I32.C\$7.L32.I
34.C\$8.L30.I36.C\$9.L28.I38.C\$10.L26.I40.C\$11.L24.I42.C\$12.L22.I44.C
\$13.L67.C\$14.L67.C\$15.L67.C\$16.L67.C\$17.L67.C\$18.L67.C\$19.L67.C\$20.
L67.C\$21.L67.C\$22.L67.C\$23.L67.C\$24.L67.C\$25.L67.C\$26.L67.C\$27.L67.
C\$28.L67.C\$29.L67.C\$30.L67.C\$31.L67.C\$32.L50.F16.C\$33.L48.F18.C\$34.
L46.F20.C\$35.L44.F22.C\$36.L42.F24.C\$37.L40.F26.C\$38.L38.F28.C\$39.L36.
F30.C\$40.L34.F32.C\$41.L32.F34.C\$42.L30.F36.C\$43.L28.F38.C\$44.L26.F40.
C\$45.L24.F42.C\$46.L22.F44.C\$47.L20.F46.C\$48.L18.F48.C\$49.L16.F50.C\$
65.F52.C\$64.F\$63.F\$62.F\$61.F\$60.F\$59.F\$58.F\$57.F\$56.F\$55.F\$54.F\$53.
F\$52.F\$51.F\$50.F\$49.F\$48.F\$47.F\$46.F\$45.F\$44.F\$43.F\$42.F\$41.F\$40.F\$
39.F\$38.F\$37.F\$36.F\$35.F\$34.F!
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

A PCA_8 reflector demonstration:

Code: Select all

``````x = 141, y = 148, rule = PCA_8:T150,150
115.A3\$81.B3\$119.H5\$17.D3\$80.A\$35.B\$30.A2\$22.A35.H4\$74.B54.H5\$53.A5\$
64.H13.A2\$97.B5\$43.D66.H3\$78.D17.H2\$22.A3\$71.B48.B\$70.A50.B5\$116.A\$
123.A\$75.B32.A3\$88.H6.A\$13.A126.A\$105.H2\$76.A\$13.B15.B39.H3\$4.A3.D2\$
18.B\$67.A4\$23.A\$58.H36.A\$59.D\$56.A4\$88.D2\$48.H48.D\$75.H24.H2\$53.D\$84.
H\$95.H40.H\$38.D2\$30.B88.B5\$45.B\$90.D\$39.H5\$78.H2\$74.B\$91.D2\$H\$20.A33.
A2\$54.B3\$99.H\$56.A2\$66.H3.B\$67.H.D\$68.D3\$35.D\$72.B13.A\$12.H5\$94.H17\$
124.H2\$79.D!
``````
Brian Prentice