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

Post by bprentice » September 3rd, 2019, 10:47 pm

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

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

Re: Partitioned Cellular Automata

Post by Hdjensofjfnen » September 3rd, 2019, 11:01 pm

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

Post by AforAmpere » September 3rd, 2019, 11:20 pm

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)

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testitemqlstudop
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Re: Partitioned Cellular Automata

Post by testitemqlstudop » September 3rd, 2019, 11:23 pm

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

Post by AforAmpere » September 3rd, 2019, 11:30 pm

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

Post by bprentice » September 3rd, 2019, 11:47 pm

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

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Gustone
Posts: 598
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Re: Partitioned Cellular Automata

Post by Gustone » September 4th, 2019, 2:28 am

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!

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

Re: Partitioned Cellular Automata

Post by Hdjensofjfnen » September 4th, 2019, 7:29 pm

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

Post by bprentice » September 5th, 2019, 1:46 pm

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

Post by bprentice » September 5th, 2019, 10:56 pm

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

Post by bprentice » September 6th, 2019, 7:11 pm

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

Post by bprentice » September 7th, 2019, 9:36 pm

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

Re: Partitioned Cellular Automata

Post by bprentice » September 8th, 2019, 11:31 pm

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

Post by bprentice » September 9th, 2019, 11:07 pm

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

Post by bprentice » September 10th, 2019, 9:07 am

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

Post by bprentice » September 10th, 2019, 10:14 pm

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

Post by bprentice » September 11th, 2019, 11:26 am

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

Post by bprentice » September 11th, 2019, 3:09 pm

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

Post by bprentice » September 11th, 2019, 4:14 pm

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

Post by bprentice » September 11th, 2019, 9:22 pm

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

Post by bprentice » September 12th, 2019, 2:39 pm

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

Post by bprentice » September 12th, 2019, 8:06 pm

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

Post by bprentice » September 13th, 2019, 9:06 pm

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

Post by bprentice » September 14th, 2019, 1:52 pm

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

Post by bprentice » September 14th, 2019, 9:15 pm

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

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