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## Partitioned Cellular Automata

For discussion of other cellular automata.

### Re: Partitioned Cellular Automata

Three new ships have been found.

This c/394 diagonal ship:

`x = 5, y = 4, rule = PCA_4A3.H2\$H.A\$.B.D!`

this 4c/1318 orthogonal ship:

`x = 4, y = 5, rule = PCA_43.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
bprentice

Posts: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

bprentice wrote:Three new ships have been found.

You missed my 7c/13589 orthogonal ship, which I think is new.
That that is, is. That that is not, is not. Is that it? It is.
A predecessor to my favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1289
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Partitioned Cellular Automata

C/27 orthogonal:
`x = 3, y = 2, rule = PCA_4F.C\$.E!`

2c/244 orthogonal:
`x = 3, y = 2, rule = PCA_4A.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)
AforAmpere

Posts: 1045
Joined: July 1st, 2016, 3:58 pm

### Re: Partitioned Cellular Automata

Current diagonal ships:

`x = 772, y = 12, rule = PCA_4633.B89.A3.H\$632.H48.A.H\$582.A48.A91.H.A\$221.B321.A35.A.D.H50.D44.H44.B.D42.A.I\$.L220.A109.B54.B60.I.B43.D47.B37.D50.D.H46.D.D\$B46.F96.A32.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:

`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.D28\$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!`

testitemqlstudop

Posts: 1059
Joined: July 21st, 2016, 11:45 am
Location: very very very very boats

### Re: Partitioned Cellular Automata

6c/1900 diagonal:
`x = 3, y = 3, rule = PCA_42.C\$.C\$L!`

C/81 orthogonal:
`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)
AforAmpere

Posts: 1045
Joined: July 1st, 2016, 3:58 pm

### 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
bprentice

Posts: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

`x = 4, y = 6, rule = PCA_42.F\$.D.D\$.A.B2\$3.B\$H!`
I like making color palettes for rules

Gustone

Posts: 418
Joined: March 6th, 2019, 2:26 am

### Re: Partitioned Cellular Automata

p1812 RRO:
`x = 4, y = 3, rule = PCA_4A.B\$3.B\$2.F!`
That that is, is. That that is not, is not. Is that it? It is.
A predecessor to my favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1289
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### 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: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Two PCA_2 oscillators with periods 501 and 2004:

`x = 77, y = 32, rule = PCA_215.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.

`x = 73, y = 30, rule = PCA_214.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: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Another Golly rule tree:

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

`@RULE PCA_5@TREEnum_states=16num_neighbors=4num_nodes=311 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 42 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 92 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 43 2 2 5 5 2 2 5 5 2 2 5 5 2 2 5 51 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 81 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 32 7 7 7 7 8 8 8 8 7 7 7 7 8 8 8 81 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 51 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 72 10 10 10 10 11 11 11 11 10 10 10 10 11 11 11 113 9 9 12 12 9 9 12 12 9 9 12 12 9 9 12 124 6 6 6 6 6 6 6 6 13 13 13 13 13 13 13 131 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 102 15 15 15 15 16 16 16 16 15 15 15 15 16 16 16 161 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 121 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 112 18 18 18 18 19 19 19 19 18 18 18 18 19 19 19 193 17 17 20 20 17 17 20 20 17 17 20 20 17 17 20 201 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 61 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 142 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 231 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 131 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 152 25 25 25 25 26 26 26 26 25 25 25 25 26 26 26 263 24 24 27 27 24 24 27 27 24 24 27 27 24 24 27 274 21 21 21 21 21 21 21 21 28 28 28 28 28 28 28 285 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:

`x = 48, y = 9, rule = PCA_5I5.IC2.IC4.IC3.IC4.IC4.IC4.IC5.IC\$.F4.LF.HLF4.LF2.HLF4.LF3.HLF4.LF4.HLF\$7.D9.D10.D11.D\$10.A\$6.ICB.IC9.A\$6.LF2.LF4.ICB2.IC10.A\$16.LF3.LF4.ICB3.IC11.A\$27.LF4.LF4.ICB4.IC\$39.LF5.LF!`

Brian Prentice
bprentice

Posts: 590
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:

`x = 5, y = 3, rule = PCA_33.H\$D3.D\$.B.E!`

`x = 5, y = 4, rule = PCA_33.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:

`c/11   S008.sqcc/12   DS001.sqc2c/28  S003.sqcc/15   S007.sqc2c/44  S002.sqc2c/48  S004.sqc3c/149 S005.sqcc/61   S009.sqc2c/124 S006.sqcc/158  DS003.sqc2c/368 S001.sqcc/242  DS002.sqc3c/642 DS004.sqcc/2188 DS005.sqc`

Two oscillator sets, the first set has periods 28 40 52 64 ...

`x = 38, y = 3, rule = PCA_3A7.A9.A11.A\$HC6.HCHC6.HCHCHC6.HCHCHCHC\$LB6.LBLB6.LBLBLB6.LBLBLBLB!`

and the second set has periods 1272 1316 1360 1404 ...

`x = 79, y = 19, rule = PCA_3HA.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.HA5.I.A\$18.DB9.L.DB18.H9.A\$38.HA10.H2.HA5.I.A\$38.DB11.L.DB20.H\$60.HA12.H2.HA\$60.DB13.L.DB!`

Brian Prentice
bprentice

Posts: 590
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:

`x = 31, y = 32, rule = PCA_315.A\$14.B2A\$13.A2B2A\$12.B2A2B2A\$11.A2B2A2B2A\$10.B2A2B2A2B2A\$9.A2B2A2B2A2B2A\$8.B2A2B2A2B2A2B2A\$7.A2B2A2B2A2B2A2B2A\$6.B2A2B2A2B2A2B2A2B2A\$5.A2B2A2B2A2B2A2B2A2B2A\$4.B2A2B2A2B2A2B2A2B2A2B2A\$3.A2B2A2B2A2B2A2B2A2B2A2B2A\$2.B2A2B2A2B2A2B2A2B2A2B2A2B2A\$.A2B2A2B2A2B2A2B2A2B2A2B2A2B2A\$B2A2B2A2B2A2B2A2B2A2B2A2B2A2B2A\$2B2A2B2A2B2A2B2A2B2A2B2A2B2A2BA\$.2B2A2B2A2B2A2B2A2B2A2B2A2B2AB\$2.2B2A2B2A2B2A2B2A2B2A2B2A2BA\$3.2B2A2B2A2B2A2B2A2B2A2B2AB\$4.2B2A2B2A2B2A2B2A2B2A2BA\$5.2B2A2B2A2B2A2B2A2B2AB\$6.2B2A2B2A2B2A2B2A2BA\$7.2B2A2B2A2B2A2B2AB\$8.2B2A2B2A2B2A2BA\$9.2B2A2B2A2B2AB\$10.2B2A2B2A2BA\$11.2B2A2B2AB\$12.2B2A2BA\$13.2B2AB\$14.2BA\$15.B!`

An example of a diagonal ship with a new speed of c/178 showing the ship together with a domino version:

`x = 26, y = 3, rule = PCA_3H21.2H\$.A21.2A\$2.K21.2K!`

Brian Prentice
bprentice

Posts: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Another PCA rule:

`  /* 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];  }`

`@RULE PCA_6@TREEnum_states=16num_neighbors=4num_nodes=311 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 92 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 43 2 2 5 5 2 2 5 5 2 2 5 5 2 2 5 51 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 41 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 32 7 7 7 7 8 8 8 8 7 7 7 7 8 8 8 81 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 51 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 72 10 10 10 10 11 11 11 11 10 10 10 10 11 11 11 113 9 9 12 12 9 9 12 12 9 9 12 12 9 9 12 124 6 6 6 6 6 6 6 6 13 13 13 13 13 13 13 131 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 81 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 102 15 15 15 15 16 16 16 16 15 15 15 15 16 16 16 161 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 121 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 112 18 18 18 18 19 19 19 19 18 18 18 18 19 19 19 193 17 17 20 20 17 17 20 20 17 17 20 20 17 17 20 201 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 61 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 142 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 231 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 131 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 152 25 25 25 25 26 26 26 26 25 25 25 25 26 26 26 263 24 24 27 27 24 24 27 27 24 24 27 27 24 24 27 274 21 21 21 21 21 21 21 21 28 28 28 28 28 28 28 285 14 29 14 29 14 29 14 29 14 29 14 29 14 29 14 29`

Two oscillator sets:

`x = 112, y = 22, rule = PCA_6102.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.DB27.HD\$36.DB29.HD\$67.DB31.HD\$100.DB!`

Periods 188, 236, 284, 332.

`x = 90, y = 69, rule = PCA_6O34.6O34.11O17\$2O33.7O33.12O17\$3O32.8O32.13O17\$4O31.9O31.14O17\$5O30.10O30.15O!`

Periods:

`1     42     43    284    285   2806    407   5208    529   83210   6411 121612   7613 167214   8815 2200`

Brian Prentice
bprentice

Posts: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Consider these four PCA_6 oscillators:

`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:

`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: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Some more PCA_6 oscillator sets:

`x = 69, y = 10, rule = PCA_668.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!`

`x = 66, y = 6, rule = PCA_665.J\$44.J19.J\$23.J19.J19.J\$2.J19.J19.J19.J\$.A19.A19.A19.A\$J19.J19.J19.J!`

Each of these sets has periods 40, 56, 72, 88 ...

c/61 orthogonal ship shuttle set:

`x = 12, y = 33, rule = PCA_6AB5.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:

`x = 66, y = 9, rule = PCA_6AB17.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: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Try patterns like this:

`x = 23, y = 22, rule = PCA_4:T150,15012.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: 590
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:

`x = 5, y = 4, rule = PCA_43.I\$2.D.J2\$A!`

`x = 4, y = 5, rule = PCA_43.H3\$C.D\$3.E!`

and three orthogonal ships with speeds of 5c/4195, 5c/8409 and c/237:

`x = 4, y = 6, rule = PCA_4A.I2\$2.C3\$3.H!`

`x = 6, y = 6, rule = PCA_45.H\$2.A\$.A.L3\$H!`

`x = 4, y = 3, rule = PCA_43.L\$J\$.C!`

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

Brian Prentice
bprentice

Posts: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Another PCA_6 oscillator set:

`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.DHDHDHDHD\$3.D.D.D.D.D.D!`

These have periods of 120, 172, 224 and 276.

A larger one with a period of 900:

`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.DHDHDHDHDHDHDHDHDHDHDHDHDHDHDHDHD\$3.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D!`

Brian Prentice
bprentice

Posts: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

A new PCA rule:

`  /* 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];  }`

`@RULE PCA_7@TREEnum_states=16num_neighbors=4num_nodes=311 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 62 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 43 2 2 5 5 2 2 5 5 2 2 5 5 2 2 5 51 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 41 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 122 7 7 7 7 8 8 8 8 7 7 7 7 8 8 8 81 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 101 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 72 10 10 10 10 11 11 11 11 10 10 10 10 11 11 11 113 9 9 12 12 9 9 12 12 9 9 12 12 9 9 12 124 6 6 6 6 6 6 6 6 13 13 13 13 13 13 13 131 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 81 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 52 15 15 15 15 16 16 16 16 15 15 15 15 16 16 16 161 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 31 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 112 18 18 18 18 19 19 19 19 18 18 18 18 19 19 19 193 17 17 20 20 17 17 20 20 17 17 20 20 17 17 20 201 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 91 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 142 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 231 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 131 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 152 25 25 25 25 26 26 26 26 25 25 25 25 26 26 26 263 24 24 27 27 24 24 27 27 24 24 27 27 24 24 27 274 21 21 21 21 21 21 21 21 28 28 28 28 28 28 28 285 14 29 14 29 14 29 14 29 14 29 14 29 14 29 14 29`

A 2c/3908 diagonal ship:

`x = 6, y = 3, rule = PCA_7H\$.A.D.B\$2.H.B!`

A nice period 67292 rotating oscillator:

`x = 5, y = 4, rule = PCA_7A3.D\$.H\$4.J\$3.H!`

and a reflector demonstration:

`x = 24, y = 29, rule = PCA_7:T150,15023.H3\$10.A2\$B2\$14.A5\$19.B5\$6.A4\$B5.D\$.L.B6\$19.D!`

Brian Prentice
bprentice

Posts: 590
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 58 different speeds. They are tabulated below:

`Diagonal Ships2c/3908  DS001.rlec/1270   DS002.rle3c/682   DS002.rlec/190    DS004.rle2c/194   DS005.rle2c/2208  DS006.rle2c/172   DS007.rlec/102    DS008.rle7c/3394  DS009.rle4c/2096  DS010.rle2c/300   DS011.rlec/316    DS012.rlec/278    DS013.rle2c/2040  DS014.rle2c/272   DS015.rle4c/3760  DS016.rlec/774    DS017.rlec/1818   DS018.rlec/400    DS019.rlec/94     DS020.rle2c/576   DS021.rlec/104    DS022.rlec/326    DS023.rlec/50     DS024.rlec/1662   DS025.rle2c/128   DS026.rlec/5458   DS027.rle3c/6190  DS028.rlec/546    DS029.rlec/2076   DS030.rlec/58     DS031.rle2c/1508  DS032.rlec/3110   DS033.rle2c/1252  DS034.rlec/240    DS035.rleOrthogonal Ships2c/180   S001.rle2c/516   S002.rlec/83     S003.rle2c/1656  S004.rlec/113    S005.rlec/27     S006.rlec/81     S007.rle4c/258   S008.rle4c/690   S009.rle6c/3548  S010.rle3c/1413  S011.rlec/415    S012.rle6c/2492  S013.rlec/2465   S014.rle4c/5618  S015.rle2c/848   S016.rle2c/608   S017.rle10c/8120 S018.rle6c/3094  S019.rle4c/76    S020.rlec/2989   S021.rle10c/6252 S022.rle5c/3015  S023.rleRotating Oscillators67292    O001.rle9644     O002.rle8160     O003.rle5972     O004.rle8320     O005.rle20420    O006.rle38464    O007.rle16908    O008.rle91596    O009.rle`

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

Brian Prentice
Last edited by bprentice on September 14th, 2019, 4:34 am, edited 3 times in total.
bprentice

Posts: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

A better reflector demonstration:

`x = 141, y = 146, rule = PCA_7:T150,150115.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.D12.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: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Rule PCA_8

`  /* 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];  }`

`@RULE PCA_8@TREEnum_states=16num_neighbors=4num_nodes=311 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 62 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 43 2 2 5 5 2 2 5 5 2 2 5 5 2 2 5 51 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 41 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 122 7 7 7 7 8 8 8 8 7 7 7 7 8 8 8 81 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 51 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 72 10 10 10 10 11 11 11 11 10 10 10 10 11 11 11 113 9 9 12 12 9 9 12 12 9 9 12 12 9 9 12 124 6 6 6 6 6 6 6 6 13 13 13 13 13 13 13 131 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 81 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 102 15 15 15 15 16 16 16 16 15 15 15 15 16 16 16 161 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 31 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 112 18 18 18 18 19 19 19 19 18 18 18 18 19 19 19 193 17 17 20 20 17 17 20 20 17 17 20 20 17 17 20 201 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 91 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 142 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 231 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 131 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 152 25 25 25 25 26 26 26 26 25 25 25 25 26 26 26 263 24 24 27 27 24 24 27 27 24 24 27 27 24 24 27 274 21 21 21 21 21 21 21 21 28 28 28 28 28 28 28 285 14 29 14 29 14 29 14 29 14 29 14 29 14 29 14 29`

An oscillator set:

`x = 219, y = 16, rule = PCA_8217.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.BA29.BA\$93.HD29.HD29.HD29.HD29.HD\$62.BA29.BA29.BA29.BA29.BA29.BA\$62.HD29.HD29.HD29.HD29.HD29.HD\$31.BA29.BA29.BA29.BA29.BA29.BA29.BA\$31.HD29.HD29.HD29.HD29.HD29.HD29.HD\$BA29.BA29.BA29.BA29.BA29.BA29.BA29.BA\$HD29.HD29.HD29.HD29.HD29.HD29.HD29.HD!`

with periods:

`       16      104     1136    12376     4464   552828  1480252 210067136`

Brian Prentice
bprentice

Posts: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

A nice period 408 oscillator:

`x = 119, y = 119, rule = PCA_784.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.I34.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: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

A PCA_8 reflector demonstration:

`x = 141, y = 148, rule = PCA_8:T150,150115.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
bprentice

Posts: 590
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

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