Page 2 of 5
Re: Partitioned Cellular Automata
Posted: September 3rd, 2019, 10:47 pm
by bprentice
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$.B!
and the c/50 record breaking diagonal ship posted by Gustone above.
Small ships with 32 different speeds have now been found in rule PCA_4.
The list of ships in this thread's introduction and the associated archive have been updated.
Brian Prentice
Re: Partitioned Cellular Automata
Posted: September 3rd, 2019, 11:01 pm
by Hdjensofjfnen
bprentice wrote:Three new ships have been found.
You missed my 7c/13589 orthogonal ship, which I think is new.
Re: Partitioned Cellular Automata
Posted: September 3rd, 2019, 11:20 pm
by AforAmpere
C/27 orthogonal:
Code: Select all
x = 3, y = 2, rule = PCA_4
F.C$.E!
2c/244 orthogonal:
Code: Select all
x = 3, y = 2, rule = PCA_4
A.O$.D!
Re: Partitioned Cellular Automata
Posted: September 3rd, 2019, 11:23 pm
by testitemqlstudop
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$.D!
Re: Partitioned Cellular Automata
Posted: September 3rd, 2019, 11:30 pm
by AforAmpere
6c/1900 diagonal:
Code: Select all
x = 3, y = 3, rule = PCA_4
2.C$.C$L!
C/81 orthogonal:
Code: Select all
x = 2, y = 3, rule = PCA_4
.J$L$.I!
Re: Partitioned Cellular Automata
Posted: September 3rd, 2019, 11:47 pm
by bprentice
AforAmpere
I will add your new ships to the list and archive tomorrow.
Hdjensofjfnen
Your ship is included, it has a period of 7c/13549.
Brian Prentice
Re: Partitioned Cellular Automata
Posted: September 4th, 2019, 2:28 am
by Gustone
Code: Select all
x = 4, y = 6, rule = PCA_4
2.F$.D.D$.A.B2$3.B$H!
Re: Partitioned Cellular Automata
Posted: September 4th, 2019, 7:29 pm
by Hdjensofjfnen
p1812 RRO:
Code: Select all
x = 4, y = 3, rule = PCA_4
A.B$3.B$2.F!
Re: Partitioned Cellular Automata
Posted: September 5th, 2019, 1:46 pm
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 5th, 2019, 10:56 pm
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 6th, 2019, 7:11 pm
by bprentice
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$39.LF5.LF!
Brian Prentice
Re: Partitioned Cellular Automata
Posted: September 7th, 2019, 9:36 pm
by bprentice
Four more PCA_3 patterns.
Two new diagonal ships with periods 3c/642 and c/2188:
Code: Select all
x = 5, y = 3, rule = PCA_3
3.H$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
Re: Partitioned Cellular Automata
Posted: September 8th, 2019, 11:31 pm
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 9th, 2019, 11:07 pm
by bprentice
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$5O30.
10O30.15O!
Periods:
Code: Select all
1 4
2 4
3 28
4 28
5 280
6 40
7 520
8 52
9 832
10 64
11 1216
12 76
13 1672
14 88
15 2200
Brian Prentice
Re: Partitioned Cellular Automata
Posted: September 10th, 2019, 9:07 am
by bprentice
Consider these four PCA_6 oscillators:
Code: Select all
x = 11, y = 74, rule = PCA_6
.B.B$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
Re: Partitioned Cellular Automata
Posted: September 10th, 2019, 10:14 pm
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 11th, 2019, 11:26 am
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 11th, 2019, 3:09 pm
by bprentice
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$.C!
The list of ships in this thread's introduction and the associated archive have been updated.
Brian Prentice
Re: Partitioned Cellular Automata
Posted: September 11th, 2019, 4:14 pm
by bprentice
Another PCA_6 oscillator set:
Code: Select all
x = 14, y = 53, rule = PCA_6
.A$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
Re: Partitioned Cellular Automata
Posted: September 11th, 2019, 9:22 pm
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 12th, 2019, 2:39 pm
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 12th, 2019, 8:06 pm
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 13th, 2019, 9:06 pm
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 14th, 2019, 1:52 pm
by bprentice
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
Re: Partitioned Cellular Automata
Posted: September 14th, 2019, 9:15 pm
by bprentice
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