Code: Select all
@RULE PCA_4
@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 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
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 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
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 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
2 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 23
1 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
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
http://bprentice.webenet.net/PCA/Two%20 ... e%20CA.pdf
The paper references:
Morita, K., Ueno, S: Computation-Universal Models of Two-Dimensional 16-state Reversible
Cellular Automata, IEICE Trans. Inf. & Syst., E75-D,1, pp.141–147 (1992).
I was unable to find a free copy on the internet. Can anyone help me obtain one?
The Golly rule tree was generated with RuleTreeGen.java which is distributed with Golly.
The rule definition that was inserted into RuleTreeGen.java is:
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[] = {0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15};
/* 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];
}
Small ships with 42 different speeds have been found and there are probably many more.
Code: Select all
Diagonal Ships
2c/172 DS001.rle
2c/1364 DS002.rle
2c/284 DS003.rle
2c/1088 DS004.rle
2c/288 DS005.rle
c/78 DS006.rle
c/112 DS007.rle
2c/604 DS008.rle
2c/410 DS009.rle
2c/450 DS010.rle
c/54 DS011.rle
2c/552 DS012.rle
4c/1930 DS013.rle
c/702 DS014.rle
3c/606 DS015.rle
3c/1324 DS016.rle
4c/2006 DS017.rle
c/394 DS018.rle
c/50 DS019.rle
c/1214 DS020.rle
c/2126 DS021.rle
2c/1488 DS022.rle
Orthogonal Ships
2c/180 S001.rle
4c/2642 S002.rle
c/39 S003.rle
2c/70 S004.rle
5c/353 S005.rle
2c/1656 S006.rle
2c/374 S007.rle
2c/216 S008.rle
c/53 S009.rle
2c/132 S010.rle
7c/13549 S011.rle
2c/516 S012.rle
4c/1318 S013.rle
c/27 S014.rle
2c/244 S015.rle
c/81 S016.rle
6c/1900 S017.rle
5c/4915 S018.rle
5c/8409 S019.rle
c/237 S020.rle
An archive containing pattern files for these ships is here:
http://bprentice.webenet.net/PCA/PCA_4%20Ships.zip
Brian Prentice
