Rule:Rule110in2d5n

@RULE rule110in2d5n

https://conwaylife.com/forums/viewtopic.php?p=37917#p38261

Embedding rule 110 elementary cellular automaton - it is Turing-complete This theorem is used for proving the universality of this 2D rule Naszvadi Peter, 2016 This is a simple embedding of Rule-110 into almost any Euclidean 2+dimensional cellular automata grid!

@TREE

num_states=5 num_neighbors=4 num_nodes=36 1 0 1 2 3 4 2 0 0 0 0 0 1 0 2 1 3 4 2 0 0 0 2 0 1 0 1 1 3 4 2 0 0 0 4 0 2 0 2 4 0 0 3 1 3 5 6 1 1 0 1 2 4 3 2 0 8 0 2 4 1 0 1 2 3 3 2 0 0 10 0 0 2 2 2 0 0 0 2 0 4 0 0 0 3 3 9 11 12 13 2 0 10 0 0 0 2 4 0 0 0 0 3 5 11 15 16 1 3 6 12 16 1 1 3 1 13 1 1 1 4 7 14 17 18 19 2 8 0 0 0 0 2 2 0 0 0 0 3 9 21 1 22 16 2 10 0 0 0 0 3 11 1 24 1 1 3 12 22 1 1 1 3 13 16 1 1 1 4 14 23 25 26 27 3 15 24 1 1 1 3 16 1 1 1 1 3 1 1 1 1 1 4 17 25 29 30 31 4 18 26 30 31 31 4 19 27 31 31 31 5 20 28 32 33 34

@TABLE

1. Format: C,N,E,S,W,C'

n_states:5 neighborhood:vonNeumann symmetries:permute

1. false: 2, 4
2. true: 1, 3
3. default empty cell: 0

1. Example topology:
3. ...b[23]-c[01]
4. | |
5. c[01]-d[01]-e[23]-f[01]
6. | |
7. f[01]-g[01]-h[23]-i[01]
8. | |
9. i[01]-j[01]...
11. means: b connected to c, c connected to b and d, etc.
12. This hack for handling the noncommutativity of the
13. neighbourhood arguments of the transition gate,
14. is necessary because Rule-110 is not amphirical

1. Currently needs 3+ dimensions to loop the tape without using
2. thoroidal canonical hypersurface for realization of the
3. neighbourhood graph of the cells

1. TBD: transitions that correctly handles cut endpoints of tape

2,1,1,4,0,1 4,1,2,2,0,3 2,3,2,0,0,1 2,1,1,3,0,1 4,1,1,1,0,3 2,3,1,0,0,1 1,1,1,3,0,2 3,1,1,1,0,4 1,3,1,0,0,2

@COLORS

1 128 255 0 2 255 128 0 3 192 255 0 4 255 64 0