State symmetry
Posted: June 14th, 2010, 7:23 pm
I was just thinking about the possibility of implementing some kind of "state symmetry" in the ruletable format.
Basically, it would allow you to have a single state which would have "varieties" for north, south, east or west if it were fourfold, or horizontal and vertical if it were twofold. Then a transition could be defined from one state to another if there was a certain variety of a certain state in a certain point in the neighborhood.
For example, take von Neumann, with 29 states. The 16 directional states could be replaced with 4 fourfold states. However, the construction method would have to change: there would be one code for constructing an arrow in the same direction, another for a left turn, another for a right turn, and another for backwards. A tentative ruletable for this would look as follows (I'm only showing the rules for construction here and no others, just to show the difference produced by having state symmetry):
The statesym line says states 1 to 12 all have fourfold symmetry, variable a is used bound for the direction of any signal which is inherited by the cell being constructed. I've used . to indicate a variation of a state, and + to indicate addition modulo 4 to the variation itself. So as you can see this allows the inputs 10 for confluent, 11000 for normal straight, 11001 for normal reverse, 11010 for normal left turn (assuming addition goes counterclockwise), 11011 for normal right turn, 11100 for special straight and so forth.
Hopefully you'll understand what I'm getting at here, and perhaps it will be of some use - the most annoying thing IMO about JvN is that you cannot just rotate a region and expect it to work, as not only are the states different but the construction codes are also different. Using state symmetry, Golly will be able to "rotate" the cells as well as the arrangements of the cells for you, and the orientation is not of any concern to the user.
Basically, it would allow you to have a single state which would have "varieties" for north, south, east or west if it were fourfold, or horizontal and vertical if it were twofold. Then a transition could be defined from one state to another if there was a certain variety of a certain state in a certain point in the neighborhood.
For example, take von Neumann, with 29 states. The 16 directional states could be replaced with 4 fourfold states. However, the construction method would have to change: there would be one code for constructing an arrow in the same direction, another for a left turn, another for a right turn, and another for backwards. A tentative ruletable for this would look as follows (I'm only showing the rules for construction here and no others, just to show the difference produced by having state symmetry):
Code: Select all
# 1: sensitised
# 2: sensitised transmission
# 3: sensitised transmission normal
# 4: sensitised transmission special
# 5: sensitised transmission normal straight
# 6: sensitised transmission normal turn
# 7: sensitised transmission special straight
# 8: sensitised transmission special turn
# 9: transmission normal inactive
# 10: transmission normal active
# 11: transmission special inactive
# 12: transmission special active
# 13: confluent quiescent
# 14: confluent excited
# 15: confluent quiescent active
# 16: confluent excited active
# C,N,E,S,W,C'
n_states:17
neighborhood:vonNeumann
symmetries:rotate4
statesym,1-12:4
var a={0,1,2,3}
var b={10,12}
0,b.a,0,0,0,1.a
1.a,0,0,0,0,13
1.a,b.a,0,0,0,2.a
2.a,0,0,0,0,3.a
2.a,b.a,0,0,0,4.a
3.a,0,0,0,0,5.a
3.a,b.a,0,0,0,6.a
4.a,0,0,0,0,7.a
4.a,b.a,0,0,0,8.a
5.a,0,0,0,0,9.a
5.a,b.a,0,0,0,9.a+2
6.a,0,0,0,0,9.a+1
6.a,b.a,0,0,0,9.a+3
7.a,0,0,0,0,11.a
7.a,b.a,0,0,0,11.a+2
8.a,0,0,0,0,11.a+1
8.a,b.a,0,0,0,11.a+3Hopefully you'll understand what I'm getting at here, and perhaps it will be of some use - the most annoying thing IMO about JvN is that you cannot just rotate a region and expect it to work, as not only are the states different but the construction codes are also different. Using state symmetry, Golly will be able to "rotate" the cells as well as the arrangements of the cells for you, and the orientation is not of any concern to the user.