Rule:RepRoller2D

@RULE RepRoller2D

@TABLE

1. 2D version of RepRoller. Thanks to Adam Goucher for the 2-phase idea!
3. contact: tim.hutton@gmail.com

n_states:17 neighborhood:vonNeumann symmetries:none

var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var b={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var c={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var d={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var e={3,4,7} var f={5,6,8} var g={1,3,5} var h={2,4,6} var i={0,1,2,9,10} var j={3,5} var k={4,6} var m={9,11,12} var n={10,13,14} var p={1,11,13} var q={2,12,14} var r={11,13} var s={12,14}

1. Horizontal phase:

1. e : carrying a 0
2. f : carrying a 1
3. g : a 0 or on top of a 0
4. h : a 1 or on top of a 1
5. i : a quiescent cell
6. j : a carrying state on top of a 0
7. k : a carrying state on top of a 1

1. 1 : 0
2. 2 : 1
3. 3 : carrying a 0 on top of a 0
4. 4 : carrying a 0 on top of a 1
5. 5 : carrying a 1 on top of a 0
6. 6 : carrying a 1 on top of a 1
7. 7 : trailing edge 0
8. 8 : trailing edge 1

1. leading edge deposits the state it is carrying

0,a,b,c,e,1 # write 0 0,a,b,c,f,2 # write 1

1. carrying states walk over things without destroying them

g,a,b,c,e,3 # step onto 0 carrying 0 h,a,b,c,e,4 # step onto 1 carrying 0 g,a,b,c,f,5 # step onto 0 carrying 1 h,a,b,c,f,6 # step onto 1 carrying 1

1. trailing edge picks up the state it is standing on

j,a,b,c,i,7 # picking up a 0 k,a,b,c,i,8 # picking up a 1

1. the trailing edge quiesces

7,a,b,0,d,9 7,a,b,c,d,1 8,a,b,0,d,10 8,a,b,c,d,2

1. Vertical phase:

1. 9 : trailing edge 0
2. 10 : trailing edge 1
3. 11 : carrying a 0 on top of a 0
4. 12 : carrying a 0 on top of a 1
5. 13 : carrying a 1 on top of a 0
6. 14 : carrying a 1 on top of a 1

1. m : carrying a 0
2. n : carrying a 1
3. p : a 0 or on top of a 0
4. q : a 1 or on top of a 1
5. r : a carrying state on top of a 0
6. s : a carrying state on top of a 1

1. leading edge deposits the state it is carrying

0,a,b,m,d,1 # write 0 0,a,b,n,d,2 # write 1

1. carrying states walk over things without destroying them

p,a,b,m,d,11 # step onto 0 carrying 0 q,a,b,m,d,12 # step onto 1 carrying 0 p,a,b,n,d,13 # step onto 0 carrying 1 q,a,b,n,d,14 # step onto 1 carrying 1

1. trailing edge picks up the state it is standing on

r,a,b,i,d,9 # picking up a 0 s,a,b,i,d,10 # picking up a 1

1. the trailing edge quiesces

9,a,b,c,d,0 10,a,b,c,d,1

1. Machine operation phase

1. 15: signal head
2. 16: signal tail

0,1,1,1,1,15 # self-triggering (best I could come up with without carrying 3 states) 1,15,b,c,d,15 1,a,15,b,c,15 1,a,b,15,b,15 1,a,b,c,15,15 15,a,b,c,d,16 16,a,b,c,d,1