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# Paterson's worms
# (by Dean Hickerson, 11/20/2008)
# Pattern #061
# Sven Kahrkling's notation 1042015
# Gardner's notation 1a2c3caca4a
# Final outcome unknown; doesn't finish within 1.3*10^18 steps.
# Very chaotic.
# Points and lines of hexagonal grid are mapped to points of square grid as
# below. "*" is a point of the hex grid, "-", "/", and # "\" are lines
# of the hex grid.
#
# +--+--+--+--+
# |- |* |- |* |
# +--+--+--+--+
# | /| \| /| \|
# +--+--+--+--+
# |* |- |* |- |
# +--+--+--+--+
#
# Each step of the worm is simulated by 2 gens in the rule. In even gens,
# there's an arrow at one point of the hex grid showing which way the worm
# will move next. In odd gens, there's an arrow on one line of the hex
# grid. The transitions from even to odd gens are the same for all worms.
# Those from odd to even depend on the specific type of worm: If a point
# (state 0 or 1) has a line with an arrow pointing at it, it becomes a
# 'point with arrow'; the direction depends on the 6 neighboring lines,
# which are the NW, N, E, S, SW, and W neighbors in the square grid.
#
# Gen 0 consists of a single point in state 1, a 'point with arrow'
# pointing east. (Starting with a point in state 2, 3, 4, 5, or 6
# would also work, rotating the whole pattern.)
#
# States are:
#
# 0 empty (unvisited point or line)
# 1-6 'point with arrow', showing direction of next movement
# (1=E; 2=SE; 3=SW; 4=W; 5=NW; 6=NE)
# 7 point that's been visited
# 8,9,10 edge - (8=line; 9=E arrow; 10=W arrow)
# 11,12,13 edge / (11=line; 12=NE arrow; 13=SW arrow)
# 14,15,16 edge \ (14=line; 15=SE arrow; 16=NW arrow)
n_states:17
neighborhood:Moore
symmetries:none
var point={1,2,3,4,5,6}
var a0={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
var a1={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
var a2={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
var a3={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
var a4={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
var a5={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
var a6={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
var a7={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
var n={8,11,14}
var o={8,11,14}
var p={8,11,14}
var q={8,11,14}
var b={0,7}
# point with arrow becomes point that's been visited
point,a0,a1,a2,a3,a4,a5,a6,a7,7
# line with arrow becomes line without arrow
9,a0,a1,a2,a3,a4,a5,a6,a7,8
10,a0,a1,a2,a3,a4,a5,a6,a7,8
12,a0,a1,a2,a3,a4,a5,a6,a7,11
13,a0,a1,a2,a3,a4,a5,a6,a7,11
15,a0,a1,a2,a3,a4,a5,a6,a7,14
16,a0,a1,a2,a3,a4,a5,a6,a7,14
# point with arrow creates line with arrow next to it
0,a0,a1,a2,a3,a4,a5,1,a6,9
0,2,a0,a1,a2,a3,a4,a5,a6,15
0,a0,3,a1,a2,a3,a4,a5,a6,13
0,a0,a1,4,a2,a3,a4,a5,a6,10
0,a0,a1,a2,5,a3,a4,a5,a6,16
0,a0,a1,a2,a3,6,a4,a5,a6,12
# 4 eaten: use only remaining direction
# 0 (straight):
b,0,a0,n,a1,o,12,p,q,6
b,n,a0,0,a1,o,p,9,q,1
b,n,a0,o,a1,0,p,q,15,2
b,13,a0,n,a1,o,0,p,q,3
b,n,a0,10,a1,o,p,0,q,4
b,n,a0,o,a1,16,p,q,0,5
# 1 (gentle right):
b,n,a0,0,a1,o,12,p,q,1
b,n,a0,o,a1,0,p,9,q,2
b,n,a0,o,a1,p,0,q,15,3
b,13,a0,n,a1,o,p,0,q,4
b,n,a0,10,a1,o,p,q,0,5
b,0,a0,n,a1,16,o,p,q,6
# 2 (sharp right):
b,n,a0,o,a1,0,12,p,q,2
b,n,a0,o,a1,p,0,9,q,3
b,n,a0,o,a1,p,q,0,15,4
b,13,a0,n,a1,o,p,q,0,5
b,0,a0,10,a1,n,o,p,q,6
b,n,a0,0,a1,16,o,p,q,1
# 4 (sharp left):
b,n,a0,o,a1,p,12,0,q,4
b,n,a0,o,a1,p,q,9,0,5
b,0,a0,n,a1,o,p,q,15,6
b,13,a0,0,a1,n,o,p,q,1
b,n,a0,10,a1,0,o,p,q,2
b,n,a0,o,a1,16,0,p,q,3
# 5 (gentle left):
b,n,a0,o,a1,p,12,q,0,5
b,0,a0,n,a1,o,p,9,q,6
b,n,a0,0,a1,o,p,q,15,1
b,13,a0,n,a1,0,o,p,q,2
b,n,a0,10,a1,o,0,p,q,3
b,n,a0,o,a1,16,p,0,q,4
# rule-specific transitions at point with arrow coming in
# rule 1042015
# none eaten: 1 = gentle right
b,0,a0,0,a1,0,12,0,0,1
b,0,a0,0,a1,0,0,9,0,2
b,0,a0,0,a1,0,0,0,15,3
b,13,a0,0,a1,0,0,0,0,4
b,0,a0,10,a1,0,0,0,0,5
b,0,a0,0,a1,16,0,0,0,6
# 1 eaten(1): 0 = straight
b,0,a0,n,a1,0,12,0,0,6
b,0,a0,0,a1,n,0,9,0,1
b,0,a0,0,a1,0,n,0,15,2
b,13,a0,0,a1,0,0,n,0,3
b,0,a0,10,a1,0,0,0,n,4
b,n,a0,0,a1,16,0,0,0,5
# 2 eaten(02): 4 = sharp left
b,n,a0,0,a1,o,12,0,0,4
b,0,a0,n,a1,0,o,9,0,5
b,0,a0,0,a1,n,0,o,15,6
b,13,a0,0,a1,0,n,0,o,1
b,o,a0,10,a1,0,0,n,0,2
b,0,a0,o,a1,16,0,0,n,3
# 2 eaten(15): 2 = sharp right
b,0,a0,o,a1,0,12,0,n,2
b,n,a0,0,a1,o,0,9,0,3
b,0,a0,n,a1,0,o,0,15,4
b,13,a0,0,a1,n,0,o,0,5
b,0,a0,10,a1,0,n,0,o,6
b,o,a0,0,a1,16,0,n,0,1
# 2 eaten(24): 0 = straight
b,0,a0,0,a1,n,12,o,0,6
b,0,a0,0,a1,0,n,9,o,1
b,o,a0,0,a1,0,0,n,15,2
b,13,a0,o,a1,0,0,0,n,3
b,n,a0,10,a1,o,0,0,0,4
b,0,a0,n,a1,16,o,0,0,5
# 2 eaten(04): 1 = gentle right
b,n,a0,0,a1,0,12,o,0,1
b,0,a0,n,a1,0,0,9,o,2
b,o,a0,0,a1,n,0,0,15,3
b,13,a0,o,a1,0,n,0,0,4
b,0,a0,10,a1,o,0,n,0,5
b,0,a0,0,a1,16,o,0,n,6
# 3 eaten(124): 5 = gentle left
b,0,a0,n,a1,o,12,p,0,5
b,0,a0,0,a1,n,o,9,p,6
b,p,a0,0,a1,0,n,o,15,1
b,13,a0,p,a1,0,0,n,o,2
b,o,a0,10,a1,p,0,0,n,3
b,n,a0,o,a1,16,p,0,0,4
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