Universality proof question
Universality proof question
I have found a CA that can emulate any logic circuits using glider guns. I can make sliding block memory, but I haven't found a way to build a gun that produces stream of gliders needed to move a block.
Do I need to find a explicit way to build a blockmoving gun to prove computational universality?
Also, does lack of kickback reaction imply lack of universal constructor?
Do I need to find a explicit way to build a blockmoving gun to prove computational universality?
Also, does lack of kickback reaction imply lack of universal constructor?
Re: Universality proof question
No, that's certainly not a requirement. When you say you can make a sliding block memory, does that mean you can hook up logic circuits to it to push, pull or check for zero location of the block? If so, doesn't that imply that you can make a blockmoving gun by stringing together a few logic circuits to repeatedly send a 'push' signal to the slidingblock memory?period54 wrote:I have found a CA that can emulate any logic circuits using glider guns. I can make sliding block memory, but I haven't found a way to build a gun that produces stream of gliders needed to move a block.
Do I need to find a explicit way to build a blockmoving gun to prove computational universality?
No, you can certainly design a U.C. that doesn't use kickback reactions. The obvious counterexample is that there's nothing like a kickback reaction in von Neumann's original 29state CA.period54 wrote:Also, does lack of kickback reaction imply lack of universal constructor?
It's necessary to stretch the definition of "universal constructor" a bit to get it to fit a CA with two states instead of 29. Mainly, in vonNeumanninspired rules supporting selfreplicators, it's generally trivial to prove that any pattern of quiescent cells (i.e., any still life) can be constructed by feeding the right program to some U.C.  precisely because those multistate rules were specifically designed to make such constructions trivial.
In Lifelike rules, still lifes in general are much more difficult to construct because they can be very delicately balanced. Just at the moment people are still working on solving the last 18bit still life in Conway's Life, for example. A general solution for constructing all possible B3/S23 still lifes seems theoretically possible but a very long way off in practice.
But Conway's original proof of B3/S23 construction universality didn't worry about whether all possible still lifes could be constructed. All that mattered was the ability to construct the objects (still lifes or oscillators) used in a universal set of logic circuitry. If you can prove that you can close the loop by designing construction circuitry that's capable of constructing itself and/or other arbitrarily complex logic circuitry, then that's a universal constructor in the same sense as Conway's original U.C. design.
Conway's proof did make extensive use of kickback reactions, but that was just the best known way in 1970 to move gliders arbitrary distances and get them lined up to do complex constructions. Things are much simpler now  for example, the GoL propagator duplicates its circuitry and glider stream without using a single kickback reaction. There aren't any twoglider collisions at all, come to think of it, unless you count the ones where two gliders on parallel paths collide with various other objects to manipulate the constructionarm "elbow".
I suspect that the big problem for proving construction universality for your rule  what is the rule, by the way?  will be to show how to collide gliders to build your various logic circuits. Especially if they're made out of the usual guns and oscillators, then there tend to be a lot of tricky timing problems to solve.
If you get that far, one idea that hasn't been explored much yet is Serizawastyle "armless constructors", which seem to be adaptable enough to work in a wide range of rules. Twoarm construction along the lines of the Gemini spaceship could also be fairly efficient.
Re: Universality proof question
No, that's my problem. Only way to push block I've found requires two gliders to be very close when colliding with it. I haven't found a way to produce gliders at that distance with guns. Pull and check for zero are very simple, though.dvgrn wrote: When you say you can make a sliding block memory, does that mean you can hook up logic circuits to it to push, pull or check for zero location of the block?
My rule is from family that is similar to outer totalistic rules, except that it has negative cells and negative neighbor counts. If cell has two positive and three negative neighbors, it's neighbor count is 1.dvgrn wrote:I suspect that the big problem for proving construction universality for your rule  what is the rule, by the way?  will be to show how to collide gliders to build your various logic circuits. Especially if they're made out of the usual guns and oscillators, then there tend to be a lot of tricky timing problems to solve.
I made a reddit post about it few days ago: http://www.reddit.com/r/cellular_automa ... ive_found/
The rule itself is this:
Code: Select all
+00000+++
00000++++++
+++00000+++++
Sorry for weird notation, couldn't think of anything better.
Here is the rule in golly format:
Code: Select all
@RULE BTCA1
@COLORS
0 0 0 0
1 32 64 255
2 255 64 32
@TABLE
# rules: 203
#
# Golly ruletable format.
# Each rule: C,N,NE,E,SE,S,SW,W,NW,C'
# N.B. Where the same variable appears multiple times in a transition,
# it takes the same value each time.
#
# Default for transitions not listed: no change
#
n_states:3
neighborhood:Moore
symmetries:rotate8reflect
var a={0,1}
var b={0,1}
var c={0,1}
var d={0,1}
var e={0,1}
var f={0,2}
var g={0,2}
var h={0,2}
var i={0,2}
var j={0,2}
var k={1,2}
var l={0,1,2}
var m={0,1,2}
var n={1,2}
var o={1,2}
0,a,b,c,d,e,1,1,1,1
0,f,g,h,i,j,2,2,2,2
0,0,a,b,c,1,0,1,1,1
0,0,f,g,h,2,0,2,2,2
0,0,0,a,1,0,0,1,1,1
0,0,a,0,1,0,1,0,1,1
0,a,b,c,1,1,1,1,2,1
0,a,b,0,1,1,1,2,1,1
0,0,a,0,1,1,2,1,1,1
0,f,g,h,1,2,2,2,2,2
0,0,0,f,2,0,0,2,2,2
0,0,f,0,2,0,2,0,2,2
0,0,f,g,2,1,2,2,2,2
0,0,f,0,2,2,1,2,2,2
f,0,0,1,0,0,1,0,1,1
0,0,a,1,0,1,1,1,2,1
0,0,a,1,0,1,1,2,1,1
f,0,0,1,0,1,2,1,1,1
f,0,0,1,0,2,1,1,1,1
0,f,g,1,0,2,2,2,2,2
0,0,a,1,1,0,1,1,2,1
0,0,a,1,1,0,1,2,1,1
f,0,0,1,1,0,2,1,1,1
0,0,a,1,1,1,0,1,2,1
f,0,0,1,1,1,0,2,1,1
0,0,a,1,1,1,1,0,2,1
0,0,f,1,2,0,2,2,2,2
0,f,g,1,2,2,0,2,2,2
0,f,0,1,2,2,2,0,2,2
a,0,0,2,0,0,2,0,2,2
a,0,0,2,0,1,2,2,2,2
a,0,0,2,0,2,1,2,2,2
a,0,0,2,0,2,2,1,2,2
a,0,0,2,1,0,2,2,2,2
a,0,0,2,1,2,0,2,2,2
a,0,0,2,2,0,1,2,2,2
f,0,1,0,1,0,1,1,2,1
f,0,1,0,1,0,1,2,1,1
f,0,1,0,1,1,0,1,2,1
f,0,1,0,1,1,0,2,1,1
f,0,1,0,1,1,1,0,2,1
a,0,1,0,2,0,2,2,2,2
a,0,1,0,2,2,0,2,2,2
f,0,1,1,0,1,1,0,2,1
0,a,1,1,1,1,1,2,2,1
0,a,1,1,1,1,2,1,2,1
f,0,1,1,1,1,2,2,1,1
0,a,1,1,1,2,1,1,2,1
f,0,1,1,1,2,1,2,1,1
f,0,1,1,1,2,2,1,1,1
0,a,1,1,2,1,1,1,2,1
f,0,1,1,2,1,1,2,1,1
f,0,1,1,2,1,2,1,1,1
0,f,1,1,2,2,2,2,2,2
a,0,1,2,0,2,0,2,2,2
a,0,1,2,0,2,2,0,2,2
f,0,1,2,1,1,1,1,2,1
f,0,1,2,1,1,1,2,1,1
0,f,1,2,1,2,2,2,2,2
a,0,1,2,2,0,2,0,2,2
0,f,1,2,2,1,2,2,2,2
0,f,1,2,2,2,1,2,2,2
a,0,1,2,2,2,2,1,2,2
a,0,1,2,2,2,2,2,1,2
a,0,2,0,2,0,2,1,2,2
f,0,2,1,1,1,1,1,2,1
a,0,2,1,1,2,2,2,2,2
a,0,2,1,2,1,2,2,2,2
a,0,2,1,2,2,1,2,2,2
a,0,2,1,2,2,2,1,2,2
a,0,2,2,1,1,2,2,2,2
a,0,2,2,1,2,1,2,2,2
k,0,0,0,0,0,0,l,m,0
k,0,0,0,0,f,1,g,l,0
k,f,0,0,0,a,l,1,2,0
k,0,0,0,a,b,l,0,2,0
1,0,0,0,0,0,2,2,2,2
k,0,0,0,0,1,f,g,n,0
k,l,0,0,0,1,a,f,2,0
k,f,0,0,g,1,l,2,1,0
k,0,0,0,a,f,b,c,2,0
1,0,0,0,0,2,0,2,2,2
k,0,a,b,f,2,c,1,2,0
k,0,0,0,1,0,f,g,n,0
k,0,0,0,n,0,l,1,2,0
k,f,0,0,1,g,l,2,1,0
k,0,0,f,l,g,2,1,1,0
k,0,0,0,n,1,0,o,2,0
k,0,0,a,1,2,b,2,n,0
k,a,0,b,1,2,l,0,2,0
1,0,0,0,1,2,2,2,2,2
k,0,0,a,2,b,c,d,2,0
1,0,0,0,2,0,0,2,2,2
k,0,a,b,f,c,1,2,2,0
1,0,0,0,2,0,2,0,2,2
k,0,0,f,g,1,l,1,2,0
1,0,0,0,2,1,2,2,2,2
1,0,0,0,2,2,1,2,2,2
k,0,0,1,0,0,n,l,2,0
k,f,0,1,0,g,1,2,l,0
k,0,0,1,f,1,g,l,2,0
k,0,0,1,f,n,g,2,1,0
k,0,0,n,0,1,a,f,2,0
k,0,0,1,0,n,2,0,o,0
k,0,0,1,a,2,b,l,2,0
k,0,0,n,f,2,g,1,1,0
1,0,0,1,0,2,2,2,2,2
k,f,0,1,1,0,g,l,2,0
k,0,0,n,1,f,1,g,2,0
k,0,0,n,1,1,f,g,2,0
1,0,0,1,1,1,1,1,1,2
k,f,0,1,a,1,l,2,2,0
k,f,0,1,a,n,2,1,2,0
k,f,g,1,1,n,2,2,1,0
k,0,0,1,1,2,2,1,1,0
k,0,0,1,2,0,0,n,2,0
1,0,0,1,2,0,0,2,1,0
k,0,a,1,2,b,f,c,2,0
1,0,0,1,2,0,2,2,2,2
k,0,f,l,2,1,a,2,1,0
k,a,b,1,2,2,c,d,2,0
1,0,0,1,2,2,0,2,2,2
k,a,0,1,f,n,1,2,2,0
1,0,0,1,2,2,2,0,2,2
k,0,0,2,0,0,2,1,2,0
1,0,0,2,0,1,0,2,2,0
k,f,g,2,a,b,1,1,2,0
k,0,a,n,0,1,2,b,2,0
k,a,b,2,c,2,d,1,2,0
k,a,b,2,2,1,1,2,2,0
k,0,1,0,1,f,l,g,2,0
k,0,1,0,1,l,2,m,2,0
k,f,1,0,1,l,a,2,2,0
1,0,1,0,1,1,1,1,1,2
k,0,n,a,1,b,2,0,2,0
k,f,1,g,1,l,2,2,1,0
k,0,1,0,1,2,a,1,2,0
k,0,n,f,1,2,a,2,1,0
k,0,1,0,2,a,l,b,2,0
k,0,1,a,2,1,f,n,2,0
1,0,1,0,2,2,1,2,2,0
1,0,1,1,0,1,1,1,1,2
k,f,1,1,0,n,2,a,2,0
k,0,n,a,f,1,2,2,1,0
1,0,1,1,1,0,1,1,1,2
k,0,1,1,n,0,o,2,2,0
k,0,1,1,1,0,2,a,2,0
k,0,1,1,1,1,0,2,2,0
k,0,n,o,1,2,0,1,2,0
k,f,1,1,a,2,0,2,n,0
k,0,1,1,1,2,1,0,2,0
k,0,1,1,2,0,1,1,2,0
k,0,1,1,2,0,1,2,1,0
k,f,1,n,2,g,2,1,1,0
k,0,1,1,2,1,1,0,2,0
1,0,1,1,2,2,2,0,2,0
1,0,1,1,2,2,2,2,2,2
1,0,1,2,0,1,2,2,2,0
k,l,1,2,a,2,b,2,1,0
k,0,1,2,1,0,1,2,1,0
k,0,1,2,1,0,2,2,2,0
k,a,1,2,1,2,0,2,2,0
k,a,1,2,1,2,2,b,n,0
1,0,1,2,1,2,2,2,2,2
k,0,1,2,2,0,1,2,2,0
k,0,1,2,2,0,2,1,2,0
k,a,1,2,2,0,2,2,1,0
k,0,1,2,2,1,0,2,2,0
k,a,1,2,2,1,2,0,2,0
1,0,1,2,2,1,2,2,2,2
k,0,1,2,2,2,1,0,2,0
1,0,1,2,2,2,1,2,2,2
k,0,2,0,2,1,1,2,2,0
k,0,2,1,1,2,0,2,2,0
k,0,2,1,2,0,2,1,2,0
1,f,2,2,2,2,2,2,2,2
1,1,1,1,1,1,1,1,2,2
k,1,1,1,n,o,2,2,2,0
1,1,1,1,2,1,2,1,2,0
k,1,2,1,2,2,1,2,2,0
2,0,0,0,0,0,1,1,1,1
2,0,0,0,0,1,0,1,1,1
2,0,0,0,1,0,0,1,1,1
2,0,0,0,1,0,1,0,1,1
2,0,0,0,1,1,1,1,2,1
2,0,0,0,1,1,1,2,1,1
2,0,0,0,1,1,2,1,1,1
2,0,0,1,0,1,1,1,2,1
2,0,0,1,0,1,1,2,1,1
2,0,0,1,1,0,1,1,2,1
2,0,0,1,1,0,1,2,1,1
2,0,0,1,1,1,0,1,2,1
2,0,0,1,1,1,1,0,2,1
2,0,0,2,2,2,2,2,2,1
2,a,1,1,1,1,1,1,1,1
2,0,1,1,1,1,1,2,2,1
2,0,1,1,1,1,2,1,2,1
2,0,1,1,1,2,1,1,2,1
2,0,1,1,2,1,1,1,2,1
2,0,2,0,2,2,2,2,2,1
2,0,2,2,0,2,2,2,2,1
2,0,2,2,2,0,2,2,2,1
2,1,2,2,2,2,2,2,2,1
Code: Select all
[M2] (golly 2.5)
#R BTCA1
1 0 1 0 1
1 1 0 1 0
2 1 2 0 0
3 0 0 3 0
4 0 0 0 4
5 0 5 0 0
1 1 1 1 1
2 0 7 0 0
1 0 2 2 2
1 2 0 2 2
2 0 0 9 10
2 0 0 0 7
1 2 2 0 2
1 2 2 2 0
2 13 14 0 0
3 8 11 12 15
2 7 0 0 0
1 0 0 1 1
2 0 0 0 18
2 0 0 7 0
1 1 1 0 0
2 0 21 0 0
3 17 19 20 22
4 0 0 16 23
3 0 0 19 0
1 0 2 0 2
1 2 2 2 2
2 0 21 26 27
1 2 0 2 0
2 0 0 29 18
2 26 27 0 18
2 29 21 0 0
3 28 30 31 32
4 25 0 33 0
3 22 0 0 0
4 35 0 0 0
5 24 34 0 36
6 0 0 6 37
7 0 0 0 38
1 0 0 2 2
1 2 2 0 0
2 40 0 41 0
2 0 1 0 0
1 1 1 1 2
2 44 7 0 0
3 0 42 43 45
1 0 0 0 2
1 0 2 0 0
2 0 47 0 48
1 0 0 2 0
1 2 0 0 0
2 50 47 51 48
1 1 1 2 1
2 53 44 0 0
3 49 52 8 54
4 46 55 0 0
2 50 0 51 0
1 0 0 0 1
2 40 0 41 58
1 2 1 1 1
2 0 7 0 60
3 57 59 17 61
1 0 0 1 2
2 0 0 63 18
1 0 0 2 1
1 0 0 1 0
2 0 0 65 66
1 2 0 1 0
2 44 7 68 0
1 0 2 0 1
1 1 2 1 1
2 53 7 70 71
3 64 67 69 72
2 0 53 0 7
1 0 1 0 0
2 40 75 41 0
3 0 74 0 76
1 1 0 2 0
2 78 0 71 7
1 0 1 0 2
2 80 44 60 7
1 1 2 0 0
2 82 21 0 0
1 2 1 0 0
1 1 0 0 0
2 84 85 0 0
3 79 81 83 86
4 62 73 77 87
5 56 88 0 0
3 42 59 0 61
2 0 0 65 63
3 64 91 69 54
2 0 60 0 53
3 0 74 42 93
2 78 0 2 0
2 0 0 0 70
2 68 0 78 0
1 0 1 2 1
2 0 98 0 7
3 95 96 97 99
4 90 92 94 100
2 0 0 18 0
2 7 50 98 2
3 102 0 103 0
2 0 0 18 60
1 1 1 2 0
2 47 18 7 106
2 53 82 7 68
3 105 107 108 0
2 7 51 44 0
2 0 0 0 47
2 2 0 68 0
2 0 1 0 60
3 110 111 112 113
2 60 78 7 0
1 1 2 1 0
2 116 0 78 0
3 115 0 117 0
4 104 109 114 118
3 0 61 0 22
2 2 0 68 65
1 2 1 0 1
1 0 2 1 1
2 0 122 123 7
2 21 51 0 0
3 121 124 54 125
4 120 126 0 0
2 0 53 0 1
3 95 128 0 0
2 63 18 44 7
2 65 63 53 44
3 130 131 0 0
4 129 132 0 0
5 101 119 127 133
6 0 0 89 134
2 50 0 7 2
2 60 68 53 78
3 136 0 137 0
2 7 2 60 68
2 53 78 7 2
3 139 0 140 0
4 138 0 141 0
1 1 0 0 2
2 60 68 7 143
2 0 0 65 40
1 1 2 2 2
2 0 27 0 146
1 2 2 2 1
2 148 27 78 0
3 144 145 147 149
2 0 0 63 65
2 0 0 40 63
1 2 2 1 2
2 153 148 0 0
2 27 153 0 0
3 151 152 154 155
2 0 153 0 27
2 68 0 29 0
2 0 146 0 41
2 78 63 153 148
3 157 158 159 160
1 0 1 2 2
2 162 27 41 85
2 148 27 0 0
3 0 151 163 164
4 150 156 161 165
1 0 2 1 2
2 148 27 0 167
2 66 0 29 0
3 145 0 168 169
2 0 27 80 148
2 85 0 0 0
2 153 29 0 0
3 171 172 173 0
4 170 0 174 0
5 142 0 166 175
1 0 1 1 1
2 0 177 0 75
2 66 0 51 0
3 0 0 178 179
2 0 0 0 58
2 0 0 177 0
2 0 177 0 0
1 1 2 2 1
2 184 85 85 0
3 181 182 183 185
4 0 0 180 186
2 0 0 0 26
3 0 0 0 188
1 0 2 1 0
2 58 190 7 53
1 0 1 2 0
2 40 192 27 0
1 1 1 1 0
2 71 194 75 58
3 181 191 193 195
4 0 189 189 196
2 0 48 0 0
3 0 198 0 0
4 199 0 0 0
5 187 197 0 200
6 0 0 176 201
7 0 0 135 202
8 39 203 0 0
9 0 204 0 0
2 0 0 50 0
3 0 0 0 206
4 0 0 207 0
5 0 0 0 208
2 40 50 27 0
3 0 0 210 0
2 0 0 66 0
2 58 0 0 0
3 212 0 213 0
2 47 27 26 146
3 0 0 0 215
4 211 0 214 216
1 2 1 2 2
2 27 50 218 29
3 0 0 219 0
4 0 0 220 0
4 0 199 0 0
2 51 0 0 0
3 223 0 0 0
4 224 0 0 0
5 217 221 222 225
2 0 13 0 190
2 10 0 75 10
1 1 1 0 1
1 2 1 1 2
2 229 230 75 229
2 190 13 0 0
3 227 228 231 232
3 206 0 0 0
4 233 234 0 0
2 0 13 0 48
2 48 13 0 0
3 236 228 0 237
4 238 234 0 0
5 208 235 239 0
6 0 209 226 240
2 47 14 0 0
2 0 18 0 0
3 0 181 242 243
4 0 0 0 244
2 66 0 0 0
1 0 1 1 0
2 0 247 0 0
3 0 181 246 248
2 0 0 18 66
2 1 0 0 0
3 0 250 172 251
4 0 0 249 252
5 245 253 0 0
2 0 58 0 0
2 18 0 66 0
3 0 212 255 256
2 0 26 0 48
2 41 0 0 0
3 0 0 258 259
4 0 0 257 260
2 0 14 41 51
3 0 0 262 223
2 18 2 1 21
3 0 0 264 198
4 0 0 263 265
5 261 266 0 0
6 0 0 254 267
7 0 0 241 268
2 13 0 48 13
3 0 0 270 0
2 0 0 40 29
1 2 2 0 1
2 26 273 0 47
2 50 0 27 51
3 272 0 274 275
4 0 0 271 276
2 0 0 0 48
3 0 0 0 278
2 0 0 26 40
2 146 68 13 0
3 280 0 281 0
4 0 0 279 282
3 198 0 0 0
2 48 0 0 0
3 0 285 0 0
4 284 286 0 0
5 277 283 287 0
2 0 48 0 1
3 0 111 0 289
2 51 0 7 247
3 206 0 291 0
4 0 0 290 292
1 1 0 1 2
2 0 294 75 21
3 0 278 0 295
2 10 50 13 0
2 2 0 21 0
3 297 0 298 0
4 0 0 296 299
2 0 75 0 0
3 0 301 0 0
4 302 0 0 0
2 14 0 51 0
3 304 0 0 0
4 199 305 0 0
5 293 300 303 306
6 0 0 288 307
1 1 0 1 1
2 58 309 18 53
3 0 0 0 310
2 78 85 44 85
3 212 0 312 0
4 0 0 311 313
2 0 0 1 2
1 1 2 1 2
1 2 1 2 1
2 40 40 316 317
3 0 315 188 318
2 50 0 29 0
3 0 0 320 0
4 0 0 319 321
2 58 1 0 0
3 0 323 0 0
4 324 224 0 0
2 41 41 1 2
3 198 326 0 0
3 0 255 0 0
4 327 328 0 0
5 314 322 325 329
2 0 0 0 2
1 0 2 2 1
2 0 332 48 146
2 40 21 148 50
3 0 331 333 334
3 0 181 172 43
4 0 0 335 336
2 75 50 47 332
1 1 2 2 0
1 2 0 0 1
2 29 0 339 340
3 0 0 338 341
4 0 0 342 0
2 18 41 1 0
2 339 0 0 0
3 344 345 0 0
4 346 0 0 0
2 0 26 0 0
3 348 183 0 0
2 194 0 85 0
3 350 0 0 0
4 349 351 0 0
5 337 343 347 352
6 0 0 330 353
7 0 0 308 354
8 269 355 0 0
2 1 66 85 26
2 0 0 27 1
3 0 0 357 358
2 66 0 309 0
3 0 0 360 0
4 0 0 359 361
2 0 48 0 177
2 41 75 194 0
3 363 364 0 172
2 0 332 0 7
3 0 366 0 0
4 365 367 0 0
2 7 0 339 0
3 369 0 0 0
2 0 18 0 1
3 371 298 0 0
4 370 372 0 0
5 362 0 368 373
2 0 0 10 50
2 58 0 18 66
3 0 0 375 376
4 0 0 377 0
2 47 0 332 27
2 2 0 0 0
3 19 212 379 380
2 58 66 229 230
3 0 0 0 382
4 0 0 381 383
2 13 29 0 0
3 385 213 0 0
2 0 58 0 1
3 0 387 0 0
4 386 388 0 0
2 0 339 21 0
3 390 223 0 0
2 0 229 41 0
3 258 392 0 0
4 391 393 0 0
5 378 384 389 394
6 0 0 374 395
2 0 1 0 1
3 0 0 212 397
2 0 0 229 7
2 0 0 7 85
2 44 317 44 53
1 1 1 2 2
2 218 7 402 7
3 399 400 401 403
4 0 0 398 404
2 0 58 75 7
2 0 85 10 0
3 0 406 111 407
4 0 0 0 408
3 172 301 0 0
2 229 60 21 21
2 60 21 21 85
3 411 412 0 0
4 410 413 0 0
1 2 1 0 2
2 0 415 0 48
2 27 0 0 21
3 416 417 0 301
4 0 418 0 0
5 405 409 414 419
3 212 0 0 0
3 0 0 0 371
4 0 0 421 422
3 0 0 246 0
4 0 0 424 0
2 0 0 85 0
2 0 26 0 13
3 426 427 0 0
2 40 40 27 27
1 0 2 2 0
2 430 58 41 177
2 48 48 0 0
3 429 431 432 0
4 428 433 0 0
2 0 9 0 0
3 111 0 435 304
4 421 436 0 0
5 423 425 434 437
6 0 0 420 438
7 0 0 396 439
2 0 0 66 13
2 0 63 58 309
2 309 190 68 0
3 0 441 442 443
2 50 0 10 0
3 445 0 0 0
4 0 0 444 446
2 0 0 58 0
2 18 66 0 0
3 0 448 0 449
2 0 0 47 9
3 0 0 451 0
4 0 0 450 452
2 0 85 0 0
3 454 0 0 0
4 455 0 0 0
1 2 1 1 0
2 9 457 48 340
2 51 0 18 0
3 458 459 0 246
4 0 460 0 0
5 447 453 456 461
2 0 0 47 40
3 0 0 0 463
3 0 0 0 375
2 26 0 0 0
2 0 50 13 10
3 0 466 0 467
2 13 0 0 0
2 0 0 58 18
3 198 469 0 470
4 464 465 468 471
3 0 0 0 467
3 0 0 0 19
4 0 0 473 474
2 1 7 0 0
3 0 476 0 375
3 198 469 0 0
4 286 477 0 478
2 0 229 0 58
3 0 480 0 8
4 286 481 0 0
5 472 475 479 482
6 0 0 462 483
3 0 0 181 212
2 0 0 0 66
3 0 0 0 486
4 0 0 485 487
3 0 0 0 212
2 0 229 0 75
2 309 0 0 0
3 490 491 0 0
4 489 0 492 0
1 1 0 2 1
2 494 53 53 494
2 85 229 0 0
3 495 172 496 380
2 58 7 0 75
3 0 498 0 0
4 497 499 0 0
2 0 50 9 153
2 0 9 0 48
1 2 2 1 1
1 1 2 0 1
2 503 504 27 316
3 172 501 502 505
2 153 50 14 0
3 206 0 507 0
2 48 14 0 0
3 0 509 0 0
4 506 508 510 0
5 488 493 500 511
3 0 0 181 0
2 75 7 0 85
3 514 246 0 0
4 0 513 0 515
5 0 0 0 516
6 0 0 512 517
7 0 0 484 518
8 440 519 0 0
9 356 520 0 0
10 205 521 0 0
2 0 0 0 1
3 0 0 523 102
4 0 0 524 0
5 0 0 0 525
2 0 0 58 177
3 0 0 0 527
2 0 194 0 0
3 0 529 0 0
4 0 528 0 530
3 22 380 0 0
2 26 27 0 0
3 172 463 0 533
4 532 0 534 0
2 0 0 0 309
2 75 229 0 0
3 536 212 537 0
2 0 0 0 27
2 0 41 0 0
3 0 539 0 540
2 0 0 29 0
3 542 0 223 0
4 538 0 541 543
5 531 535 544 0
6 526 0 545 0
7 0 0 546 0
8 547 0 0 0
9 548 0 0 0
10 549 0 0 0
11 0 0 522 550
The collisions that move block forward and back:
Code: Select all
x = 492, y = 352, rule = BTCA1
3.B$.3B$.3B$3B39$45.B$43.3B$43.3B$42.3B11$59.B$57.3B$57.3B$56.3B$63.B
$61.3B$61.3B$60.3B27$93.B$91.3B$91.3B$90.3B39$135.B$133.3B$133.3B$
132.3B11$149.B$147.3B$147.3B$146.3B$153.B$151.3B$151.3B$150.3B27$183.
B$181.3B$181.3B$180.3B39$225.B$223.3B$223.3B$222.3B11$239.B$237.3B$
237.3B$236.3B$243.B$241.3B$241.3B$240.3B27$273.B$271.3B$271.3B$270.3B
39$315.B$313.3B$313.3B$312.3B11$329.B$327.3B$327.3B$326.3B$333.B139.B
$331.3B137.3B$331.3B137.3B$330.3B137.3B17$350.2B138.2B$350.2B138.2B!
This can be used as eater, but gliders must be of opposite color:
Code: Select all
x = 3, y = 3, rule = BTCA1
.A$.A$3A!
I'll be searching for a way to construct gun with gliders, it doesn't seem to be extremely hard because it's built from relatively common patterns.
Re: Universality proof question
A 23 cell pattern in this rule that takes 62087 generations to stabilize.
Code: Select all
x = 25, y = 10, rule = BTCA1
13B6$22.3B$21.3B$21.3B$21.B!
 A for awesome
 Posts: 2065
 Joined: September 13th, 2014, 5:36 pm
 Location: 0x1
 Contact:
Re: Universality proof question
28,412gen 15cell methuselah:
Edit:
I'm beginning to like this rule .
Code: Select all
x = 11, y = 7, rule = BTCA1
2.A$2.A$3A2$.A8.B$.A.A4.3B$.A.A6.B!
Code: Select all
x = 123, y = 72, rule = BTCA1
121.2B$121.2B67$3B$3B$3B$3.B!
Last edited by A for awesome on November 14th, 2014, 6:02 pm, edited 1 time in total.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$
http://conwaylife.com/wiki/A_for_all
Aidan F. Pierce
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$
http://conwaylife.com/wiki/A_for_all
Aidan F. Pierce
Re: Universality proof question
Yeah, it looks tricky to put one glider that close behind the other. Maybe gliders next to each other would be easier?period54 wrote:No, that's my problem. Only way to push block I've found requires two gliders to be very close when colliding with it. I haven't found a way to produce gliders at that distance with guns.dvgrn wrote: When you say you can make a sliding block memory, does that mean you can hook up logic circuits to it to push, pull or check for zero location of the block?
Code: Select all
x = 134, y = 134, rule = BTCA1
10.B$8.3B$8.3B$7.3B4$3.B$.3B$.3B$3B31$51.B$49.3B$49.3B$48.3B4$44.B$
42.3B$42.3B$41.3B31$92.B$90.3B$90.3B$89.3B4$85.B$83.3B$83.3B$82.3B31$
133.B$131.3B$131.3B$130.3B4$126.B$124.3B4.2B$124.3B4.2B$123.3B!
It's also interesting that almost any monochromatic nearhorizontal line will stabilize into a string of striped diamonds, which sits there quietly until something touches it, then explodes into chaos. (You can tell I've been scribbling...)
 I think that early on I saw one of these diamondshaped areas growing slowly for a while instead of exploding. There may be a way for a nearby pattern to progressively turn on cells at one corner or edge of a diamond so that the stability is maintained. Has anyone else seen that happening?
Re: Universality proof question
Diagonally symmetric patterns tend to have longer lifespans than other patterns. For example, here is a 25022generation methuselah with 12 cells.A for awesome wrote:Edit:[RLE for 15735generation methuselah]
Code: Select all
x = 22, y = 22, rule = BTCA1
.2A$3A$3A18$20.2A$20.2A!
Re: Universality proof question
Another methuselah: 15 cells, stabilizes in 76708 generations. Curiously, it lacks symmetry.
It seems to be relatively common. My search program found three random soups that produce it.
The growth you have noticed is probably result of two diamonds merging together:
And you can grow a diamond with gliders:
It would require a gliderproducing puffer to make a diamond grow infinitely.
Also, there is another oscillator that explodes rather chaotically:
You can extend it by adding more segments.
Code: Select all
x = 3, y = 6, rule = BTCA1
.B$3B$3B$3B$BAB$.2B!
It seems easier indeed. I should search for 90 degree reflectors.dvgrn wrote: Yeah, it looks tricky to put one glider that close behind the other. Maybe gliders next to each other would be easier?
Metaphor of matter/antimatter is what actually led me to research of this family of rules. And some of things you stated were my actual criteria when I was searching for a rule.dvgrn wrote:I like the matter/antimatter effect of the two different colors, and the way that random patterns tend to develop a predominant color, but that even if you start with all one color, oppositecolor patches can appear on occasion, and spread or even take over if they're very lucky.
Yeah, this is one of my favorite things about this rule. It's even weirder when you collide a glider with a huge diamond. Chaos seems to spread very unevenly across it, and even leave triangular or linear patches of stable patterns.dvgrn wrote:It's also interesting that almost any monochromatic nearhorizontal line will stabilize into a string of striped diamonds, which sits there quietly until something touches it, then explodes into chaos. (You can tell I've been scribbling...)
The growth you have noticed is probably result of two diamonds merging together:
Code: Select all
x = 3, y = 26, rule = BTCA1
2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$B$B$B$B$B$B$B$B$B
$B$B$B$B!
Code: Select all
x = 23, y = 15, rule = BTCA1
16.A2$14.5A2$3.A8.9A$.3A$.3A6.13A$3A$10.13A$4.3A$3.3A6.9A$3.3A$3.A10.
5A2$16.A!
Also, there is another oscillator that explodes rather chaotically:
Code: Select all
x = 37, y = 36, rule = BTCA1
30.3B$30.B$28.3B$28.B$26.3B$26.B$24.3B$24.B$22.3B$22.B$20.3B$20.B$18.
3B$18.B$16.3B$16.B$14.3B$14.B$12.3B$12.B$10.3B$10.B$8.3B$8.B$6.3B$6.B
$4.3B$4.B$2.3B$2.B$3B$B$B33.3B$33.3B$33.3B$33.B!
Re: Universality proof question
And another: 10 cells, 59529 generations.
Code: Select all
x = 5, y = 6, rule = BTCA1
2.3B$3.B$.B$.B$2B$.2B!

 Posts: 487
 Joined: April 9th, 2013, 11:03 pm
Re: Universality proof question
Since the fate of a cell in the next generation is determined by the sum of the values of its neighbors, the ruletable for Golly could be made far simpler by using 'symmetries:permute' instead of 'symmetries:rotate8reflect'. Permute symmetry is useful if the order of the neighbors around a given cell does not matter. Then you won't need to have, for example, both "0,0,0,f,2,0,0,2,2,2" and "0,0,f,0,2,0,2,0,2,2". Additionally, variable declarations can reference preceding variable declarations, which still cuts down the size but not nearly as much as changing to permute.
Pretty cool rule, though
Pretty cool rule, though
Re: Universality proof question
Wondering what other interesting rules can be found in this rule family, I implemented this rule in Square Cell. Once this was done the Java code defining the rule was inserted into the Golly provided RuleTreeGen.java file and used to create a Golly rule tree. Thus providing another easy way to generate a Golly implementation of the rule.
Here is the modified RuleTreeGen.java file and the resulting rule tree file. Notice the rule definition in lines 6 thru 39 of the Java file.
Brian Prentice
Here is the modified RuleTreeGen.java file and the resulting rule tree file. Notice the rule definition in lines 6 thru 39 of the Java file.
Code: Select all
import java.util.*;
public class RuleTreeGen
{
/* Put your state count, neighbor count, and function here */
final static int numStates = 3;
final static int numNeighbors = 8;
final static int ruleTable[][] =
{
{1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2},
{1, 1, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 2, 2},
{1, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2}
};
/* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */
/* order for five neighbors is n, w, e, s, c */
private int getState(int s)
{
if (s == 1)
return 1;
else if (s == 2)
return 1;
return 0;
}
int f(int[] a)
{
int neighborCount =
getState(a[0]) +
getState(a[1]) +
getState(a[2]) +
getState(a[3]) +
getState(a[4]) +
getState(a[5]) +
getState(a[6]) +
getState(a[7]);
return ruleTable[a[8]][neighborCount + 8];
}
final static int numParams = numNeighbors + 1;
HashMap<String, Integer> world = new HashMap<String, Integer>();
ArrayList<String> r = new ArrayList<String>();
int[] params = new int[numParams];
int nodeSeq = 0;
int getNode(String n)
{
Integer found = world.get(n);
if (found == null)
{
found = nodeSeq++;
r.add(n);
world.put(n, found);
}
return found;
}
int recur(int at)
{
if (at == 0)
return f(params);
String n = "" + at;
for (int i=0; i<numStates; i++)
{
params[numParamsat] = i;
n += " " + recur(at1);
}
return getNode(n);
}
void writeRuleTree()
{
System.out.println("num_states=" + numStates);
System.out.println("num_neighbors=" + numNeighbors);
System.out.println("num_nodes=" + r.size());
for (int i=0; i<r.size(); i++)
System.out.println(r.get(i));
}
public static void main(String[] args) throws Exception
{
RuleTreeGen rtg = new RuleTreeGen();
rtg.recur(numParams);
rtg.writeRuleTree();
}
}
Code: Select all
@RULE PlusMinus001
@TREE
num_states=3
num_neighbors=8
num_nodes=69
1 0 0 0
2 0 0 0
3 1 1 1
1 1 1 1
2 0 3 0
3 1 4 1
1 2 2 2
2 0 0 6
3 1 1 7
4 2 5 8
1 1 1 2
2 3 10 0
3 4 11 1
4 5 12 2
1 2 1 2
2 6 0 14
3 7 1 15
4 8 2 16
5 9 13 17
2 10 10 3
3 11 19 4
4 12 20 5
5 13 21 9
2 14 6 14
3 15 7 23
4 16 8 24
5 17 9 25
6 18 22 26
1 1 2 2
2 10 28 10
3 19 29 11
4 20 30 12
5 21 31 13
6 22 32 18
1 2 1 1
2 14 14 34
3 23 15 35
4 24 16 36
5 25 17 37
6 26 18 38
7 27 33 39
2 28 3 10
3 29 41 19
4 30 42 20
5 31 43 21
6 32 44 22
7 33 45 27
2 34 14 6
3 35 23 47
4 36 24 48
5 37 25 49
6 38 26 50
7 39 27 51
8 40 46 52
2 3 3 28
3 41 54 29
4 42 55 30
5 43 56 31
6 44 57 32
7 45 58 33
8 46 59 40
2 6 34 6
3 47 35 61
4 48 36 62
5 49 37 63
6 50 38 64
7 51 39 65
8 52 40 66
9 53 60 67
Re: Universality proof question
Although this does not compare to period54's new methuselah, it does have an interesting history and a fourfold symmetry.
Code: Select all
x = 13, y = 13, rule = BTCA1
11.B$10.3B$11.B8$.B$3B$.B!
Re: Universality proof question
Not wanting to pollute this thread with other rules, I have started a new thread describing another member of this rule family here:
viewtopic.php?f=11&t=1501
The new rule does not have the elegance of this rule but does seem to have potential.
Brian Prentice
viewtopic.php?f=11&t=1501
The new rule does not have the elegance of this rule but does seem to have potential.
Brian Prentice
Re: Universality proof question
Yet another 10 cell methuselah. Lives 184420 generations, three times more than previous.
Code: Select all
x = 19, y = 16, rule = BTCA1
17.2A$17.2A$17.A$17.A10$A$.2A$.A!
Re: Universality proof question
First puffer discovered in this rule!
Code: Select all
x = 12, y = 12, rule = BTCA1
10.B$9.3B$8.3BA$9.BA2$7.2A$6.4A$5.3A2B.A$2.B2.2AB2A$.3B2.AB2A$3BA$.BA
4.A!
Re: Universality proof question
And another puffer.
Code: Select all
x = 15, y = 19, rule = BTCA1
8.3B$7.3B$7.3B$7.B$4.3A5.3B$4.3A4.3B$4.3A4.3B$.3B7.B$3B$3B$B$5.3B$4.
3B$4.3B$4.B$9.3B$8.3B$8.3B$8.B!
Re: Universality proof question
Here is a way to create puffers of arbitrarily high periods.period54 wrote:And another puffer.
Code: Select all
x = 447, y = 443, rule = BTCA1
8.3B$7.3B$7.3B$7.B$4.3A5.3B$4.3A4.3B$4.3A4.3B$.3B7.B$3B13.3B$3B12.3B$
B14.3B$5.3B7.B$4.3B13.3B$4.3B12.3B$4.B14.3B$9.3B7.B$8.3B13.3B$8.3B12.
3B$8.B14.3B$13.3B7.B$12.3B13.3B$12.3B12.3B$12.B14.3B$17.3B7.B$16.3B
13.3B$16.3B12.3B$16.B14.3B$21.3B7.B$20.3B13.3B$20.3B12.3B$20.B14.3B$
25.3B7.B$24.3B13.3B$24.3B12.3B$24.B14.3B$29.3B7.B$28.3B13.3B$28.3B12.
3B$28.B14.3B$33.3B7.B$32.3B13.3B$32.3B12.3B$32.B14.3B$37.3B7.B$36.3B
13.3B$36.3B12.3B$36.B14.3B$41.3B7.B$40.3B13.3B$40.3B12.3B$40.B14.3B$
45.3B7.B$44.3B13.3B$44.3B12.3B$44.B14.3B$49.3B7.B$48.3B13.3B$48.3B12.
3B$48.B14.3B$53.3B7.B$52.3B13.3B$52.3B12.3B$52.B14.3B$57.3B7.B$56.3B
13.3B$56.3B12.3B$56.B14.3B$61.3B7.B$60.3B13.3B$60.3B12.3B$60.B14.3B$
65.3B7.B$64.3B13.3B$64.3B12.3B$64.B14.3B$69.3B7.B$68.3B13.3B$68.3B12.
3B$68.B14.3B$73.3B7.B$72.3B13.3B$72.3B12.3B$72.B14.3B$77.3B7.B$76.3B
13.3B$76.3B12.3B$76.B14.3B$81.3B7.B$80.3B13.3B$80.3B12.3B$80.B14.3B$
85.3B7.B$84.3B13.3B$84.3B12.3B$84.B14.3B$89.3B7.B$88.3B13.3B$88.3B12.
3B$88.B14.3B$93.3B7.B$92.3B13.3B$92.3B12.3B$92.B14.3B$97.3B7.B$96.3B
13.3B$96.3B12.3B$96.B14.3B$101.3B7.B$100.3B13.3B$100.3B12.3B$100.B14.
3B$105.3B7.B$104.3B13.3B$104.3B12.3B$104.B14.3B$109.3B7.B$108.3B13.3B
$108.3B12.3B$108.B14.3B$113.3B7.B$112.3B13.3B$112.3B12.3B$112.B14.3B$
117.3B7.B$116.3B13.3B$116.3B12.3B$116.B14.3B$121.3B7.B$120.3B13.3B$
120.3B12.3B$120.B14.3B$125.3B7.B$124.3B13.3B$124.3B12.3B$124.B14.3B$
129.3B7.B$128.3B13.3B$128.3B12.3B$128.B14.3B$133.3B7.B$132.3B13.3B$
132.3B12.3B$132.B14.3B$137.3B7.B$136.3B13.3B$136.3B12.3B$136.B14.3B$
141.3B7.B$140.3B13.3B$140.3B12.3B$140.B14.3B$145.3B7.B$144.3B13.3B$
144.3B12.3B$144.B14.3B$149.3B7.B$148.3B13.3B$148.3B12.3B$148.B14.3B$
153.3B7.B$152.3B13.3B$152.3B12.3B$152.B14.3B$157.3B7.B$156.3B13.3B$
156.3B12.3B$156.B14.3B$161.3B7.B$160.3B13.3B$160.3B12.3B$160.B14.3B$
165.3B7.B$164.3B13.3B$164.3B12.3B$164.B14.3B$169.3B7.B$168.3B13.3B$
168.3B12.3B$168.B14.3B$173.3B7.B$172.3B13.3B$172.3B12.3B$172.B14.3B$
177.3B7.B$176.3B13.3B$176.3B12.3B$176.B14.3B$181.3B7.B$180.3B13.3B$
180.3B12.3B$180.B14.3B$185.3B7.B$184.3B13.3B$184.3B12.3B$184.B14.3B$
189.3B7.B$188.3B13.3B$188.3B12.3B$188.B14.3B$193.3B7.B$192.3B13.3B$
192.3B12.3B$192.B14.3B$197.3B7.B$196.3B13.3B$196.3B12.3B$196.B14.3B$
201.3B7.B$200.3B13.3B$200.3B12.3B$200.B14.3B$205.3B7.B$204.3B13.3B$
204.3B12.3B$204.B14.3B$209.3B7.B$208.3B13.3B$208.3B12.3B$208.B14.3B$
213.3B7.B$212.3B13.3B$212.3B12.3B$212.B14.3B$217.3B7.B$216.3B13.3B$
216.3B12.3B$216.B14.3B$221.3B7.B$220.3B13.3B$220.3B12.3B$220.B14.3B$
225.3B7.B$224.3B13.3B$224.3B12.3B$224.B14.3B$229.3B7.B$228.3B13.3B$
228.3B12.3B$228.B14.3B$233.3B7.B$232.3B13.3B$232.3B12.3B$232.B14.3B$
237.3B7.B$236.3B13.3B$236.3B12.3B$236.B14.3B$241.3B7.B$240.3B13.3B$
240.3B12.3B$240.B14.3B$245.3B7.B$244.3B13.3B$244.3B12.3B$244.B14.3B$
249.3B7.B$248.3B13.3B$248.3B12.3B$248.B14.3B$253.3B7.B$252.3B13.3B$
252.3B12.3B$252.B14.3B$257.3B7.B$256.3B13.3B$256.3B12.3B$256.B14.3B$
261.3B7.B$260.3B13.3B$260.3B12.3B$260.B14.3B$265.3B7.B$264.3B13.3B$
264.3B12.3B$264.B14.3B$269.3B7.B$268.3B13.3B$268.3B12.3B$268.B14.3B$
273.3B7.B$272.3B13.3B$272.3B12.3B$272.B14.3B$277.3B7.B$276.3B13.3B$
276.3B12.3B$276.B14.3B$281.3B7.B$280.3B13.3B$280.3B12.3B$280.B14.3B$
285.3B7.B$284.3B13.3B$284.3B12.3B$284.B14.3B$289.3B7.B$288.3B13.3B$
288.3B12.3B$288.B14.3B$293.3B7.B$292.3B13.3B$292.3B12.3B$292.B14.3B$
297.3B7.B$296.3B13.3B$296.3B12.3B$296.B14.3B$301.3B7.B$300.3B13.3B$
300.3B12.3B$300.B14.3B$305.3B7.B$304.3B13.3B$304.3B12.3B$304.B14.3B$
309.3B7.B$308.3B13.3B$308.3B12.3B$308.B14.3B$313.3B7.B$312.3B13.3B$
312.3B12.3B$312.B14.3B$317.3B7.B$316.3B13.3B$316.3B12.3B$316.B14.3B$
321.3B7.B$320.3B13.3B$320.3B12.3B$320.B14.3B$325.3B7.B$324.3B13.3B$
324.3B12.3B$324.B14.3B$329.3B7.B$328.3B13.3B$328.3B12.3B$328.B14.3B$
333.3B7.B$332.3B13.3B$332.3B12.3B$332.B14.3B$337.3B7.B$336.3B13.3B$
336.3B12.3B$336.B14.3B$341.3B7.B$340.3B13.3B$340.3B12.3B$340.B14.3B$
345.3B7.B$344.3B13.3B$344.3B12.3B$344.B14.3B$349.3B7.B$348.3B13.3B$
348.3B12.3B$348.B14.3B$353.3B7.B$352.3B13.3B$352.3B12.3B$352.B14.3B$
357.3B7.B$356.3B13.3B$356.3B12.3B$356.B14.3B$361.3B7.B$360.3B13.3B$
360.3B12.3B$360.B14.3B$365.3B7.B$364.3B13.3B$364.3B12.3B$364.B14.3B$
369.3B7.B$368.3B13.3B$368.3B12.3B$368.B14.3B$373.3B7.B$372.3B13.3B$
372.3B12.3B$372.B14.3B$377.3B7.B$376.3B13.3B$376.3B12.3B$376.B14.3B$
381.3B7.B$380.3B13.3B$380.3B12.3B$380.B14.3B$385.3B7.B$384.3B13.3B$
384.3B12.3B$384.B14.3B$389.3B7.B$388.3B13.3B$388.3B12.3B$388.B14.3B$
393.3B7.B$392.3B13.3B$392.3B12.3B$392.B14.3B$397.3B7.B$396.3B13.3B$
396.3B12.3B$396.B14.3B$401.3B7.B$400.3B13.3B$400.3B12.3B$400.B14.3B$
405.3B7.B$404.3B13.3B$404.3B12.3B$404.B14.3B$409.3B7.B$408.3B13.3B$
408.3B12.3B$408.B14.3B$413.3B7.B$412.3B13.3B$412.3B12.3B$412.B14.3B$
417.3B7.B$416.3B13.3B$416.3B12.3B$416.B14.3B$421.3B7.B$420.3B13.3B$
420.3B12.3B$420.B14.3B$425.3B7.B$424.3B13.3B$424.3B12.3B$424.B14.3B$
429.3B7.B$428.3B13.3B$428.3B12.3B$428.B14.3B$433.3B7.B$432.3B$432.3B$
432.B!
Re: Universality proof question
Yeah, also you can make huge and extremely messy puffers by combining "engines".
Code: Select all
x = 684, y = 684, rule = BTCA1
673.3B$672.3B$672.3B$672.B$669.3A5.3B$669.3A4.3B$669.3A4.3B$666.3B7.B
$665.3B13.3B$665.3B12.3B$665.B14.3B$662.3A5.3B7.B$662.3A4.3B$662.3A4.
3B$659.3B7.B$658.3B$658.3B$658.B$655.3A5.3B$655.3A4.3B$655.3A4.3B$
652.3B7.B$651.3B13.3B$651.3B12.3B$651.B14.3B$648.3A5.3B7.B$648.3A4.3B
$648.3A4.3B$645.3B7.B$644.3B$644.3B$644.B$641.3A5.3B$641.3A4.3B$641.
3A4.3B$638.3B7.B$637.3B13.3B$637.3B12.3B$637.B14.3B$634.3A5.3B7.B$
634.3A4.3B$634.3A4.3B$631.3B7.B$630.3B$630.3B$630.B$627.3A5.3B$627.3A
4.3B$627.3A4.3B$624.3B7.B$623.3B13.3B$623.3B12.3B$623.B14.3B$620.3A5.
3B7.B$620.3A4.3B$620.3A4.3B$617.3B7.B$616.3B$616.3B$616.B$613.3A5.3B$
613.3A4.3B$613.3A4.3B$610.3B7.B$609.3B13.3B$609.3B12.3B$609.B14.3B$
606.3A5.3B7.B$606.3A4.3B$606.3A4.3B$603.3B7.B$602.3B$602.3B$602.B$
599.3A5.3B$599.3A4.3B$599.3A4.3B$596.3B7.B$595.3B13.3B$595.3B12.3B$
595.B14.3B$592.3A5.3B7.B$592.3A4.3B$592.3A4.3B$589.3B7.B$588.3B$588.
3B$588.B$585.3A5.3B$585.3A4.3B$585.3A4.3B$582.3B7.B$581.3B13.3B$581.
3B12.3B$581.B14.3B$578.3A5.3B7.B$578.3A4.3B$578.3A4.3B$575.3B7.B$574.
3B$574.3B$574.B$571.3A5.3B$571.3A4.3B$571.3A4.3B$568.3B7.B$567.3B13.
3B$567.3B12.3B$567.B14.3B$564.3A5.3B7.B$564.3A4.3B$564.3A4.3B$561.3B
7.B$560.3B$560.3B$560.B$557.3A5.3B$557.3A4.3B$557.3A4.3B$554.3B7.B$
553.3B13.3B$553.3B12.3B$553.B14.3B$550.3A5.3B7.B$550.3A4.3B$550.3A4.
3B$547.3B7.B$546.3B$546.3B$546.B$543.3A5.3B$543.3A4.3B$543.3A4.3B$
540.3B7.B$539.3B13.3B$539.3B12.3B$539.B14.3B$536.3A5.3B7.B$536.3A4.3B
$536.3A4.3B$533.3B7.B$532.3B$532.3B$532.B$529.3A5.3B$529.3A4.3B$529.
3A4.3B$526.3B7.B$525.3B13.3B$525.3B12.3B$525.B14.3B$522.3A5.3B7.B$
522.3A4.3B$522.3A4.3B$519.3B7.B$518.3B$518.3B$518.B$515.3A5.3B$515.3A
4.3B$515.3A4.3B$512.3B7.B$511.3B13.3B$511.3B12.3B$511.B14.3B$508.3A5.
3B7.B$508.3A4.3B$508.3A4.3B$505.3B7.B$504.3B$504.3B$504.B$501.3A5.3B$
501.3A4.3B$501.3A4.3B$498.3B7.B$497.3B13.3B$497.3B12.3B$497.B14.3B$
494.3A5.3B7.B$494.3A4.3B$494.3A4.3B$491.3B7.B$490.3B$490.3B$490.B$
487.3A5.3B$487.3A4.3B$487.3A4.3B$484.3B7.B$483.3B13.3B$483.3B12.3B$
483.B14.3B$480.3A5.3B7.B$480.3A4.3B$480.3A4.3B$477.3B7.B$476.3B$476.
3B$476.B$473.3A5.3B$473.3A4.3B$473.3A4.3B$470.3B7.B$469.3B13.3B$469.
3B12.3B$469.B14.3B$466.3A5.3B7.B$466.3A4.3B$466.3A4.3B$463.3B7.B$462.
3B$462.3B$462.B$459.3A5.3B$459.3A4.3B$459.3A4.3B$456.3B7.B$455.3B13.
3B$455.3B12.3B$455.B14.3B$452.3A5.3B7.B$452.3A4.3B$452.3A4.3B$449.3B
7.B$448.3B$448.3B$448.B$445.3A5.3B$445.3A4.3B$445.3A4.3B$442.3B7.B$
441.3B13.3B$441.3B12.3B$441.B14.3B$438.3A5.3B7.B$438.3A4.3B$438.3A4.
3B$435.3B7.B$434.3B$434.3B$434.B$431.3A5.3B$431.3A4.3B$431.3A4.3B$
428.3B7.B$427.3B13.3B$427.3B12.3B$427.B14.3B$424.3A5.3B7.B$424.3A4.3B
$424.3A4.3B$421.3B7.B$420.3B$420.3B$420.B$417.3A5.3B$417.3A4.3B$417.
3A4.3B$414.3B7.B$413.3B13.3B$413.3B12.3B$413.B14.3B$410.3A5.3B7.B$
410.3A4.3B$410.3A4.3B$407.3B7.B$406.3B$406.3B$406.B$403.3A5.3B$403.3A
4.3B$403.3A4.3B$400.3B7.B$399.3B13.3B$399.3B12.3B$399.B14.3B$396.3A5.
3B7.B$396.3A4.3B$396.3A4.3B$393.3B7.B$392.3B$392.3B$392.B$389.3A5.3B$
389.3A4.3B$389.3A4.3B$386.3B7.B$385.3B13.3B$385.3B12.3B$385.B14.3B$
382.3A5.3B7.B$382.3A4.3B$382.3A4.3B$379.3B7.B$378.3B$378.3B$378.B$
375.3A5.3B$375.3A4.3B$375.3A4.3B$372.3B7.B$371.3B13.3B$371.3B12.3B$
371.B14.3B$368.3A5.3B7.B$368.3A4.3B$368.3A4.3B$365.3B7.B$364.3B$364.
3B$364.B$361.3A5.3B$361.3A4.3B$361.3A4.3B$358.3B7.B$357.3B13.3B$357.
3B12.3B$357.B14.3B$354.3A5.3B7.B$354.3A4.3B$354.3A4.3B$351.3B7.B$350.
3B$350.3B$350.B$347.3A5.3B$347.3A4.3B$347.3A4.3B$344.3B7.B$343.3B13.
3B$343.3B12.3B$343.B14.3B$340.3A5.3B7.B$340.3A4.3B$340.3A4.3B$337.3B
7.B$336.3B$336.3B$336.B$333.3A5.3B$333.3A4.3B$333.3A4.3B$330.3B7.B$
329.3B13.3B$329.3B12.3B$329.B14.3B$326.3A5.3B7.B$326.3A4.3B$326.3A4.
3B$323.3B7.B$322.3B$322.3B$322.B$319.3A5.3B$319.3A4.3B$319.3A4.3B$
316.3B7.B$315.3B13.3B$315.3B12.3B$315.B14.3B$312.3A5.3B7.B$312.3A4.3B
$312.3A4.3B$309.3B7.B$308.3B$308.3B$308.B$305.3A5.3B$305.3A4.3B$305.
3A4.3B$302.3B7.B$301.3B13.3B$301.3B12.3B$301.B14.3B$298.3A5.3B7.B$
298.3A4.3B$298.3A4.3B$295.3B7.B$294.3B$294.3B$294.B$291.3A5.3B$291.3A
4.3B$291.3A4.3B$288.3B7.B$287.3B13.3B$287.3B12.3B$287.B14.3B$284.3A5.
3B7.B$284.3A4.3B$284.3A4.3B$281.3B7.B$280.3B$280.3B$280.B$277.3A5.3B$
277.3A4.3B$277.3A4.3B$274.3B7.B$273.3B13.3B$273.3B12.3B$273.B14.3B$
270.3A5.3B7.B$270.3A4.3B$270.3A4.3B$267.3B7.B$266.3B$266.3B$266.B$
263.3A5.3B$263.3A4.3B$263.3A4.3B$260.3B7.B$259.3B13.3B$259.3B12.3B$
259.B14.3B$256.3A5.3B7.B$256.3A4.3B$256.3A4.3B$253.3B7.B$252.3B$252.
3B$252.B$249.3A5.3B$249.3A4.3B$249.3A4.3B$246.3B7.B$245.3B13.3B$245.
3B12.3B$245.B14.3B$242.3A5.3B7.B$242.3A4.3B$242.3A4.3B$239.3B7.B$238.
3B$238.3B$238.B$235.3A5.3B$235.3A4.3B$235.3A4.3B$232.3B7.B$231.3B13.
3B$231.3B12.3B$231.B14.3B$228.3A5.3B7.B$228.3A4.3B$228.3A4.3B$225.3B
7.B$224.3B$224.3B$224.B$221.3A5.3B$221.3A4.3B$221.3A4.3B$218.3B7.B$
217.3B13.3B$217.3B12.3B$217.B14.3B$214.3A5.3B7.B$214.3A4.3B$214.3A4.
3B$211.3B7.B$210.3B$210.3B$210.B$207.3A5.3B$207.3A4.3B$207.3A4.3B$
204.3B7.B$203.3B13.3B$203.3B12.3B$203.B14.3B$200.3A5.3B7.B$200.3A4.3B
$200.3A4.3B$197.3B7.B$196.3B$196.3B$196.B$193.3A5.3B$193.3A4.3B$193.
3A4.3B$190.3B7.B$189.3B13.3B$189.3B12.3B$189.B14.3B$186.3A5.3B7.B$
186.3A4.3B$186.3A4.3B$183.3B7.B$182.3B$182.3B$182.B$179.3A5.3B$179.3A
4.3B$179.3A4.3B$176.3B7.B$175.3B13.3B$175.3B12.3B$175.B14.3B$172.3A5.
3B7.B$172.3A4.3B$172.3A4.3B$169.3B7.B$168.3B$168.3B$168.B$165.3A5.3B$
165.3A4.3B$165.3A4.3B$162.3B7.B$161.3B13.3B$161.3B12.3B$161.B14.3B$
158.3A5.3B7.B$158.3A4.3B$158.3A4.3B$155.3B7.B$154.3B$154.3B$154.B$
151.3A5.3B$151.3A4.3B$151.3A4.3B$148.3B7.B$147.3B13.3B$147.3B12.3B$
147.B14.3B$144.3A5.3B7.B$144.3A4.3B$144.3A4.3B$141.3B7.B$140.3B$140.
3B$140.B$137.3A5.3B$137.3A4.3B$137.3A4.3B$134.3B7.B$133.3B13.3B$133.
3B12.3B$133.B14.3B$130.3A5.3B7.B$130.3A4.3B$130.3A4.3B$127.3B7.B$126.
3B$126.3B$126.B$123.3A5.3B$123.3A4.3B$123.3A4.3B$120.3B7.B$119.3B13.
3B$119.3B12.3B$119.B14.3B$116.3A5.3B7.B$116.3A4.3B$116.3A4.3B$113.3B
7.B$112.3B$112.3B$112.B$109.3A5.3B$109.3A4.3B$109.3A4.3B$106.3B7.B$
105.3B13.3B$105.3B12.3B$105.B14.3B$102.3A5.3B7.B$102.3A4.3B$102.3A4.
3B$99.3B7.B$98.3B$98.3B$98.B$95.3A5.3B$95.3A4.3B$95.3A4.3B$92.3B7.B$
91.3B13.3B$91.3B12.3B$91.B14.3B$88.3A5.3B7.B$88.3A4.3B$88.3A4.3B$85.
3B7.B$84.3B$84.3B$84.B$81.3A5.3B$81.3A4.3B$81.3A4.3B$78.3B7.B$77.3B
13.3B$77.3B12.3B$77.B14.3B$74.3A5.3B7.B$74.3A4.3B$74.3A4.3B$71.3B7.B$
70.3B$70.3B$70.B$67.3A5.3B$67.3A4.3B$67.3A4.3B$64.3B7.B$63.3B13.3B$
63.3B12.3B$63.B14.3B$60.3A5.3B7.B$60.3A4.3B$60.3A4.3B$57.3B7.B$56.3B$
56.3B$56.B$53.3A5.3B$53.3A4.3B$53.3A4.3B$50.3B7.B$49.3B13.3B$49.3B12.
3B$49.B14.3B$46.3A5.3B7.B$46.3A4.3B$46.3A4.3B$43.3B7.B$42.3B$42.3B$
42.B$39.3A5.3B$39.3A4.3B$39.3A4.3B$36.3B7.B$35.3B13.3B$35.3B12.3B$35.
B14.3B$32.3A5.3B7.B$32.3A4.3B$32.3A4.3B$29.3B7.B$28.3B$28.3B$28.B$25.
3A5.3B$25.3A4.3B$25.3A4.3B$22.3B7.B$21.3B13.3B$21.3B12.3B$21.B14.3B$
18.3A5.3B7.B$18.3A4.3B$18.3A4.3B$15.3B7.B$14.3B$14.3B$14.B$11.3A5.3B$
11.3A4.3B$11.3A4.3B$8.3B7.B$7.3B13.3B$7.3B12.3B$7.B14.3B$4.3A5.3B7.B$
4.3A4.3B$4.3A4.3B$.3B7.B$3B$3B$B$5.3B$4.3B$4.3B$4.B$9.3B$8.3B$8.3B$8.
B!
Re: Universality proof question
I found a smoking ship that generates a fairly large spark. It is shown below deleting all the reflections and rotations of the seven most common oscillators and still lifes.
Code: Select all
x = 653, y = 236, rule = BTCA1
225.3B$134.3B87.3B$40.3B90.3B88.3B96.3B$39.3B91.3B88.B97.3B$39.3B91.B
87.3A5.3B90.3B85.3B$39.B56.A33.3A5.3B46.A33.3A4.3B91.B86.3B$36.3A5.3B
47.3A33.3A4.3B47.A.A31.3A4.3B88.3A5.3B79.3B$.A34.3A4.3B49.3A32.3A4.3B
47.A30.3B7.B56.3A31.3A4.3B80.B$.2A33.3A4.3B49.A31.3B7.B79.3B13.3B49.A
33.3A4.3B77.3A5.3B$A32.3B7.B82.3B13.3B72.3B12.3B50.A30.3B7.B44.2A33.
3A4.3B$32.3B13.3B75.3B12.3B73.B14.3B80.3B13.3B36.2A34.3A4.3B91.3B104.
3B$32.3B12.3B76.B14.3B70.3A5.3B7.B82.3B12.3B70.3B7.B92.3B104.3B$32.B
14.3B73.3A5.3B7.B72.3A4.3B13.3B75.B14.3B69.3B13.3B85.3B104.3B$29.3A5.
3B7.B75.3A4.3B13.3B65.3A4.3B12.3B73.3A5.3B7.B71.3B12.3B86.B106.B$29.
3A4.3B13.3B68.3A4.3B12.3B63.3B7.B14.3B73.3A4.3B13.3B64.B14.3B83.3A5.
3B63.A32.3A5.3B$29.3A4.3B12.3B66.3B7.B14.3B62.3B13.3B7.B75.3A4.3B12.
3B62.3A5.3B7.B53.2A30.3A4.3B64.A32.3A4.3B$26.3B7.B14.3B65.3B13.3B7.B
64.3B12.3B13.3B65.3B7.B14.3B62.3A4.3B13.3B46.2A30.3A4.3B63.3A31.3A4.
3B$25.3B13.3B7.B67.3B12.3B13.3B57.B14.3B12.3B65.3B13.3B7.B64.3A4.3B
12.3B76.3B7.B96.3B7.B$25.3B12.3B13.3B60.B14.3B12.3B63.3B7.B14.3B65.3B
12.3B13.3B54.3B7.B14.3B75.3B13.3B88.3B13.3B$25.B14.3B12.3B66.3B7.B14.
3B62.3B13.3B7.B67.B14.3B12.3B54.3B13.3B7.B77.3B12.3B89.3B12.3B$30.3B
7.B14.3B65.3B13.3B7.B64.3B12.3B13.3B65.3B7.B14.3B54.3B12.3B13.3B70.B
14.3B89.B14.3B$29.3B13.3B7.B67.3B12.3B13.3B57.B14.3B12.3B65.3B13.3B7.
B56.B14.3B12.3B68.3A5.3B7.B88.3A5.3B7.B$29.3B12.3B13.3B60.B14.3B12.3B
63.3B7.B14.3B65.3B12.3B13.3B54.3B7.B14.3B68.3A4.3B13.3B81.3A4.3B13.3B
$29.B14.3B12.3B66.3B7.B14.3B62.3B13.3B7.B67.B14.3B12.3B54.3B13.3B7.B
70.3A4.3B12.3B82.3A4.3B12.3B$34.3B7.B14.3B65.3B13.3B7.B64.3B12.3B13.
3B65.3B7.B14.3B54.3B12.3B13.3B60.3B7.B14.3B79.3B7.B14.3B$33.3B13.3B7.
B67.3B12.3B13.3B57.B14.3B12.3B65.3B13.3B7.B56.B14.3B12.3B60.3B13.3B7.
B80.3B13.3B7.B$33.3B12.3B13.3B60.B14.3B12.3B63.3B7.B14.3B65.3B12.3B
13.3B54.3B7.B14.3B60.3B12.3B13.3B73.3B12.3B13.3B$33.B14.3B12.3B66.3B
7.B14.3B62.3B13.3B7.B67.B14.3B12.3B54.3B13.3B7.B62.B14.3B12.3B74.B14.
3B12.3B$38.3B7.B14.3B65.3B13.3B7.B64.3B12.3B13.3B65.3B7.B14.3B54.3B
12.3B13.3B60.3B7.B14.3B79.3B7.B14.3B$37.3B13.3B7.B67.3B12.3B13.3B57.B
14.3B12.3B65.3B13.3B7.B56.B14.3B12.3B60.3B13.3B7.B80.3B13.3B7.B$37.3B
12.3B13.3B60.B14.3B12.3B63.3B7.B14.3B65.3B12.3B13.3B54.3B7.B14.3B60.
3B12.3B13.3B73.3B12.3B13.3B$37.B14.3B12.3B66.3B7.B14.3B62.3B13.3B7.B
67.B14.3B12.3B54.3B13.3B7.B62.B14.3B12.3B74.B14.3B12.3B$42.3B7.B14.3B
65.3B13.3B7.B64.3B12.3B13.3B65.3B7.B14.3B54.3B12.3B13.3B60.3B7.B14.3B
79.3B7.B14.3B$41.3B13.3B7.B67.3B12.3B13.3B57.B14.3B12.3B65.3B13.3B7.B
56.B14.3B12.3B60.3B13.3B7.B80.3B13.3B7.B$41.3B12.3B13.3B60.B14.3B12.
3B63.3B7.B14.3B65.3B12.3B13.3B54.3B7.B14.3B60.3B12.3B13.3B73.3B12.3B
13.3B$41.B14.3B12.3B66.3B7.B14.3B62.3B13.3B7.B67.B14.3B12.3B54.3B13.
3B7.B62.B14.3B12.3B74.B14.3B12.3B$46.3B7.B14.3B65.3B13.3B7.B64.3B12.
3B81.3B7.B14.3B54.3B12.3B13.3B60.3B7.B14.3B79.3B7.B14.3B$45.3B13.3B7.
B67.3B12.3B73.B14.3B80.3B13.3B7.B56.B14.3B12.3B60.3B13.3B7.B80.3B13.
3B7.B$45.3B12.3B76.B14.3B78.3B7.B82.3B12.3B70.3B7.B14.3B60.3B12.3B13.
3B73.3B12.3B13.3B$45.B14.3B81.3B7.B79.3B13.3B75.B14.3B69.3B13.3B7.B
62.B14.3B12.3B74.B14.3B12.3B$50.3B7.B82.3B13.3B72.3B12.3B81.3B7.B71.
3B12.3B76.3B7.B14.3B79.3B7.B14.3B$49.3B13.3B75.3B12.3B73.B14.3B80.3B
13.3B64.B14.3B75.3B13.3B7.B80.3B13.3B7.B$49.3B12.3B76.B14.3B78.3B7.B
82.3B12.3B70.3B7.B77.3B12.3B13.3B73.3B12.3B13.3B$49.B14.3B81.3B7.B79.
3B13.3B75.B14.3B69.3B13.3B70.B14.3B12.3B74.B14.3B12.3B$54.3B7.B82.3B
13.3B72.3B12.3B81.3B7.B71.3B12.3B76.3B7.B14.3B79.3B7.B14.3B$53.3B13.
3B75.3B12.3B73.B14.3B80.3B13.3B64.B14.3B75.3B13.3B7.B80.3B13.3B7.B$
53.3B12.3B76.B14.3B78.3B7.B82.3B12.3B70.3B7.B77.3B12.3B89.3B12.3B$53.
B14.3B81.3B7.B79.3B91.B14.3B69.3B13.3B70.B14.3B89.B14.3B$58.3B7.B82.
3B88.3B96.3B7.B71.3B12.3B76.3B7.B96.3B7.B$57.3B91.3B88.B97.3B80.B14.
3B75.3B13.3B88.3B13.3B$57.3B91.B188.3B85.3B7.B77.3B12.3B89.3B12.3B$
57.B282.B86.3B86.B14.3B89.B14.3B$427.3B91.3B7.B96.3B7.B$427.B92.3B13.
3B88.3B13.3B$520.3B12.3B89.3B12.3B$520.B14.3B89.B14.3B$525.3B7.B96.3B
7.B$524.3B104.3B$524.3B104.3B$524.B106.B120$47.3B$46.3B182.3B$46.3B
181.3B$46.B183.3B94.3B$43.3A5.3B176.B95.3B$6.A36.3A4.3B174.3A5.3B88.
3B82.3B$7.2A34.3A4.3B174.3A4.3B89.B83.3B$7.A32.3B7.B141.3A32.3A4.3B
86.3A5.3B76.3B205.3B$39.3B13.3B166.3B7.B52.A35.3A4.3B77.B206.3B$39.3B
12.3B136.A29.3B13.3B45.A35.3A4.3B74.3A5.3B199.3B$39.B14.3B166.3B12.3B
46.3A30.3B7.B76.3A4.3B200.B$36.3A5.3B7.B168.B14.3B78.3B13.3B39.A29.3A
4.3B163.A33.3A5.3B$36.3A4.3B13.3B158.3A5.3B7.B80.3B12.3B40.2A25.3B7.B
165.3A31.3A4.3B$36.3A4.3B12.3B159.3A4.3B13.3B73.B14.3B41.A24.3B13.3B
158.A33.3A4.3B$33.3B7.B14.3B159.3A4.3B12.3B71.3A5.3B7.B68.3B12.3B190.
3B7.B$32.3B13.3B7.B158.3B7.B14.3B71.3A4.3B13.3B61.B14.3B189.3B13.3B$
32.3B12.3B13.3B150.3B13.3B7.B73.3A4.3B12.3B59.3A5.3B7.B191.3B12.3B$
32.B14.3B12.3B151.3B12.3B13.3B63.3B7.B14.3B59.3A4.3B13.3B184.B14.3B$
37.3B7.B14.3B151.B14.3B12.3B63.3B13.3B7.B61.3A4.3B12.3B182.3A5.3B7.B$
36.3B13.3B7.B158.3B7.B14.3B63.3B12.3B13.3B51.3B7.B14.3B182.3A4.3B13.
3B$36.3B12.3B13.3B150.3B13.3B7.B65.B14.3B12.3B51.3B13.3B7.B184.3A4.3B
12.3B$36.B14.3B12.3B151.3B12.3B13.3B63.3B7.B14.3B51.3B12.3B13.3B174.
3B7.B14.3B$41.3B7.B14.3B151.B14.3B12.3B63.3B13.3B7.B53.B14.3B12.3B
174.3B13.3B7.B$40.3B13.3B7.B158.3B7.B14.3B63.3B12.3B13.3B51.3B7.B14.
3B174.3B12.3B13.3B$40.3B12.3B13.3B150.3B13.3B7.B65.B14.3B12.3B51.3B
13.3B7.B176.B14.3B12.3B$40.B14.3B12.3B151.3B12.3B13.3B63.3B7.B14.3B
51.3B12.3B13.3B174.3B7.B14.3B$45.3B7.B14.3B151.B14.3B12.3B63.3B13.3B
7.B53.B14.3B12.3B174.3B13.3B7.B$44.3B13.3B7.B158.3B7.B14.3B63.3B12.3B
13.3B51.3B7.B14.3B174.3B12.3B13.3B$44.3B12.3B13.3B150.3B13.3B7.B65.B
14.3B12.3B51.3B13.3B7.B176.B14.3B12.3B$44.B14.3B12.3B151.3B12.3B13.3B
63.3B7.B14.3B51.3B12.3B13.3B174.3B7.B14.3B$49.3B7.B14.3B151.B14.3B12.
3B63.3B13.3B7.B53.B14.3B12.3B174.3B13.3B7.B$48.3B13.3B7.B158.3B7.B14.
3B63.3B12.3B13.3B51.3B7.B14.3B174.3B12.3B13.3B$48.3B12.3B13.3B150.3B
13.3B7.B65.B14.3B12.3B51.3B13.3B7.B176.B14.3B12.3B$48.B14.3B12.3B151.
3B12.3B13.3B63.3B7.B14.3B51.3B12.3B13.3B174.3B7.B14.3B$53.3B7.B14.3B
151.B14.3B12.3B63.3B13.3B7.B53.B14.3B12.3B174.3B13.3B7.B$52.3B13.3B7.
B158.3B7.B14.3B63.3B12.3B13.3B51.3B7.B14.3B174.3B12.3B13.3B$52.3B12.
3B166.3B13.3B7.B65.B14.3B12.3B51.3B13.3B7.B176.B14.3B12.3B$52.B14.3B
166.3B12.3B79.3B7.B14.3B51.3B12.3B13.3B174.3B7.B14.3B$57.3B7.B168.B
14.3B78.3B13.3B7.B53.B14.3B12.3B174.3B13.3B7.B$56.3B13.3B166.3B7.B80.
3B12.3B67.3B7.B14.3B174.3B12.3B13.3B$56.3B12.3B166.3B13.3B73.B14.3B
66.3B13.3B7.B176.B14.3B12.3B$56.B14.3B166.3B12.3B79.3B7.B68.3B12.3B
190.3B7.B14.3B$61.3B7.B168.B14.3B78.3B13.3B61.B14.3B189.3B13.3B7.B$
60.3B13.3B166.3B7.B80.3B12.3B67.3B7.B191.3B12.3B$60.3B12.3B166.3B13.
3B73.B14.3B66.3B13.3B184.B14.3B$60.B14.3B166.3B12.3B79.3B7.B68.3B12.
3B190.3B7.B$65.3B7.B168.B14.3B78.3B13.3B61.B14.3B189.3B13.3B$64.3B
182.3B7.B80.3B12.3B67.3B7.B191.3B12.3B$64.3B181.3B89.B14.3B66.3B13.3B
184.B14.3B$64.B183.3B94.3B7.B68.3B12.3B190.3B7.B$248.B95.3B77.B14.3B
189.3B13.3B$344.3B82.3B7.B191.3B12.3B$344.B83.3B200.B14.3B$428.3B205.
3B7.B$428.B206.3B$635.3B$635.B!
Re: Universality proof question
c0b0p0 wrote:Here is a way to create puffers of arbitrarily high periods.
Well done!c0b0p0 wrote:I found a smoking ship that generates a fairly large spark.
By combining variations of your puffer and ship a large assortment of additional puffers and ships can easily be constructed.
Some examples:
Code: Select all
x = 271, y = 261, rule = BTCA1
5.A$4.4A$5.5A$2.A.ABABABA$.3AB.2AB3A$.4A.5A$3ABA4.A$.ABA$.3A28$35.3A
$36.A$36.A4$52.A$50.3A$50.2ABA$49.2ABA$51.A12$110.2B$111.3A$107.A.5A
$107.9A$108.2A.5A$105.A3.5AB2A$106.A2.2BA.BABA$102.2A5.2BA2.ABA$103.
2A3.BABA3.A$102.4A2B3A12.A$67.3A30.B.2A.A3B2A11.4A$68.A31.B8A12.2AB
AB2A$68.A32.5A15.8A$101.5AB13.3A2.4A$103.2AB2A13.2AB2.4A$103.3A2BA12.
3A3.A6.A6.A$105.3A13.3A3.A13.A$120.2AB2A8.3A$118.2A2BA6.2A4.A$118.2A
BA6.3A2.A$113.A3.A2B2A5.4A.BA$111.7AB2A7.AB2.B$110.7ABA4.B2A3.A$109.
2ABA.B3A4.B3A8.A$110.3A4.A4.4A4.5A$110.AB2A8.3A7.A$111.4A17.A$96.A14.
6A3.A$96.A15.3A4.3A$95.3A16.A3.3ABA$118.3A3.A$100.A23.A$98.3A19.2B2.
3A$99.3A15.A.2A3.A$99.A15.A.A5.2A$117.2A2$153.2A$151.6A$149.8A$148.
3AB2A3BA$115.2A30.4A4.5A$99.3A44.2ABAB.6A.2A$100.A44.2A2BA2.AB3A3B2A
$100.A43.A2B2A2.B4AB4A$143.AB3A.A4.2A3BAB$142.2AB2A2.2AB.B2A2BA$141.
2AB2A7.6A.B3A$140.2A2BA6.10AB2A$139.5A.2A6.2A5.AB2A$139.3AB3.A14.A4.
2A$138.2AB3.B.B.A14.6A$138.3A.3A3.A12.A2.2A2B2A$137.4A.ABA.B3A12.3A
.B2A$137.3AB.8A14.A2.2A$138.2AB8A14.2A.A$138.2AB3A3B2A14.A$140.3ABA
2B2A14.2AB$141.A.BAB3A14.A2.B$128.A12.2AB2A2.A16.BA$128.A13.3AB.B2A
$127.3A13.A3.A2BA.A23.AB$147.3A3.A21.A3B$132.A14.3A.A.A.4A16.3B$130.
3A18.5A.A7.AB9.B$131.3A17.2A4.B.B4.A3B12.AB$131.A18.2A2B.A2.BA4.3B12.
A3B$150.2AB2A10.B13.3B$151.4A14.AB9.B$152.A15.A3B12.AB$168.3B12.A3B
$169.B13.3B$173.AB9.B$172.A3B12.AB$131.3A38.3B12.A3B$132.A29.AB9.B13.
3B$132.A28.A3B12.AB9.B$161.3B12.A3B12.AB$162.B13.3B12.A3B$166.AB9.B
13.3B$165.A3B12.AB9.B$165.3B12.A3B12.AB$166.B13.3B12.A3B$170.AB9.B13.
3B$169.A3B12.AB9.B$169.3B12.A3B12.AB$170.B13.3B12.A3B$174.AB9.B13.3B
$173.A3B12.AB9.B$173.3B12.A3B12.AB$174.B13.3B12.A3B$160.A17.AB9.B13.
3B$160.A16.A3B12.AB9.B$159.3A15.3B12.A3B5.A6.AB$178.B13.3B5.4A3.A3B
$164.A17.AB9.B7.A5.3B$162.3A16.A3B12.AB2.A3.A2.B$163.3A15.3B12.A3B5.
A$163.A18.B13.3B4.4A$186.AB9.B7.A$185.A3B5.A6.AB$185.3B5.4A3.A3B$186.
B7.A5.3B$190.AB2.A3.A2.B$189.A3B5.A$189.3B4.4A$163.3A24.B7.A$164.A29.
AB$164.A28.A3B$193.3B$194.B8$209.A$207.5A$207.3ABA$206.4ABA$206.2A2B
2A$192.A13.7A$192.A12.5A.3A$191.3A11.4AB.B3A$204.5A.A.B$196.A13.3A$
194.3A13.3A$195.3A13.A$195.A2$204.3A$205.3A$205.A4$195.3A$196.A$196.
A9$223.A$220.5A$219.2A.2ABA$218.A2B3.3A$218.3A.B2.A$218.3A.B2.3A$218.
2AB4.A.A$225.B.B.A$223.3A.A$224.4A$224.3A9.B$230.A4.BA2B$229.3A2.BA
2B$225.B2.3ABA2.3B$224.BA2B.A3B2.B4.B$223.BA2B3.AB3A4.BA2B$224.3B5.
2A4.BA2B$224.B4.B2.A6.3B$228.BA2B7.B4.B$227.BA2B12.BA2B$228.3B11.BA
2B$228.B4.B9.3B$232.BA2B7.B4.B$231.BA2B12.BA2B$232.3B11.BA2B$232.B4.
B9.3B$236.BA2B7.B4.B$235.BA2B12.BA2B$236.3B11.BA2B$236.B4.B9.3B$240.
BA2B7.B4.B$239.BA2B7.A4.BA2B$240.3B6.3A2.BA2B$240.B4.B2.3ABA2.3B$244.
BA2B.A3B2.B4.B$243.BA2B3.ABABA4.BA2B$244.3B5.3BA2.BA2B$244.B4.B2.AB
ABA2.3B$248.BA2B.A3B2.B4.B$247.BA2B3.ABABA4.BA2B$248.3B5.3BA2.BA2B$
248.B4.B2.ABABA2.3B$252.BA2B.A3B2.B4.B$251.BA2B3.ABABA4.BA2B$252.3B
5.3BA2.BA2B$252.B4.B2.ABABA2.3B$256.BA2B.A3B2.B$255.BA2B3.AB3A$256.
3B5.2A$256.B4.B2.A$260.BA2B$259.BA2B$260.3B$260.B!
Code: Select all
x = 26, y = 26, rule = BTCA1
17.B$15.3B$15.3B$6.B7.3B$4.3B14.B$4.3B12.3B$3.3B13.3B$10.B7.3B$8.3B
14.B$8.3B12.3B$7.3B13.3B$14.B7.3B$12.3B4.3A$12.3B4.3A$3.B7.3B5.3A$.
3B14.B$.3B12.3B$3B13.3B$7.B7.3B$5.3B4.3A$5.3B4.3A$4.3B5.3A$11.B$9.3B
$9.3B$8.3B!
Code: Select all
x = 35, y = 35, rule = BTCA1
16.B$15.BA2B$14.BA2B$15.3B$15.B4.B$19.BA2B$18.BA2B$19.3B$19.B4.B$23.
BA2B$22.BA2B$13.B6.A2.3B$12.BA2B3.2A2.B4.B$11.BA2B3.5A4.BA2B$2.B9.3B
5.2A4.BA2B$.BA2B7.B4.B2.A6.3B$BA2B12.BA2B7.B4.B$.3B11.BA2B12.BA2B$.
B4.B6.A2.3B11.BA2B$5.BA2B3.2A2.B4.B6.A2.3B$4.BA2B3.5A4.BA2B3.2A2.B$
5.3B5.2A4.BA2B3.5A$5.B4.B2.A6.3B5.2A$9.BA2B7.B4.B2.A$8.BA2B12.BA2B$
9.3B11.BA2B$9.B4.B6.A2.3B$13.BA2B3.2A2.B$12.BA2B3.5A$13.3B5.2A$13.B
4.B2.A$17.BA2B$16.BA2B$17.3B$17.B!
Re: Universality proof question
It's unfortunate that nothing which can clean it is known! (Even the shortestperiod known smoking ship, shown at the end of this post, is p96.)bprentice wrote:Code: Select all
x = 26, y = 26, rule = BTCA1 17.B$15.3B$15.3B$6.B7.3B$4.3B14.B$4.3B12.3B$3.3B13.3B$10.B7.3B$8.3B 14.B$8.3B12.3B$7.3B13.3B$14.B7.3B$12.3B4.3A$12.3B4.3A$3.B7.3B5.3A$. 3B14.B$.3B12.3B$3B13.3B$7.B7.3B$5.3B4.3A$5.3B4.3A$4.3B5.3A$11.B$9.3B $9.3B$8.3B!
Code: Select all
x = 46, y = 43, rule = BTCA1
37.A$35.3A$35.3A$26.A7.3A$24.3A14.A$24.3A12.3A$23.3A13.3A$30.A7.3A$
28.3A14.A$28.3A12.3A$27.3A13.3A$34.A7.3A$32.3A4.3B$32.3A4.3B$23.A7.3A
5.3B$21.3A14.A$21.3A12.3A$17.B2.3A13.3A$15.3B9.A7.3A$15.3B7.3A4.3B$6.
B7.3B8.3A4.3B$4.3B14.B2.3A5.3B$4.3B12.3B9.A$3.3B13.3B7.3A$10.B7.3B8.
3A$8.3B14.B2.3A$8.3B12.3B$7.3B13.3B$14.B7.3B$12.3B4.3A$12.3B4.3A$3.B
7.3B5.3A$.3B14.B$.3B12.3B$3B13.3B$7.B7.3B$5.3B4.3A$5.3B4.3A$4.3B5.3A$
11.B$9.3B$9.3B$8.3B!
Code: Select all
x = 315, y = 213, rule = BTCA1
14.A$12.3A$12.3A$3.A7.3A$.3A14.A$.3A12.3A$3A13.3A$7.A7.3A$5.3A14.A$5.
3A12.3A$4.3A13.3A$11.A7.3A$9.3A14.A$9.3A12.3A$8.3A13.3A$15.A7.3A$13.
3A14.A$13.3A12.3A$12.3A13.3A$19.A7.3A$17.3A4.3B$17.3A4.3B$16.3A5.3B$
23.A$21.3A$21.3A$12.A7.3A67$156.A$154.3A$154.3A$145.A7.3A$143.3A14.A$
143.3A12.3A$142.3A13.3A$149.A7.3A$147.3A14.A$147.3A12.3A$146.3A13.3A$
153.A7.3A$151.3A14.A$151.3A12.3A$150.3A13.3A$157.A7.3A$155.3A14.A$
155.3A12.3A$154.3A13.3A$161.A7.3A$159.3A4.3B$159.3A4.3B$158.3A5.3B$
165.A$163.3A$163.3A$154.A7.3A67$298.A$296.3A$296.3A$287.A7.3A$285.3A
14.A$285.3A12.3A$284.3A13.3A$291.A7.3A$289.3A14.A$289.3A12.3A$288.3A
13.3A$295.A7.3A$293.3A14.A$293.3A12.3A$292.3A13.3A$299.A7.3A$297.3A
14.A$297.3A12.3A$296.3A13.3A$303.A7.3A$301.3A4.3B$301.3A4.3B$300.3A5.
3B$307.A$305.3A$305.3A$296.A7.3A!
Code: Select all
x = 200, y = 204, rule = BTCA1
14.A$12.3A$12.3A$3.A7.3A$.3A14.A$.3A12.3A$3A13.3A$7.A7.3A$5.3A14.A$5.
3A12.3A$4.3A13.3A$11.A7.3A$9.3A14.A$9.3A12.3A$8.3A13.3A$15.A7.3A$13.
3A14.A$13.3A12.3A$12.3A13.3A$19.A7.3A$17.3A14.A$17.3A12.3A$16.3A13.3A
$23.A7.3A$21.3A14.A$21.3A12.3A$20.3A13.3A$27.A7.3A$25.3A14.A$25.3A12.
3A$24.3A13.3A$31.A7.3A$29.3A4.3B$29.3A4.3B$28.3A5.3B$35.A$33.3A$33.3A
$24.A7.3A127$171.A$169.3A$169.3A$160.A7.3A$158.3A14.A$158.3A12.3A$
157.3A13.3A$164.A7.3A$162.3A14.A$162.3A12.3A$161.3A13.3A$168.A7.3A$
166.3A14.A$166.3A12.3A$165.3A13.3A$172.A7.3A$170.3A14.A$170.3A12.3A$
169.3A13.3A$176.A7.3A$174.3A14.A$174.3A12.3A$173.3A13.3A$180.A7.3A$
178.3A14.A$178.3A12.3A$177.3A13.3A$184.A7.3A$182.3A14.A$182.3A12.3A$
181.3A13.3A$188.A7.3A$186.3A4.3B$186.3A4.3B$185.3A5.3B$192.A$190.3A$
190.3A$181.A7.3A!
 A for awesome
 Posts: 2065
 Joined: September 13th, 2014, 5:36 pm
 Location: 0x1
 Contact:
Re: Universality proof question
A reaction that doubles the period of a gun:
Code: Select all
x = 85, y = 33, rule = BTCA1
27.A30.A$25.3A28.3A$26.3A28.3A$26.A30.A5$21.A40.A$21.3A38.3A$20.3A38.
3A$22.A6.B33.A$27.B.B.B22.3B$28.BAB22.2BA2B$26.2BA.A2B20.BABAB$28.BAB
22.2BA2B$27.B.B.B22.3B$29.B3$10.A64.A$8.3A62.3A$9.3A62.3A$9.A64.A2$.A
25.B28.B25.A$.3A10.B11.BA2B26.3B23.3A$3A9.B.B.B8.BA2B27.3B10.3B9.3A$
2.A10.BAB10.3B28.3B8.2BA2B10.A$11.2BA.A2B8.B41.BABAB$13.BAB52.2BA2B$
12.B.B.B52.3B$14.B!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$
http://conwaylife.com/wiki/A_for_all
Aidan F. Pierce
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$
http://conwaylife.com/wiki/A_for_all
Aidan F. Pierce
Re: Universality proof question
Some gliderproducing puffers (periods: 1024, 512, 256 and 128):
Code: Select all
x = 1471, y = 2376, rule = BTCA1
1352.3B$1351.3B$1351.3B$1351.B$1348.3A5.3B$1348.3A4.3B$1348.3A4.3B$
1345.3B7.B$1344.3B13.3B$1344.3B12.3B$1344.B14.3B$1341.3A5.3B7.B$1341.
3A4.3B13.3B$1341.3A4.3B12.3B$1338.3B7.B14.3B$1337.3B13.3B7.B$1337.3B
12.3B13.3B$1337.B14.3B12.3B$1342.3B7.B14.3B$1341.3B13.3B7.B$1341.3B
12.3B13.3B$1341.B14.3B12.3B$1346.3B7.B14.3B$1345.3B13.3B7.B$1345.3B
12.3B13.3B$1345.B14.3B12.3B$1350.3B7.B14.3B$1349.3B13.3B7.B$1349.3B
12.3B13.3B$1349.B14.3B12.3B$1354.3B7.B14.3B$1353.3B13.3B7.B$1353.3B
12.3B13.3B$1353.B14.3B12.3B$1358.3B7.B14.3B$1357.3B13.3B7.B$1357.3B
12.3B13.3B$1357.B14.3B12.3B$1362.3B7.B14.3B$1361.3B13.3B7.B$1361.3B
12.3B13.3B$1361.B14.3B12.3B$1366.3B7.B14.3B$1365.3B13.3B7.B$1365.3B
12.3B13.3B$1365.B14.3B12.3B$1370.3B7.B14.3B$1369.3B13.3B7.B$1369.3B
12.3B13.3B$1369.B14.3B12.3B$1374.3B7.B14.3B$1373.3B13.3B7.B$1373.3B
12.3B13.3B$1373.B14.3B12.3B$1378.3B7.B14.3B$1377.3B13.3B7.B$1377.3B
12.3B13.3B$1377.B14.3B12.3B$1382.3B7.B14.3B$1381.3B13.3B7.B$1381.3B
12.3B13.3B$1381.B14.3B12.3B$1386.3B7.B14.3B$1385.3B13.3B7.B$1385.3B
12.3B13.3B$1385.B14.3B12.3B$1390.3B7.B14.3B$1389.3B13.3B7.B$1389.3B
12.3B13.3B$1389.B14.3B12.3B$1394.3B7.B14.3B$1393.3B13.3B7.B$1393.3B
12.3B13.3B$1393.B14.3B12.3B$1398.3B7.B14.3B$1397.3B13.3B7.B$1397.3B
12.3B13.3B$1397.B14.3B12.3B$1402.3B7.B14.3B$1401.3B13.3B7.B$1401.3B
12.3B13.3B$1401.B14.3B12.3B$1406.3B7.B14.3B$1405.3B13.3B7.B$1405.3B
12.3B13.3B$1405.B14.3B12.3B$1410.3B7.B14.3B$1409.3B13.3B7.B$1409.3B
12.3B13.3B$1409.B14.3B12.3B$1414.3B7.B14.3B$1413.3B13.3B7.B$1413.3B
12.3B13.3B$1413.B14.3B12.3B$1418.3B7.B14.3B$1417.3B13.3B7.B$1417.3B
12.3B13.3B$1417.B14.3B12.3B$1422.3B7.B14.3B$1421.3B13.3B7.B$1421.3B
12.3B13.3B$1421.B14.3B12.3B$1426.3B7.B14.3B$1425.3B13.3B7.B$1425.3B
12.3B13.3B$1425.B14.3B12.3B$1430.3B7.B14.3B$1429.3B13.3B7.B$1429.3B
12.3B13.3B$1429.B14.3B12.3B$1434.3B7.B14.3B$1433.3B13.3B7.B$1433.3B
12.3B13.3B$1433.B14.3B12.3B$1438.3B7.B14.3B$1437.3B13.3B7.B$1437.3B
12.3B13.3B$1437.B14.3B12.3B$1442.3B7.B14.3B$1441.3B13.3B7.B$1441.3B
12.3B$1441.B14.3B$1446.3B7.B$1445.3B$1445.3B$1445.B$1450.3B$1449.3B$
1449.3B$1449.B$1454.3B$1453.3B$1453.3B$1453.B141$1044.3B$1043.3B$
1043.3B$1043.B$1040.3A5.3B$1040.3A4.3B$1040.3A4.3B$1037.3B7.B$1036.3B
13.3B$1036.3B12.3B$1036.B14.3B$1033.3A5.3B7.B$1033.3A4.3B13.3B$1033.
3A4.3B12.3B$1030.3B7.B14.3B$1029.3B13.3B7.B$1029.3B12.3B13.3B$1029.B
14.3B12.3B$1034.3B7.B14.3B$1033.3B13.3B7.B$1033.3B12.3B13.3B$1033.B
14.3B12.3B$1038.3B7.B14.3B$1037.3B13.3B7.B$1037.3B12.3B13.3B$1037.B
14.3B12.3B$1042.3B7.B14.3B$1041.3B13.3B7.B$1041.3B12.3B13.3B$1041.B
14.3B12.3B$1046.3B7.B14.3B$1045.3B13.3B7.B$1045.3B12.3B13.3B$1045.B
14.3B12.3B$1050.3B7.B14.3B$1049.3B13.3B7.B$1049.3B12.3B13.3B$1049.B
14.3B12.3B$1054.3B7.B14.3B$1053.3B13.3B7.B$1053.3B12.3B13.3B$1053.B
14.3B12.3B$1058.3B7.B14.3B$1057.3B13.3B7.B$1057.3B12.3B13.3B$1057.B
14.3B12.3B$1062.3B7.B14.3B$1061.3B13.3B7.B$1061.3B12.3B13.3B$1061.B
14.3B12.3B$1066.3B7.B14.3B$1065.3B13.3B7.B$1065.3B12.3B13.3B$1065.B
14.3B12.3B$1070.3B7.B14.3B$1069.3B13.3B7.B$1069.3B12.3B13.3B$1069.B
14.3B12.3B$1074.3B7.B14.3B$1073.3B13.3B7.B$1073.3B12.3B13.3B$1073.B
14.3B12.3B$1078.3B7.B14.3B$1077.3B13.3B7.B$1077.3B12.3B13.3B$1077.B
14.3B12.3B$1082.3B7.B14.3B$1081.3B13.3B7.B$1081.3B12.3B13.3B$1081.B
14.3B12.3B$1086.3B7.B14.3B$1085.3B13.3B7.B$1085.3B12.3B13.3B$1085.B
14.3B12.3B$1090.3B7.B14.3B$1089.3B13.3B7.B$1089.3B12.3B13.3B$1089.B
14.3B12.3B$1094.3B7.B14.3B$1093.3B13.3B7.B$1093.3B12.3B13.3B$1093.B
14.3B12.3B$1098.3B7.B14.3B$1097.3B13.3B7.B$1097.3B12.3B13.3B$1097.B
14.3B12.3B$1102.3B7.B14.3B$1101.3B13.3B7.B$1101.3B12.3B13.3B$1101.B
14.3B12.3B$1106.3B7.B14.3B$1105.3B13.3B7.B$1105.3B12.3B13.3B$1105.B
14.3B12.3B$1110.3B7.B14.3B$1109.3B13.3B7.B$1109.3B12.3B13.3B$1109.B
14.3B12.3B$1114.3B7.B14.3B$1113.3B13.3B7.B$1113.3B12.3B13.3B$1113.B
14.3B12.3B$1118.3B7.B14.3B$1117.3B13.3B7.B$1117.3B12.3B13.3B$1117.B
14.3B12.3B$1122.3B7.B14.3B$1121.3B13.3B7.B$1121.3B12.3B13.3B$1121.B
14.3B12.3B$1126.3B7.B14.3B$1125.3B13.3B7.B$1125.3B12.3B13.3B$1125.B
14.3B12.3B$1130.3B7.B14.3B$1129.3B13.3B7.B$1129.3B12.3B13.3B$1129.B
14.3B12.3B$1134.3B7.B14.3B$1133.3B13.3B7.B$1133.3B12.3B13.3B$1133.B
14.3B12.3B$1138.3B7.B14.3B$1137.3B13.3B7.B$1137.3B12.3B13.3B$1137.B
14.3B12.3B$1142.3B7.B14.3B$1141.3B13.3B7.B$1141.3B12.3B13.3B$1141.B
14.3B12.3B$1146.3B7.B14.3B$1145.3B13.3B7.B$1145.3B12.3B13.3B$1145.B
14.3B12.3B$1150.3B7.B14.3B$1149.3B13.3B7.B$1149.3B12.3B13.3B$1149.B
14.3B12.3B$1154.3B7.B14.3B$1153.3B13.3B7.B$1153.3B12.3B13.3B$1153.B
14.3B12.3B$1158.3B7.B14.3B$1157.3B13.3B7.B$1157.3B12.3B13.3B$1157.B
14.3B12.3B$1162.3B7.B14.3B$1161.3B13.3B7.B$1161.3B12.3B13.3B$1161.B
14.3B12.3B$1166.3B7.B14.3B$1165.3B13.3B7.B$1165.3B12.3B13.3B$1165.B
14.3B12.3B$1170.3B7.B14.3B$1169.3B13.3B7.B$1169.3B12.3B13.3B$1169.B
14.3B12.3B$1174.3B7.B14.3B$1173.3B13.3B7.B$1173.3B12.3B13.3B$1173.B
14.3B12.3B$1178.3B7.B14.3B$1177.3B13.3B7.B$1177.3B12.3B13.3B$1177.B
14.3B12.3B$1182.3B7.B14.3B$1181.3B13.3B7.B$1181.3B12.3B13.3B$1181.B
14.3B12.3B$1186.3B7.B14.3B$1185.3B13.3B7.B$1185.3B12.3B13.3B$1185.B
14.3B12.3B$1190.3B7.B14.3B$1189.3B13.3B7.B$1189.3B12.3B13.3B$1189.B
14.3B12.3B$1194.3B7.B14.3B$1193.3B13.3B7.B$1193.3B12.3B13.3B$1193.B
14.3B12.3B$1198.3B7.B14.3B$1197.3B13.3B7.B$1197.3B12.3B13.3B$1197.B
14.3B12.3B$1202.3B7.B14.3B$1201.3B13.3B7.B$1201.3B12.3B13.3B$1201.B
14.3B12.3B$1206.3B7.B14.3B$1205.3B13.3B7.B$1205.3B12.3B13.3B$1205.B
14.3B12.3B$1210.3B7.B14.3B$1209.3B13.3B7.B$1209.3B12.3B13.3B$1209.B
14.3B12.3B$1214.3B7.B14.3B$1213.3B13.3B7.B$1213.3B12.3B13.3B$1213.B
14.3B12.3B$1218.3B7.B14.3B$1217.3B13.3B7.B$1217.3B12.3B13.3B$1217.B
14.3B12.3B$1222.3B7.B14.3B$1221.3B13.3B7.B$1221.3B12.3B13.3B$1221.B
14.3B12.3B$1226.3B7.B14.3B$1225.3B13.3B7.B$1225.3B12.3B13.3B$1225.B
14.3B12.3B$1230.3B7.B14.3B$1229.3B13.3B7.B$1229.3B12.3B13.3B$1229.B
14.3B12.3B$1234.3B7.B14.3B$1233.3B13.3B7.B$1233.3B12.3B13.3B$1233.B
14.3B12.3B$1238.3B7.B14.3B$1237.3B13.3B7.B$1237.3B12.3B13.3B$1237.B
14.3B12.3B$1242.3B7.B14.3B$1241.3B13.3B7.B$1241.3B12.3B13.3B$1241.B
14.3B12.3B$1246.3B7.B14.3B$1245.3B13.3B7.B$1245.3B12.3B13.3B$1245.B
14.3B12.3B$1250.3B7.B14.3B$1249.3B13.3B7.B$1249.3B12.3B13.3B$1249.B
14.3B12.3B$1254.3B7.B14.3B$1253.3B13.3B7.B$1253.3B12.3B13.3B$1253.B
14.3B12.3B$1258.3B7.B14.3B$1257.3B13.3B7.B$1257.3B12.3B13.3B$1257.B
14.3B12.3B$1262.3B7.B14.3B$1261.3B13.3B7.B$1261.3B12.3B$1261.B14.3B$
1266.3B7.B$1265.3B$1265.3B$1265.B$1270.3B$1269.3B$1269.3B$1269.B$
1274.3B$1273.3B$1273.3B$1273.B162$625.3B$624.3B$624.3B$624.B$621.3A5.
3B$621.3A4.3B$621.3A4.3B$618.3B7.B$617.3B13.3B$617.3B12.3B$617.B14.3B
$614.3A5.3B7.B$614.3A4.3B13.3B$614.3A4.3B12.3B$611.3B7.B14.3B$610.3B
13.3B7.B$610.3B12.3B13.3B$610.B14.3B12.3B$615.3B7.B14.3B$614.3B13.3B
7.B$614.3B12.3B13.3B$614.B14.3B12.3B$619.3B7.B14.3B$618.3B13.3B7.B$
618.3B12.3B13.3B$618.B14.3B12.3B$623.3B7.B14.3B$622.3B13.3B7.B$622.3B
12.3B13.3B$622.B14.3B12.3B$627.3B7.B14.3B$626.3B13.3B7.B$626.3B12.3B
13.3B$626.B14.3B12.3B$631.3B7.B14.3B$630.3B13.3B7.B$630.3B12.3B13.3B$
630.B14.3B12.3B$635.3B7.B14.3B$634.3B13.3B7.B$634.3B12.3B13.3B$634.B
14.3B12.3B$639.3B7.B14.3B$638.3B13.3B7.B$638.3B12.3B13.3B$638.B14.3B
12.3B$643.3B7.B14.3B$642.3B13.3B7.B$642.3B12.3B13.3B$642.B14.3B12.3B$
647.3B7.B14.3B$646.3B13.3B7.B$646.3B12.3B13.3B$646.B14.3B12.3B$651.3B
7.B14.3B$650.3B13.3B7.B$650.3B12.3B13.3B$650.B14.3B12.3B$655.3B7.B14.
3B$654.3B13.3B7.B$654.3B12.3B13.3B$654.B14.3B12.3B$659.3B7.B14.3B$
658.3B13.3B7.B$658.3B12.3B13.3B$658.B14.3B12.3B$663.3B7.B14.3B$662.3B
13.3B7.B$662.3B12.3B13.3B$662.B14.3B12.3B$667.3B7.B14.3B$666.3B13.3B
7.B$666.3B12.3B13.3B$666.B14.3B12.3B$671.3B7.B14.3B$670.3B13.3B7.B$
670.3B12.3B13.3B$670.B14.3B12.3B$675.3B7.B14.3B$674.3B13.3B7.B$674.3B
12.3B13.3B$674.B14.3B12.3B$679.3B7.B14.3B$678.3B13.3B7.B$678.3B12.3B
13.3B$678.B14.3B12.3B$683.3B7.B14.3B$682.3B13.3B7.B$682.3B12.3B13.3B$
682.B14.3B12.3B$687.3B7.B14.3B$686.3B13.3B7.B$686.3B12.3B13.3B$686.B
14.3B12.3B$691.3B7.B14.3B$690.3B13.3B7.B$690.3B12.3B13.3B$690.B14.3B
12.3B$695.3B7.B14.3B$694.3B13.3B7.B$694.3B12.3B13.3B$694.B14.3B12.3B$
699.3B7.B14.3B$698.3B13.3B7.B$698.3B12.3B13.3B$698.B14.3B12.3B$703.3B
7.B14.3B$702.3B13.3B7.B$702.3B12.3B13.3B$702.B14.3B12.3B$707.3B7.B14.
3B$706.3B13.3B7.B$706.3B12.3B13.3B$706.B14.3B12.3B$711.3B7.B14.3B$
710.3B13.3B7.B$710.3B12.3B13.3B$710.B14.3B12.3B$715.3B7.B14.3B$714.3B
13.3B7.B$714.3B12.3B13.3B$714.B14.3B12.3B$719.3B7.B14.3B$718.3B13.3B
7.B$718.3B12.3B13.3B$718.B14.3B12.3B$723.3B7.B14.3B$722.3B13.3B7.B$
722.3B12.3B13.3B$722.B14.3B12.3B$727.3B7.B14.3B$726.3B13.3B7.B$726.3B
12.3B13.3B$726.B14.3B12.3B$731.3B7.B14.3B$730.3B13.3B7.B$730.3B12.3B
13.3B$730.B14.3B12.3B$735.3B7.B14.3B$734.3B13.3B7.B$734.3B12.3B13.3B$
734.B14.3B12.3B$739.3B7.B14.3B$738.3B13.3B7.B$738.3B12.3B13.3B$738.B
14.3B12.3B$743.3B7.B14.3B$742.3B13.3B7.B$742.3B12.3B13.3B$742.B14.3B
12.3B$747.3B7.B14.3B$746.3B13.3B7.B$746.3B12.3B13.3B$746.B14.3B12.3B$
751.3B7.B14.3B$750.3B13.3B7.B$750.3B12.3B13.3B$750.B14.3B12.3B$755.3B
7.B14.3B$754.3B13.3B7.B$754.3B12.3B13.3B$754.B14.3B12.3B$759.3B7.B14.
3B$758.3B13.3B7.B$758.3B12.3B13.3B$758.B14.3B12.3B$763.3B7.B14.3B$
762.3B13.3B7.B$762.3B12.3B13.3B$762.B14.3B12.3B$767.3B7.B14.3B$766.3B
13.3B7.B$766.3B12.3B13.3B$766.B14.3B12.3B$771.3B7.B14.3B$770.3B13.3B
7.B$770.3B12.3B13.3B$770.B14.3B12.3B$775.3B7.B14.3B$774.3B13.3B7.B$
774.3B12.3B13.3B$774.B14.3B12.3B$779.3B7.B14.3B$778.3B13.3B7.B$778.3B
12.3B13.3B$778.B14.3B12.3B$783.3B7.B14.3B$782.3B13.3B7.B$782.3B12.3B
13.3B$782.B14.3B12.3B$787.3B7.B14.3B$786.3B13.3B7.B$786.3B12.3B13.3B$
786.B14.3B12.3B$791.3B7.B14.3B$790.3B13.3B7.B$790.3B12.3B13.3B$790.B
14.3B12.3B$795.3B7.B14.3B$794.3B13.3B7.B$794.3B12.3B13.3B$794.B14.3B
12.3B$799.3B7.B14.3B$798.3B13.3B7.B$798.3B12.3B13.3B$798.B14.3B12.3B$
803.3B7.B14.3B$802.3B13.3B7.B$802.3B12.3B13.3B$802.B14.3B12.3B$807.3B
7.B14.3B$806.3B13.3B7.B$806.3B12.3B13.3B$806.B14.3B12.3B$811.3B7.B14.
3B$810.3B13.3B7.B$810.3B12.3B13.3B$810.B14.3B12.3B$815.3B7.B14.3B$
814.3B13.3B7.B$814.3B12.3B13.3B$814.B14.3B12.3B$819.3B7.B14.3B$818.3B
13.3B7.B$818.3B12.3B13.3B$818.B14.3B12.3B$823.3B7.B14.3B$822.3B13.3B
7.B$822.3B12.3B13.3B$822.B14.3B12.3B$827.3B7.B14.3B$826.3B13.3B7.B$
826.3B12.3B13.3B$826.B14.3B12.3B$831.3B7.B14.3B$830.3B13.3B7.B$830.3B
12.3B13.3B$830.B14.3B12.3B$835.3B7.B14.3B$834.3B13.3B7.B$834.3B12.3B
13.3B$834.B14.3B12.3B$839.3B7.B14.3B$838.3B13.3B7.B$838.3B12.3B13.3B$
838.B14.3B12.3B$843.3B7.B14.3B$842.3B13.3B7.B$842.3B12.3B13.3B$842.B
14.3B12.3B$847.3B7.B14.3B$846.3B13.3B7.B$846.3B12.3B13.3B$846.B14.3B
12.3B$851.3B7.B14.3B$850.3B13.3B7.B$850.3B12.3B13.3B$850.B14.3B12.3B$
855.3B7.B14.3B$854.3B13.3B7.B$854.3B12.3B13.3B$854.B14.3B12.3B$859.3B
7.B14.3B$858.3B13.3B7.B$858.3B12.3B13.3B$858.B14.3B12.3B$863.3B7.B14.
3B$862.3B13.3B7.B$862.3B12.3B13.3B$862.B14.3B12.3B$867.3B7.B14.3B$
866.3B13.3B7.B$866.3B12.3B13.3B$866.B14.3B12.3B$871.3B7.B14.3B$870.3B
13.3B7.B$870.3B12.3B13.3B$870.B14.3B12.3B$875.3B7.B14.3B$874.3B13.3B
7.B$874.3B12.3B13.3B$874.B14.3B12.3B$879.3B7.B14.3B$878.3B13.3B7.B$
878.3B12.3B13.3B$878.B14.3B12.3B$883.3B7.B14.3B$882.3B13.3B7.B$882.3B
12.3B13.3B$882.B14.3B12.3B$887.3B7.B14.3B$886.3B13.3B7.B$886.3B12.3B
13.3B$886.B14.3B12.3B$891.3B7.B14.3B$890.3B13.3B7.B$890.3B12.3B13.3B$
890.B14.3B12.3B$895.3B7.B14.3B$894.3B13.3B7.B$894.3B12.3B13.3B$894.B
14.3B12.3B$899.3B7.B14.3B$898.3B13.3B7.B$898.3B12.3B13.3B$898.B14.3B
12.3B$903.3B7.B14.3B$902.3B13.3B7.B$902.3B12.3B13.3B$902.B14.3B12.3B$
907.3B7.B14.3B$906.3B13.3B7.B$906.3B12.3B13.3B$906.B14.3B12.3B$911.3B
7.B14.3B$910.3B13.3B7.B$910.3B12.3B13.3B$910.B14.3B12.3B$915.3B7.B14.
3B$914.3B13.3B7.B$914.3B12.3B13.3B$914.B14.3B12.3B$919.3B7.B14.3B$
918.3B13.3B7.B$918.3B12.3B13.3B$918.B14.3B12.3B$923.3B7.B14.3B$922.3B
13.3B7.B$922.3B12.3B13.3B$922.B14.3B12.3B$927.3B7.B14.3B$926.3B13.3B
7.B$926.3B12.3B13.3B$926.B14.3B12.3B$931.3B7.B14.3B$930.3B13.3B7.B$
930.3B12.3B13.3B$930.B14.3B12.3B$935.3B7.B14.3B$934.3B13.3B7.B$934.3B
12.3B13.3B$934.B14.3B12.3B$939.3B7.B14.3B$938.3B13.3B7.B$938.3B12.3B
13.3B$938.B14.3B12.3B$943.3B7.B14.3B$942.3B13.3B7.B$942.3B12.3B13.3B$
942.B14.3B12.3B$947.3B7.B14.3B$946.3B13.3B7.B$946.3B12.3B13.3B$946.B
14.3B12.3B$951.3B7.B14.3B$950.3B13.3B7.B$950.3B12.3B13.3B$950.B14.3B
12.3B$955.3B7.B14.3B$954.3B13.3B7.B$954.3B12.3B13.3B$954.B14.3B12.3B$
959.3B7.B14.3B$958.3B13.3B7.B$958.3B12.3B13.3B$958.B14.3B12.3B$963.3B
7.B14.3B$962.3B13.3B7.B$962.3B12.3B13.3B$962.B14.3B12.3B$967.3B7.B14.
3B$966.3B13.3B7.B$966.3B12.3B13.3B$966.B14.3B12.3B$971.3B7.B14.3B$
970.3B13.3B7.B$970.3B12.3B13.3B$970.B14.3B12.3B$975.3B7.B14.3B$974.3B
13.3B7.B$974.3B12.3B13.3B$974.B14.3B12.3B$979.3B7.B14.3B$978.3B13.3B
7.B$978.3B12.3B13.3B$978.B14.3B12.3B$983.3B7.B14.3B$982.3B13.3B7.B$
982.3B12.3B13.3B$982.B14.3B12.3B$987.3B7.B14.3B$986.3B13.3B7.B$986.3B
12.3B13.3B$986.B14.3B12.3B$991.3B7.B14.3B$990.3B13.3B7.B$990.3B12.3B
13.3B$990.B14.3B12.3B$995.3B7.B14.3B$994.3B13.3B7.B$994.3B12.3B13.3B$
994.B14.3B12.3B$999.3B7.B14.3B$998.3B13.3B7.B$998.3B12.3B13.3B$998.B
14.3B12.3B$1003.3B7.B14.3B$1002.3B13.3B7.B$1002.3B12.3B13.3B$1002.B
14.3B12.3B$1007.3B7.B14.3B$1006.3B13.3B7.B$1006.3B12.3B13.3B$1006.B
14.3B12.3B$1011.3B7.B14.3B$1010.3B13.3B7.B$1010.3B12.3B13.3B$1010.B
14.3B12.3B$1015.3B7.B14.3B$1014.3B13.3B7.B$1014.3B12.3B13.3B$1014.B
14.3B12.3B$1019.3B7.B14.3B$1018.3B13.3B7.B$1018.3B12.3B13.3B$1018.B
14.3B12.3B$1023.3B7.B14.3B$1022.3B13.3B7.B$1022.3B12.3B13.3B$1022.B
14.3B12.3B$1027.3B7.B14.3B$1026.3B13.3B7.B$1026.3B12.3B13.3B$1026.B
14.3B12.3B$1031.3B7.B14.3B$1030.3B13.3B7.B$1030.3B12.3B13.3B$1030.B
14.3B12.3B$1035.3B7.B14.3B$1034.3B13.3B7.B$1034.3B12.3B13.3B$1034.B
14.3B12.3B$1039.3B7.B14.3B$1038.3B13.3B7.B$1038.3B12.3B13.3B$1038.B
14.3B12.3B$1043.3B7.B14.3B$1042.3B13.3B7.B$1042.3B12.3B13.3B$1042.B
14.3B12.3B$1047.3B7.B14.3B$1046.3B13.3B7.B$1046.3B12.3B13.3B$1046.B
14.3B12.3B$1051.3B7.B14.3B$1050.3B13.3B7.B$1050.3B12.3B13.3B$1050.B
14.3B12.3B$1055.3B7.B14.3B$1054.3B13.3B7.B$1054.3B12.3B13.3B$1054.B
14.3B12.3B$1059.3B7.B14.3B$1058.3B13.3B7.B$1058.3B12.3B13.3B$1058.B
14.3B12.3B$1063.3B7.B14.3B$1062.3B13.3B7.B$1062.3B12.3B13.3B$1062.B
14.3B12.3B$1067.3B7.B14.3B$1066.3B13.3B7.B$1066.3B12.3B13.3B$1066.B
14.3B12.3B$1071.3B7.B14.3B$1070.3B13.3B7.B$1070.3B12.3B13.3B$1070.B
14.3B12.3B$1075.3B7.B14.3B$1074.3B13.3B7.B$1074.3B12.3B13.3B$1074.B
14.3B12.3B$1079.3B7.B14.3B$1078.3B13.3B7.B$1078.3B12.3B13.3B$1078.B
14.3B12.3B$1083.3B7.B14.3B$1082.3B13.3B7.B$1082.3B12.3B13.3B$1082.B
14.3B12.3B$1087.3B7.B14.3B$1086.3B13.3B7.B$1086.3B12.3B13.3B$1086.B
14.3B12.3B$1091.3B7.B14.3B$1090.3B13.3B7.B$1090.3B12.3B13.3B$1090.B
14.3B12.3B$1095.3B7.B14.3B$1094.3B13.3B7.B$1094.3B12.3B13.3B$1094.B
14.3B12.3B$1099.3B7.B14.3B$1098.3B13.3B7.B$1098.3B12.3B$1098.B14.3B$
1103.3B7.B$1102.3B$1102.3B$1102.B$1107.3B$1106.3B$1106.3B$1106.B$
1111.3B$1110.3B$1110.3B$1110.B132$15.3B$14.3B$14.3B$14.B$11.3A5.3B$
11.3A4.3B$11.3A4.3B$8.3B7.B$7.3B13.3B$7.3B12.3B$7.B14.3B$4.3A5.3B7.B$
4.3A4.3B13.3B$4.3A4.3B12.3B$.3B7.B14.3B$3B13.3B7.B$3B12.3B13.3B$B14.
3B12.3B$5.3B7.B14.3B$4.3B13.3B7.B$4.3B12.3B13.3B$4.B14.3B12.3B$9.3B7.
B14.3B$8.3B13.3B7.B$8.3B12.3B13.3B$8.B14.3B12.3B$13.3B7.B14.3B$12.3B
13.3B7.B$12.3B12.3B13.3B$12.B14.3B12.3B$17.3B7.B14.3B$16.3B13.3B7.B$
16.3B12.3B13.3B$16.B14.3B12.3B$21.3B7.B14.3B$20.3B13.3B7.B$20.3B12.3B
13.3B$20.B14.3B12.3B$25.3B7.B14.3B$24.3B13.3B7.B$24.3B12.3B13.3B$24.B
14.3B12.3B$29.3B7.B14.3B$28.3B13.3B7.B$28.3B12.3B13.3B$28.B14.3B12.3B
$33.3B7.B14.3B$32.3B13.3B7.B$32.3B12.3B13.3B$32.B14.3B12.3B$37.3B7.B
14.3B$36.3B13.3B7.B$36.3B12.3B13.3B$36.B14.3B12.3B$41.3B7.B14.3B$40.
3B13.3B7.B$40.3B12.3B13.3B$40.B14.3B12.3B$45.3B7.B14.3B$44.3B13.3B7.B
$44.3B12.3B13.3B$44.B14.3B12.3B$49.3B7.B14.3B$48.3B13.3B7.B$48.3B12.
3B13.3B$48.B14.3B12.3B$53.3B7.B14.3B$52.3B13.3B7.B$52.3B12.3B13.3B$
52.B14.3B12.3B$57.3B7.B14.3B$56.3B13.3B7.B$56.3B12.3B13.3B$56.B14.3B
12.3B$61.3B7.B14.3B$60.3B13.3B7.B$60.3B12.3B13.3B$60.B14.3B12.3B$65.
3B7.B14.3B$64.3B13.3B7.B$64.3B12.3B13.3B$64.B14.3B12.3B$69.3B7.B14.3B
$68.3B13.3B7.B$68.3B12.3B13.3B$68.B14.3B12.3B$73.3B7.B14.3B$72.3B13.
3B7.B$72.3B12.3B13.3B$72.B14.3B12.3B$77.3B7.B14.3B$76.3B13.3B7.B$76.
3B12.3B13.3B$76.B14.3B12.3B$81.3B7.B14.3B$80.3B13.3B7.B$80.3B12.3B13.
3B$80.B14.3B12.3B$85.3B7.B14.3B$84.3B13.3B7.B$84.3B12.3B13.3B$84.B14.
3B12.3B$89.3B7.B14.3B$88.3B13.3B7.B$88.3B12.3B13.3B$88.B14.3B12.3B$
93.3B7.B14.3B$92.3B13.3B7.B$92.3B12.3B13.3B$92.B14.3B12.3B$97.3B7.B
14.3B$96.3B13.3B7.B$96.3B12.3B13.3B$96.B14.3B12.3B$101.3B7.B14.3B$
100.3B13.3B7.B$100.3B12.3B13.3B$100.B14.3B12.3B$105.3B7.B14.3B$104.3B
13.3B7.B$104.3B12.3B13.3B$104.B14.3B12.3B$109.3B7.B14.3B$108.3B13.3B
7.B$108.3B12.3B13.3B$108.B14.3B12.3B$113.3B7.B14.3B$112.3B13.3B7.B$
112.3B12.3B13.3B$112.B14.3B12.3B$117.3B7.B14.3B$116.3B13.3B7.B$116.3B
12.3B13.3B$116.B14.3B12.3B$121.3B7.B14.3B$120.3B13.3B7.B$120.3B12.3B
13.3B$120.B14.3B12.3B$125.3B7.B14.3B$124.3B13.3B7.B$124.3B12.3B13.3B$
124.B14.3B12.3B$129.3B7.B14.3B$128.3B13.3B7.B$128.3B12.3B13.3B$128.B
14.3B12.3B$133.3B7.B14.3B$132.3B13.3B7.B$132.3B12.3B13.3B$132.B14.3B
12.3B$137.3B7.B14.3B$136.3B13.3B7.B$136.3B12.3B13.3B$136.B14.3B12.3B$
141.3B7.B14.3B$140.3B13.3B7.B$140.3B12.3B13.3B$140.B14.3B12.3B$145.3B
7.B14.3B$144.3B13.3B7.B$144.3B12.3B13.3B$144.B14.3B12.3B$149.3B7.B14.
3B$148.3B13.3B7.B$148.3B12.3B13.3B$148.B14.3B12.3B$153.3B7.B14.3B$
152.3B13.3B7.B$152.3B12.3B13.3B$152.B14.3B12.3B$157.3B7.B14.3B$156.3B
13.3B7.B$156.3B12.3B13.3B$156.B14.3B12.3B$161.3B7.B14.3B$160.3B13.3B
7.B$160.3B12.3B13.3B$160.B14.3B12.3B$165.3B7.B14.3B$164.3B13.3B7.B$
164.3B12.3B13.3B$164.B14.3B12.3B$169.3B7.B14.3B$168.3B13.3B7.B$168.3B
12.3B13.3B$168.B14.3B12.3B$173.3B7.B14.3B$172.3B13.3B7.B$172.3B12.3B
13.3B$172.B14.3B12.3B$177.3B7.B14.3B$176.3B13.3B7.B$176.3B12.3B13.3B$
176.B14.3B12.3B$181.3B7.B14.3B$180.3B13.3B7.B$180.3B12.3B13.3B$180.B
14.3B12.3B$185.3B7.B14.3B$184.3B13.3B7.B$184.3B12.3B13.3B$184.B14.3B
12.3B$189.3B7.B14.3B$188.3B13.3B7.B$188.3B12.3B13.3B$188.B14.3B12.3B$
193.3B7.B14.3B$192.3B13.3B7.B$192.3B12.3B13.3B$192.B14.3B12.3B$197.3B
7.B14.3B$196.3B13.3B7.B$196.3B12.3B13.3B$196.B14.3B12.3B$201.3B7.B14.
3B$200.3B13.3B7.B$200.3B12.3B13.3B$200.B14.3B12.3B$205.3B7.B14.3B$
204.3B13.3B7.B$204.3B12.3B13.3B$204.B14.3B12.3B$209.3B7.B14.3B$208.3B
13.3B7.B$208.3B12.3B13.3B$208.B14.3B12.3B$213.3B7.B14.3B$212.3B13.3B
7.B$212.3B12.3B13.3B$212.B14.3B12.3B$217.3B7.B14.3B$216.3B13.3B7.B$
216.3B12.3B13.3B$216.B14.3B12.3B$221.3B7.B14.3B$220.3B13.3B7.B$220.3B
12.3B13.3B$220.B14.3B12.3B$225.3B7.B14.3B$224.3B13.3B7.B$224.3B12.3B
13.3B$224.B14.3B12.3B$229.3B7.B14.3B$228.3B13.3B7.B$228.3B12.3B13.3B$
228.B14.3B12.3B$233.3B7.B14.3B$232.3B13.3B7.B$232.3B12.3B13.3B$232.B
14.3B12.3B$237.3B7.B14.3B$236.3B13.3B7.B$236.3B12.3B13.3B$236.B14.3B
12.3B$241.3B7.B14.3B$240.3B13.3B7.B$240.3B12.3B13.3B$240.B14.3B12.3B$
245.3B7.B14.3B$244.3B13.3B7.B$244.3B12.3B13.3B$244.B14.3B12.3B$249.3B
7.B14.3B$248.3B13.3B7.B$248.3B12.3B13.3B$248.B14.3B12.3B$253.3B7.B14.
3B$252.3B13.3B7.B$252.3B12.3B13.3B$252.B14.3B12.3B$257.3B7.B14.3B$
256.3B13.3B7.B$256.3B12.3B13.3B$256.B14.3B12.3B$261.3B7.B14.3B$260.3B
13.3B7.B$260.3B12.3B13.3B$260.B14.3B12.3B$265.3B7.B14.3B$264.3B13.3B
7.B$264.3B12.3B13.3B$264.B14.3B12.3B$269.3B7.B14.3B$268.3B13.3B7.B$
268.3B12.3B13.3B$268.B14.3B12.3B$273.3B7.B14.3B$272.3B13.3B7.B$272.3B
12.3B13.3B$272.B14.3B12.3B$277.3B7.B14.3B$276.3B13.3B7.B$276.3B12.3B
13.3B$276.B14.3B12.3B$281.3B7.B14.3B$280.3B13.3B7.B$280.3B12.3B13.3B$
280.B14.3B12.3B$285.3B7.B14.3B$284.3B13.3B7.B$284.3B12.3B13.3B$284.B
14.3B12.3B$289.3B7.B14.3B$288.3B13.3B7.B$288.3B12.3B13.3B$288.B14.3B
12.3B$293.3B7.B14.3B$292.3B13.3B7.B$292.3B12.3B13.3B$292.B14.3B12.3B$
297.3B7.B14.3B$296.3B13.3B7.B$296.3B12.3B13.3B$296.B14.3B12.3B$301.3B
7.B14.3B$300.3B13.3B7.B$300.3B12.3B13.3B$300.B14.3B12.3B$305.3B7.B14.
3B$304.3B13.3B7.B$304.3B12.3B13.3B$304.B14.3B12.3B$309.3B7.B14.3B$
308.3B13.3B7.B$308.3B12.3B13.3B$308.B14.3B12.3B$313.3B7.B14.3B$312.3B
13.3B7.B$312.3B12.3B13.3B$312.B14.3B12.3B$317.3B7.B14.3B$316.3B13.3B
7.B$316.3B12.3B13.3B$316.B14.3B12.3B$321.3B7.B14.3B$320.3B13.3B7.B$
320.3B12.3B13.3B$320.B14.3B12.3B$325.3B7.B14.3B$324.3B13.3B7.B$324.3B
12.3B13.3B$324.B14.3B12.3B$329.3B7.B14.3B$328.3B13.3B7.B$328.3B12.3B
13.3B$328.B14.3B12.3B$333.3B7.B14.3B$332.3B13.3B7.B$332.3B12.3B13.3B$
332.B14.3B12.3B$337.3B7.B14.3B$336.3B13.3B7.B$336.3B12.3B13.3B$336.B
14.3B12.3B$341.3B7.B14.3B$340.3B13.3B7.B$340.3B12.3B13.3B$340.B14.3B
12.3B$345.3B7.B14.3B$344.3B13.3B7.B$344.3B12.3B13.3B$344.B14.3B12.3B$
349.3B7.B14.3B$348.3B13.3B7.B$348.3B12.3B13.3B$348.B14.3B12.3B$353.3B
7.B14.3B$352.3B13.3B7.B$352.3B12.3B13.3B$352.B14.3B12.3B$357.3B7.B14.
3B$356.3B13.3B7.B$356.3B12.3B13.3B$356.B14.3B12.3B$361.3B7.B14.3B$
360.3B13.3B7.B$360.3B12.3B13.3B$360.B14.3B12.3B$365.3B7.B14.3B$364.3B
13.3B7.B$364.3B12.3B13.3B$364.B14.3B12.3B$369.3B7.B14.3B$368.3B13.3B
7.B$368.3B12.3B13.3B$368.B14.3B12.3B$373.3B7.B14.3B$372.3B13.3B7.B$
372.3B12.3B13.3B$372.B14.3B12.3B$377.3B7.B14.3B$376.3B13.3B7.B$376.3B
12.3B13.3B$376.B14.3B12.3B$381.3B7.B14.3B$380.3B13.3B7.B$380.3B12.3B
13.3B$380.B14.3B12.3B$385.3B7.B14.3B$384.3B13.3B7.B$384.3B12.3B13.3B$
384.B14.3B12.3B$389.3B7.B14.3B$388.3B13.3B7.B$388.3B12.3B13.3B$388.B
14.3B12.3B$393.3B7.B14.3B$392.3B13.3B7.B$392.3B12.3B13.3B$392.B14.3B
12.3B$397.3B7.B14.3B$396.3B13.3B7.B$396.3B12.3B13.3B$396.B14.3B12.3B$
401.3B7.B14.3B$400.3B13.3B7.B$400.3B12.3B13.3B$400.B14.3B12.3B$405.3B
7.B14.3B$404.3B13.3B7.B$404.3B12.3B13.3B$404.B14.3B12.3B$409.3B7.B14.
3B$408.3B13.3B7.B$408.3B12.3B13.3B$408.B14.3B12.3B$413.3B7.B14.3B$
412.3B13.3B7.B$412.3B12.3B13.3B$412.B14.3B12.3B$417.3B7.B14.3B$416.3B
13.3B7.B$416.3B12.3B13.3B$416.B14.3B12.3B$421.3B7.B14.3B$420.3B13.3B
7.B$420.3B12.3B13.3B$420.B14.3B12.3B$425.3B7.B14.3B$424.3B13.3B7.B$
424.3B12.3B13.3B$424.B14.3B12.3B$429.3B7.B14.3B$428.3B13.3B7.B$428.3B
12.3B13.3B$428.B14.3B12.3B$433.3B7.B14.3B$432.3B13.3B7.B$432.3B12.3B
13.3B$432.B14.3B12.3B$437.3B7.B14.3B$436.3B13.3B7.B$436.3B12.3B13.3B$
436.B14.3B12.3B$441.3B7.B14.3B$440.3B13.3B7.B$440.3B12.3B13.3B$440.B
14.3B12.3B$445.3B7.B14.3B$444.3B13.3B7.B$444.3B12.3B13.3B$444.B14.3B
12.3B$449.3B7.B14.3B$448.3B13.3B7.B$448.3B12.3B13.3B$448.B14.3B12.3B$
453.3B7.B14.3B$452.3B13.3B7.B$452.3B12.3B13.3B$452.B14.3B12.3B$457.3B
7.B14.3B$456.3B13.3B7.B$456.3B12.3B13.3B$456.B14.3B12.3B$461.3B7.B14.
3B$460.3B13.3B7.B$460.3B12.3B13.3B$460.B14.3B12.3B$465.3B7.B14.3B$
464.3B13.3B7.B$464.3B12.3B13.3B$464.B14.3B12.3B$469.3B7.B14.3B$468.3B
13.3B7.B$468.3B12.3B13.3B$468.B14.3B12.3B$473.3B7.B14.3B$472.3B13.3B
7.B$472.3B12.3B13.3B$472.B14.3B12.3B$477.3B7.B14.3B$476.3B13.3B7.B$
476.3B12.3B13.3B$476.B14.3B12.3B$481.3B7.B14.3B$480.3B13.3B7.B$480.3B
12.3B13.3B$480.B14.3B12.3B$485.3B7.B14.3B$484.3B13.3B7.B$484.3B12.3B
13.3B$484.B14.3B12.3B$489.3B7.B14.3B$488.3B13.3B7.B$488.3B12.3B13.3B$
488.B14.3B12.3B$493.3B7.B14.3B$492.3B13.3B7.B$492.3B12.3B13.3B$492.B
14.3B12.3B$497.3B7.B14.3B$496.3B13.3B7.B$496.3B12.3B13.3B$496.B14.3B
12.3B$501.3B7.B14.3B$500.3B13.3B7.B$500.3B12.3B13.3B$500.B14.3B12.3B$
505.3B7.B14.3B$504.3B13.3B7.B$504.3B12.3B13.3B$504.B14.3B12.3B$509.3B
7.B14.3B$508.3B13.3B7.B$508.3B12.3B13.3B$508.B14.3B12.3B$513.3B7.B14.
3B$512.3B13.3B7.B$512.3B12.3B13.3B$512.B14.3B12.3B$517.3B7.B14.3B$
516.3B13.3B7.B$516.3B12.3B13.3B$516.B14.3B12.3B$521.3B7.B14.3B$520.3B
13.3B7.B$520.3B12.3B13.3B$520.B14.3B12.3B$525.3B7.B14.3B$524.3B13.3B
7.B$524.3B12.3B13.3B$524.B14.3B12.3B$529.3B7.B14.3B$528.3B13.3B7.B$
528.3B12.3B13.3B$528.B14.3B12.3B$533.3B7.B14.3B$532.3B13.3B7.B$532.3B
12.3B13.3B$532.B14.3B12.3B$537.3B7.B14.3B$536.3B13.3B7.B$536.3B12.3B
13.3B$536.B14.3B12.3B$541.3B7.B14.3B$540.3B13.3B7.B$540.3B12.3B13.3B$
540.B14.3B12.3B$545.3B7.B14.3B$544.3B13.3B7.B$544.3B12.3B13.3B$544.B
14.3B12.3B$549.3B7.B14.3B$548.3B13.3B7.B$548.3B12.3B13.3B$548.B14.3B
12.3B$553.3B7.B14.3B$552.3B13.3B7.B$552.3B12.3B13.3B$552.B14.3B12.3B$
557.3B7.B14.3B$556.3B13.3B7.B$556.3B12.3B13.3B$556.B14.3B12.3B$561.3B
7.B14.3B$560.3B13.3B7.B$560.3B12.3B13.3B$560.B14.3B12.3B$565.3B7.B14.
3B$564.3B13.3B7.B$564.3B12.3B13.3B$564.B14.3B12.3B$569.3B7.B14.3B$
568.3B13.3B7.B$568.3B12.3B13.3B$568.B14.3B12.3B$573.3B7.B14.3B$572.3B
13.3B7.B$572.3B12.3B13.3B$572.B14.3B12.3B$577.3B7.B14.3B$576.3B13.3B
7.B$576.3B12.3B13.3B$576.B14.3B12.3B$581.3B7.B14.3B$580.3B13.3B7.B$
580.3B12.3B13.3B$580.B14.3B12.3B$585.3B7.B14.3B$584.3B13.3B7.B$584.3B
12.3B13.3B$584.B14.3B12.3B$589.3B7.B14.3B$588.3B13.3B7.B$588.3B12.3B
13.3B$588.B14.3B12.3B$593.3B7.B14.3B$592.3B13.3B7.B$592.3B12.3B13.3B$
592.B14.3B12.3B$597.3B7.B14.3B$596.3B13.3B7.B$596.3B12.3B13.3B$596.B
14.3B12.3B$601.3B7.B14.3B$600.3B13.3B7.B$600.3B12.3B13.3B$600.B14.3B
12.3B$605.3B7.B14.3B$604.3B13.3B7.B$604.3B12.3B13.3B$604.B14.3B12.3B$
609.3B7.B14.3B$608.3B13.3B7.B$608.3B12.3B13.3B$608.B14.3B12.3B$613.3B
7.B14.3B$612.3B13.3B7.B$612.3B12.3B13.3B$612.B14.3B12.3B$617.3B7.B14.
3B$616.3B13.3B7.B$616.3B12.3B13.3B$616.B14.3B12.3B$621.3B7.B14.3B$
620.3B13.3B7.B$620.3B12.3B13.3B$620.B14.3B12.3B$625.3B7.B14.3B$624.3B
13.3B7.B$624.3B12.3B13.3B$624.B14.3B12.3B$629.3B7.B14.3B$628.3B13.3B
7.B$628.3B12.3B13.3B$628.B14.3B12.3B$633.3B7.B14.3B$632.3B13.3B7.B$
632.3B12.3B13.3B$632.B14.3B12.3B$637.3B7.B14.3B$636.3B13.3B7.B$636.3B
12.3B13.3B$636.B14.3B12.3B$641.3B7.B14.3B$640.3B13.3B7.B$640.3B12.3B
13.3B$640.B14.3B12.3B$645.3B7.B14.3B$644.3B13.3B7.B$644.3B12.3B13.3B$
644.B14.3B12.3B$649.3B7.B14.3B$648.3B13.3B7.B$648.3B12.3B13.3B$648.B
14.3B12.3B$653.3B7.B14.3B$652.3B13.3B7.B$652.3B12.3B13.3B$652.B14.3B
12.3B$657.3B7.B14.3B$656.3B13.3B7.B$656.3B12.3B13.3B$656.B14.3B12.3B$
661.3B7.B14.3B$660.3B13.3B7.B$660.3B12.3B13.3B$660.B14.3B12.3B$665.3B
7.B14.3B$664.3B13.3B7.B$664.3B12.3B13.3B$664.B14.3B12.3B$669.3B7.B14.
3B$668.3B13.3B7.B$668.3B12.3B13.3B$668.B14.3B12.3B$673.3B7.B14.3B$
672.3B13.3B7.B$672.3B12.3B13.3B$672.B14.3B12.3B$677.3B7.B14.3B$676.3B
13.3B7.B$676.3B12.3B13.3B$676.B14.3B12.3B$681.3B7.B14.3B$680.3B13.3B
7.B$680.3B12.3B13.3B$680.B14.3B12.3B$685.3B7.B14.3B$684.3B13.3B7.B$
684.3B12.3B13.3B$684.B14.3B12.3B$689.3B7.B14.3B$688.3B13.3B7.B$688.3B
12.3B13.3B$688.B14.3B12.3B$693.3B7.B14.3B$692.3B13.3B7.B$692.3B12.3B
13.3B$692.B14.3B12.3B$697.3B7.B14.3B$696.3B13.3B7.B$696.3B12.3B13.3B$
696.B14.3B12.3B$701.3B7.B14.3B$700.3B13.3B7.B$700.3B12.3B13.3B$700.B
14.3B12.3B$705.3B7.B14.3B$704.3B13.3B7.B$704.3B12.3B13.3B$704.B14.3B
12.3B$709.3B7.B14.3B$708.3B13.3B7.B$708.3B12.3B13.3B$708.B14.3B12.3B$
713.3B7.B14.3B$712.3B13.3B7.B$712.3B12.3B13.3B$712.B14.3B12.3B$717.3B
7.B14.3B$716.3B13.3B7.B$716.3B12.3B13.3B$716.B14.3B12.3B$721.3B7.B14.
3B$720.3B13.3B7.B$720.3B12.3B13.3B$720.B14.3B12.3B$725.3B7.B14.3B$
724.3B13.3B7.B$724.3B12.3B13.3B$724.B14.3B12.3B$729.3B7.B14.3B$728.3B
13.3B7.B$728.3B12.3B13.3B$728.B14.3B12.3B$733.3B7.B14.3B$732.3B13.3B
7.B$732.3B12.3B13.3B$732.B14.3B12.3B$737.3B7.B14.3B$736.3B13.3B7.B$
736.3B12.3B13.3B$736.B14.3B12.3B$741.3B7.B14.3B$740.3B13.3B7.B$740.3B
12.3B13.3B$740.B14.3B12.3B$745.3B7.B14.3B$744.3B13.3B7.B$744.3B12.3B
13.3B$744.B14.3B12.3B$749.3B7.B14.3B$748.3B13.3B7.B$748.3B12.3B13.3B$
748.B14.3B12.3B$753.3B7.B14.3B$752.3B13.3B7.B$752.3B12.3B13.3B$752.B
14.3B12.3B$757.3B7.B14.3B$756.3B13.3B7.B$756.3B12.3B13.3B$756.B14.3B
12.3B$761.3B7.B14.3B$760.3B13.3B7.B$760.3B12.3B13.3B$760.B14.3B12.3B$
765.3B7.B14.3B$764.3B13.3B7.B$764.3B12.3B13.3B$764.B14.3B12.3B$769.3B
7.B14.3B$768.3B13.3B7.B$768.3B12.3B13.3B$768.B14.3B12.3B$773.3B7.B14.
3B$772.3B13.3B7.B$772.3B12.3B13.3B$772.B14.3B12.3B$777.3B7.B14.3B$
776.3B13.3B7.B$776.3B12.3B13.3B$776.B14.3B12.3B$781.3B7.B14.3B$780.3B
13.3B7.B$780.3B12.3B13.3B$780.B14.3B12.3B$785.3B7.B14.3B$784.3B13.3B
7.B$784.3B12.3B13.3B$784.B14.3B12.3B$789.3B7.B14.3B$788.3B13.3B7.B$
788.3B12.3B13.3B$788.B14.3B12.3B$793.3B7.B14.3B$792.3B13.3B7.B$792.3B
12.3B13.3B$792.B14.3B12.3B$797.3B7.B14.3B$796.3B13.3B7.B$796.3B12.3B
13.3B$796.B14.3B12.3B$801.3B7.B14.3B$800.3B13.3B7.B$800.3B12.3B13.3B$
800.B14.3B12.3B$805.3B7.B14.3B$804.3B13.3B7.B$804.3B12.3B13.3B$804.B
14.3B12.3B$809.3B7.B14.3B$808.3B13.3B7.B$808.3B12.3B13.3B$808.B14.3B
12.3B$813.3B7.B14.3B$812.3B13.3B7.B$812.3B12.3B13.3B$812.B14.3B12.3B$
817.3B7.B14.3B$816.3B13.3B7.B$816.3B12.3B13.3B$816.B14.3B12.3B$821.3B
7.B14.3B$820.3B13.3B7.B$820.3B12.3B13.3B$820.B14.3B12.3B$825.3B7.B14.
3B$824.3B13.3B7.B$824.3B12.3B13.3B$824.B14.3B12.3B$829.3B7.B14.3B$
828.3B13.3B7.B$828.3B12.3B13.3B$828.B14.3B12.3B$833.3B7.B14.3B$832.3B
13.3B7.B$832.3B12.3B13.3B$832.B14.3B12.3B$837.3B7.B14.3B$836.3B13.3B
7.B$836.3B12.3B13.3B$836.B14.3B12.3B$841.3B7.B14.3B$840.3B13.3B7.B$
840.3B12.3B13.3B$840.B14.3B12.3B$845.3B7.B14.3B$844.3B13.3B7.B$844.3B
12.3B13.3B$844.B14.3B12.3B$849.3B7.B14.3B$848.3B13.3B7.B$848.3B12.3B
13.3B$848.B14.3B12.3B$853.3B7.B14.3B$852.3B13.3B7.B$852.3B12.3B13.3B$
852.B14.3B12.3B$857.3B7.B14.3B$856.3B13.3B7.B$856.3B12.3B13.3B$856.B
14.3B12.3B$861.3B7.B14.3B$860.3B13.3B7.B$860.3B12.3B13.3B$860.B14.3B
12.3B$865.3B7.B14.3B$864.3B13.3B7.B$864.3B12.3B13.3B$864.B14.3B12.3B$
869.3B7.B14.3B$868.3B13.3B7.B$868.3B12.3B13.3B$868.B14.3B12.3B$873.3B
7.B14.3B$872.3B13.3B7.B$872.3B12.3B13.3B$872.B14.3B12.3B$877.3B7.B14.
3B$876.3B13.3B7.B$876.3B12.3B13.3B$876.B14.3B12.3B$881.3B7.B14.3B$
880.3B13.3B7.B$880.3B12.3B13.3B$880.B14.3B12.3B$885.3B7.B14.3B$884.3B
13.3B7.B$884.3B12.3B13.3B$884.B14.3B12.3B$889.3B7.B14.3B$888.3B13.3B
7.B$888.3B12.3B13.3B$888.B14.3B12.3B$893.3B7.B14.3B$892.3B13.3B7.B$
892.3B12.3B13.3B$892.B14.3B12.3B$897.3B7.B14.3B$896.3B13.3B7.B$896.3B
12.3B13.3B$896.B14.3B12.3B$901.3B7.B14.3B$900.3B13.3B7.B$900.3B12.3B
13.3B$900.B14.3B12.3B$905.3B7.B14.3B$904.3B13.3B7.B$904.3B12.3B13.3B$
904.B14.3B12.3B$909.3B7.B14.3B$908.3B13.3B7.B$908.3B12.3B13.3B$908.B
14.3B12.3B$913.3B7.B14.3B$912.3B13.3B7.B$912.3B12.3B13.3B$912.B14.3B
12.3B$917.3B7.B14.3B$916.3B13.3B7.B$916.3B12.3B13.3B$916.B14.3B12.3B$
921.3B7.B14.3B$920.3B13.3B7.B$920.3B12.3B13.3B$920.B14.3B12.3B$925.3B
7.B14.3B$924.3B13.3B7.B$924.3B12.3B13.3B$924.B14.3B12.3B$929.3B7.B14.
3B$928.3B13.3B7.B$928.3B12.3B13.3B$928.B14.3B12.3B$933.3B7.B14.3B$
932.3B13.3B7.B$932.3B12.3B13.3B$932.B14.3B12.3B$937.3B7.B14.3B$936.3B
13.3B7.B$936.3B12.3B13.3B$936.B14.3B12.3B$941.3B7.B14.3B$940.3B13.3B
7.B$940.3B12.3B13.3B$940.B14.3B12.3B$945.3B7.B14.3B$944.3B13.3B7.B$
944.3B12.3B13.3B$944.B14.3B12.3B$949.3B7.B14.3B$948.3B13.3B7.B$948.3B
12.3B13.3B$948.B14.3B12.3B$953.3B7.B14.3B$952.3B13.3B7.B$952.3B12.3B
13.3B$952.B14.3B12.3B$957.3B7.B14.3B$956.3B13.3B7.B$956.3B12.3B13.3B$
956.B14.3B12.3B$961.3B7.B14.3B$960.3B13.3B7.B$960.3B12.3B13.3B$960.B
14.3B12.3B$965.3B7.B14.3B$964.3B13.3B7.B$964.3B12.3B13.3B$964.B14.3B
12.3B$969.3B7.B14.3B$968.3B13.3B7.B$968.3B12.3B13.3B$968.B14.3B12.3B$
973.3B7.B14.3B$972.3B13.3B7.B$972.3B12.3B13.3B$972.B14.3B12.3B$977.3B
7.B14.3B$976.3B13.3B7.B$976.3B12.3B13.3B$976.B14.3B12.3B$981.3B7.B14.
3B$980.3B13.3B7.B$980.3B12.3B13.3B$980.B14.3B12.3B$985.3B7.B14.3B$
984.3B13.3B7.B$984.3B12.3B13.3B$984.B14.3B12.3B$989.3B7.B14.3B$988.3B
13.3B7.B$988.3B12.3B13.3B$988.B14.3B12.3B$993.3B7.B14.3B$992.3B13.3B
7.B$992.3B12.3B13.3B$992.B14.3B12.3B$997.3B7.B14.3B$996.3B13.3B7.B$
996.3B12.3B13.3B$996.B14.3B12.3B$1001.3B7.B14.3B$1000.3B13.3B7.B$
1000.3B12.3B$1000.B14.3B$1005.3B7.B$1004.3B$1004.3B$1004.B$1009.3B$
1008.3B$1008.3B$1008.B$1013.3B$1012.3B$1012.3B$1012.B!
Re: Universality proof question
So, I made something similar to sliding block memory. It is extremely ugly and practically useless, but at least it works, and probably proves that this rule is Turing complete.
Construction:
I'll try to explain how it works:
There are three puffers: A, B and C. A has period of 256, B and C  128.
Glider streams from B and C collide, using reaction A for awesome found, resulting in period 256 stream B/C.
Single block is pulled by both glider stream from A and B/C. Since both streams have same period, it stays in place.
It can be incremented by skipping one glider in B/C stream and decremented by skipping one in C.
You can check if block is in particular position using this reaction:
Construction:
Code: Select all
x = 2815, y = 2943, rule = BTCA1
15.3B$14.3B$14.3B$14.B$11.3A5.3B$11.3A4.3B$11.3A4.3B$8.3B7.B$7.3B13.
3B$7.3B12.3B$7.B14.3B$4.3A5.3B7.B$4.3A4.3B13.3B$4.3A4.3B12.3B$.3B7.B
14.3B$3B13.3B7.B$3B12.3B13.3B$B14.3B12.3B$5.3B7.B14.3B$4.3B13.3B7.B$
4.3B12.3B13.3B$4.B14.3B12.3B$9.3B7.B14.3B$8.3B13.3B7.B$8.3B12.3B13.3B
$8.B14.3B12.3B$13.3B7.B14.3B$12.3B13.3B7.B$12.3B12.3B13.3B$12.B14.3B
12.3B$17.3B7.B14.3B$16.3B13.3B7.B$16.3B12.3B13.3B$16.B14.3B12.3B$21.
3B7.B14.3B$20.3B13.3B7.B$20.3B12.3B13.3B$20.B14.3B12.3B$25.3B7.B14.3B
$24.3B13.3B7.B$24.3B12.3B13.3B$24.B14.3B12.3B$29.3B7.B14.3B$28.3B13.
3B7.B$28.3B12.3B13.3B$28.B14.3B12.3B$33.3B7.B14.3B$32.3B13.3B7.B$32.
3B12.3B13.3B$32.B14.3B12.3B$37.3B7.B14.3B$36.3B13.3B7.B$36.3B12.3B13.
3B$36.B14.3B12.3B$41.3B7.B14.3B$40.3B13.3B7.B$40.3B12.3B13.3B$40.B14.
3B12.3B$45.3B7.B14.3B$44.3B13.3B7.B$44.3B12.3B13.3B$44.B14.3B12.3B$
49.3B7.B14.3B$48.3B13.3B7.B$48.3B12.3B13.3B$48.B14.3B12.3B$53.3B7.B
14.3B$52.3B13.3B7.B$52.3B12.3B13.3B$52.B14.3B12.3B$57.3B7.B14.3B$56.
3B13.3B7.B$56.3B12.3B13.3B$56.B14.3B12.3B$61.3B7.B14.3B$60.3B13.3B7.B
$60.3B12.3B13.3B$60.B14.3B12.3B$65.3B7.B14.3B$64.3B13.3B7.B$64.3B12.
3B13.3B$64.B14.3B12.3B$69.3B7.B14.3B$68.3B13.3B7.B$68.3B12.3B13.3B$
68.B14.3B12.3B$73.3B7.B14.3B$72.3B13.3B7.B$72.3B12.3B13.3B$72.B14.3B
12.3B$77.3B7.B14.3B$76.3B13.3B7.B$76.3B12.3B13.3B$76.B14.3B12.3B$81.
3B7.B14.3B$80.3B13.3B7.B$80.3B12.3B13.3B$80.B14.3B12.3B$85.3B7.B14.3B
$84.3B13.3B7.B$84.3B12.3B13.3B$84.B14.3B12.3B$89.3B7.B14.3B$88.3B13.
3B7.B$88.3B12.3B13.3B$88.B14.3B12.3B$93.3B7.B14.3B$92.3B13.3B7.B$92.
3B12.3B13.3B$92.B14.3B12.3B$97.3B7.B14.3B$96.3B13.3B7.B$96.3B12.3B13.
3B$96.B14.3B12.3B$101.3B7.B14.3B$100.3B13.3B7.B$100.3B12.3B13.3B$100.
B14.3B12.3B$105.3B7.B14.3B$104.3B13.3B7.B$104.3B12.3B13.3B$104.B14.3B
12.3B$109.3B7.B14.3B$108.3B13.3B7.B$108.3B12.3B13.3B$108.B14.3B12.3B$
113.3B7.B14.3B$112.3B13.3B7.B$112.3B12.3B13.3B$112.B14.3B12.3B$117.3B
7.B14.3B$116.3B13.3B7.B$116.3B12.3B13.3B$116.B14.3B12.3B$121.3B7.B14.
3B$120.3B13.3B7.B$120.3B12.3B13.3B$120.B14.3B12.3B$125.3B7.B14.3B$
124.3B13.3B7.B$124.3B12.3B13.3B$124.B14.3B12.3B$129.3B7.B14.3B$128.3B
13.3B7.B$128.3B12.3B13.3B$128.B14.3B12.3B$133.3B7.B14.3B$132.3B13.3B
7.B$132.3B12.3B13.3B$132.B14.3B12.3B$137.3B7.B14.3B$136.3B13.3B7.B$
136.3B12.3B13.3B$136.B14.3B12.3B$141.3B7.B14.3B$140.3B13.3B7.B$140.3B
12.3B13.3B$140.B14.3B12.3B$145.3B7.B14.3B$144.3B13.3B7.B$144.3B12.3B
13.3B$144.B14.3B12.3B$149.3B7.B14.3B$148.3B13.3B7.B$148.3B12.3B13.3B$
148.B14.3B12.3B$153.3B7.B14.3B$152.3B13.3B7.B$152.3B12.3B13.3B$152.B
14.3B12.3B$157.3B7.B14.3B$156.3B13.3B7.B$156.3B12.3B13.3B$156.B14.3B
12.3B$161.3B7.B14.3B$160.3B13.3B7.B$160.3B12.3B13.3B$160.B14.3B12.3B$
165.3B7.B14.3B$164.3B13.3B7.B$164.3B12.3B13.3B$164.B14.3B12.3B$169.3B
7.B14.3B$168.3B13.3B7.B$168.3B12.3B13.3B$168.B14.3B12.3B$173.3B7.B14.
3B$172.3B13.3B7.B$172.3B12.3B13.3B$172.B14.3B12.3B$177.3B7.B14.3B$
176.3B13.3B7.B$176.3B12.3B13.3B$176.B14.3B12.3B$181.3B7.B14.3B$180.3B
13.3B7.B$180.3B12.3B13.3B$180.B14.3B12.3B$185.3B7.B14.3B$184.3B13.3B
7.B$184.3B12.3B13.3B$184.B14.3B12.3B$189.3B7.B14.3B$188.3B13.3B7.B$
188.3B12.3B13.3B$188.B14.3B12.3B$193.3B7.B14.3B$192.3B13.3B7.B$192.3B
12.3B13.3B$192.B14.3B12.3B$197.3B7.B14.3B$196.3B13.3B7.B$196.3B12.3B
13.3B$196.B14.3B12.3B$201.3B7.B14.3B$200.3B13.3B7.B$200.3B12.3B13.3B$
200.B14.3B12.3B$205.3B7.B14.3B$204.3B13.3B7.B$204.3B12.3B13.3B$204.B
14.3B12.3B$209.3B7.B14.3B$208.3B13.3B7.B$208.3B12.3B13.3B$208.B14.3B
12.3B$213.3B7.B14.3B$212.3B13.3B7.B$212.3B12.3B13.3B$212.B14.3B12.3B$
217.3B7.B14.3B$216.3B13.3B7.B$216.3B12.3B13.3B$216.B14.3B12.3B$221.3B
7.B14.3B$220.3B13.3B7.B$220.3B12.3B13.3B$220.B14.3B12.3B$225.3B7.B14.
3B$224.3B13.3B7.B$224.3B12.3B13.3B$224.B14.3B12.3B$229.3B7.B14.3B$
228.3B13.3B7.B$228.3B12.3B13.3B$228.B14.3B12.3B$233.3B7.B14.3B$232.3B
13.3B7.B$232.3B12.3B$232.B14.3B$237.3B7.B$236.3B$236.3B$236.B$241.3B$
240.3B$240.3B$240.B$245.3B$244.3B$244.3B$244.B1306$1567.2A$1567.2A
1113$2696.AB$2695.A3B$2695.3B$2696.B$2700.AB$2699.A3B$2699.3B$2700.B$
2704.AB$2703.A3B$2703.3B$2693.AB9.B$2692.A3B12.AB$2692.3B12.A3B$2682.
AB9.B13.3B$2681.A3B12.AB9.B$2681.3B12.A3B12.AB$2682.B13.3B12.A3B$
2686.AB9.B13.3B$2685.A3B12.AB9.B$2685.3B12.A3B12.AB$2686.B13.3B12.A3B
$2690.AB9.B13.3B$2689.A3B12.AB9.B$2689.3B12.A3B12.AB$2690.B13.3B12.A
3B$2694.AB9.B13.3B$2693.A3B12.AB9.B$2693.3B12.A3B12.AB$2694.B13.3B12.
A3B$2698.AB9.B13.3B$2697.A3B12.AB9.B$2697.3B12.A3B12.AB$2698.B13.3B
12.A3B$2702.AB9.B13.3B$2701.A3B12.AB9.B$2701.3B12.A3B12.AB$2702.B13.
3B12.A3B$2706.AB9.B13.3B$2705.A3B12.AB9.B$2705.3B12.A3B12.AB$2706.B
13.3B12.A3B$2710.AB9.B13.3B$2709.A3B12.AB9.B$2709.3B12.A3B12.AB$2710.
B13.3B12.A3B$2714.AB9.B13.3B$2713.A3B12.AB9.B$2713.3B12.A3B12.AB$
2714.B13.3B12.A3B$2718.AB9.B13.3B$2717.A3B12.AB9.B$2717.3B12.A3B12.AB
$2718.B13.3B12.A3B$2722.AB9.B13.3B$2721.A3B12.AB9.B$2721.3B12.A3B12.A
B$2722.B13.3B12.A3B$2726.AB9.B13.3B$2725.A3B12.AB9.B$2725.3B12.A3B12.
AB$2726.B13.3B12.A3B$2730.AB9.B13.3B$2729.A3B12.AB9.B$2729.3B12.A3B
12.AB$2730.B13.3B12.A3B$2734.AB9.B13.3B$2733.A3B12.AB9.B$2733.3B12.A
3B12.AB$2734.B13.3B12.A3B$2738.AB9.B13.3B$2737.A3B12.AB9.B$2737.3B12.
A3B12.AB$2738.B13.3B12.A3B$2742.AB9.B13.3B$2741.A3B12.AB9.B$2741.3B
12.A3B12.AB$2742.B13.3B12.A3B$2746.AB9.B13.3B$2745.A3B12.AB9.B$2745.
3B12.A3B12.AB$2746.B13.3B12.A3B$2750.AB9.B13.3B$2749.A3B12.AB9.B$
2749.3B12.A3B12.AB$2750.B13.3B12.A3B$2754.AB9.B13.3B$2753.A3B12.AB9.B
$2753.3B12.A3B12.AB$2754.B13.3B12.A3B$2758.AB9.B13.3B$2757.A3B12.AB9.
B$2757.3B12.A3B12.AB$2758.B13.3B12.A3B$2762.AB9.B13.3B$2761.A3B12.AB
9.B$2761.3B12.A3B12.AB$2762.B13.3B12.A3B$2766.AB9.B13.3B$2765.A3B12.A
B9.B$2765.3B12.A3B12.AB$2766.B13.3B12.A3B$2770.AB9.B13.3B$2769.A3B12.
AB9.B$2769.3B12.A3B12.AB$2770.B13.3B12.A3B$2774.AB9.B13.3B$2773.A3B
12.AB9.B$2773.3B12.A3B12.AB$2774.B13.3B12.A3B$2778.AB9.B13.3B$2777.A
3B12.AB9.B$2777.3B12.A3B12.AB$2778.B13.3B12.A3B$2782.AB9.B13.3B$2781.
A3B12.AB9.B$2781.3B12.A3B12.AB$2782.B13.3B12.A3B$2786.AB9.B9.A3.3B$
2785.A3B12.AB3.4A2.B$2785.3B12.A3B3.ABA$2786.B13.3B4.4A$2790.AB9.B7.A
$2789.A3B12.AB$2789.3B12.A3B$2790.B9.A3.3B$2794.AB3.4A2.B$2793.A3B3.A
BA$1358.B1434.3B4.4A$1358.3B1433.B7.A$1358.3B1437.AB$1359.3B1435.A3B$
1354.B1442.3B$1354.3B1441.B$1354.3B$1355.3B$1350.B$1350.3B$1350.3B$
1351.3B7.B$1346.B14.3B$1346.3B12.3B$1346.3B13.3B7.B$1347.3B7.B14.3B$
1342.B14.3B12.3B$1342.3B12.3B13.3B$1342.3B13.3B7.B$1343.3B7.B14.3B$
1338.B14.3B12.3B$1338.3B12.3B13.3B$1338.3B13.3B7.B$1339.3B7.B14.3B$
1334.B14.3B12.3B$1334.3B12.3B13.3B$1334.3B13.3B7.B$1335.3B7.B14.3B$
1330.B14.3B12.3B$1330.3B12.3B13.3B$1330.3B13.3B7.B$1331.3B7.B14.3B$
1326.B14.3B12.3B$1326.3B12.3B13.3B$1326.3B13.3B7.B$1327.3B7.B14.3B$
1322.B14.3B12.3B$1322.3B12.3B13.3B$1322.3B13.3B7.B$1323.3B7.B14.3B$
1318.B14.3B12.3B$1318.3B12.3B13.3B$1318.3B13.3B7.B$1319.3B7.B14.3B$
1314.B14.3B12.3B$1314.3B12.3B13.3B$1314.3B13.3B7.B$1315.3B7.B14.3B$
1310.B14.3B12.3B$1310.3B12.3B13.3B$1310.3B13.3B7.B$1311.3B7.B14.3B$
1306.B14.3B12.3B$1306.3B12.3B13.3B$1306.3B13.3B7.B$1307.3B7.B14.3B$
1302.B14.3B12.3B$1302.3B12.3B13.3B$1302.3B13.3B7.B$1303.3B7.B14.3B$
1298.B14.3B12.3B$1298.3B12.3B13.3B$1298.3B13.3B7.B$1299.3B7.B14.3B$
1294.B14.3B12.3B$1294.3B12.3B13.3B$1294.3B13.3B7.B$1295.3B7.B14.3B$
1290.B14.3B12.3B$1290.3B12.3B13.3B$1290.3B13.3B7.B$1291.3B7.B14.3B$
1286.B14.3B12.3B$1286.3B12.3B13.3B$1286.3B13.3B7.B$1287.3B7.B14.3B$
1282.B14.3B12.3B$1282.3B12.3B13.3B$1282.3B13.3B7.B$1283.3B7.B14.3B$
1278.B14.3B12.3B$1278.3B12.3B13.3B$1278.3B13.3B7.B$1279.3B7.B14.3B$
1274.B14.3B12.3B$1274.3B12.3B13.3B$1274.3B13.3B7.B$1275.3B7.B14.3B$
1270.B14.3B12.3B$1270.3B12.3B13.3B$1270.3B13.3B7.B$1271.3B7.B14.3B$
1266.B14.3B12.3B$1266.3B12.3B13.3B$1266.3B13.3B7.B$1267.3B7.B14.3B$
1262.B14.3B12.3B$1262.3B12.3B13.3B$1262.3B13.3B7.B$1263.3B7.B14.3B$
1258.B14.3B12.3B$1258.3B12.3B13.3B$1258.3B13.3B7.B$1259.3B7.B14.3B$
1254.B14.3B12.3B$1254.3B12.3B13.3B$1254.3B13.3B7.B$1255.3B7.B14.3B$
1250.B14.3B12.3B$1250.3B12.3B13.3B$1250.3B13.3B7.B$1251.3B7.B14.3B$
1246.B14.3B12.3B$1246.3B12.3B13.3B$1246.3B13.3B7.B$1247.3B7.B14.3B$
1242.B14.3B12.3B$1242.3B12.3B13.3B$1242.3B3.3A7.3B7.B$1243.3B2.3A2.B
14.3B$1246.5A2.3B12.3B$1246.3A4.3B13.3B$1246.3A5.3B7.B$1249.B14.3B$
1249.3B12.3B$1249.3B3.3A7.3B$1250.3B2.3A2.B$1253.5A2.3B$1253.3A4.3B$
1253.3A5.3B$1256.B$1256.3B$1256.3B$1257.3B!
There are three puffers: A, B and C. A has period of 256, B and C  128.
Glider streams from B and C collide, using reaction A for awesome found, resulting in period 256 stream B/C.
Single block is pulled by both glider stream from A and B/C. Since both streams have same period, it stays in place.
It can be incremented by skipping one glider in B/C stream and decremented by skipping one in C.
You can check if block is in particular position using this reaction:
Code: Select all
x = 24, y = 29, rule = BTCA1
20.B$20.3B$20.3B$21.3B15$2.B$2.3B$2.3B$3.3B6$2A$2A!

 Posts: 566
 Joined: May 31st, 2009, 12:08 am
Re: Universality proof question
Spaceship converter is periodic:
Stream shown is p560 but could be lower period. The p70 osc can be increased by 12n (n=1,2,3...) and possibly decreased. Other combinations of periods may be possible because the reflector on one end of the osc can be a different phase giving +/ 6n possibilities.
Code: Select all
x = 119, y = 23, rule = BTCA1
101.B$99.3B$100.3B$97.B.AB$97.3B$96.3B$98.B4$107.3A$.B31.B33.B30.2B6.
3A$3B31.2B29.3B29.BA2B5.3A$4B26.B3.2B27.2B2A2B28.4B5.A$4B26.B3.2B27.
2B2A2B28.4B$3B31.2B29.3B29.BA2B$.B31.B33.B30.2B17.B$115.3B$116.3B$
113.B.AB$113.3B$112.3B$114.B!