KnightLife

Tropylium · Post by **Tropylium** » September 11th, 2012, 4:30 pm

As first discussed in this topic, this is a CA family that uses the neighborhood of a chess knight:

.*.*.
*...*
..O..
*...*
.*.*.

Here's a probably incredibly inefficient ruletable that still at least does the job it's supposed to. Currently set to B3/S0123. Save as knightlife.table:

Edit: fixed a bug in the behavior of B3.

Code: Select all

n_states:32
neighborhood:Moore
symmetries:none

var a = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31}
var b = {a}
var c = {a}
var d = {a}
var e = {a}
var f = {a}
var g = {a}
var h = {a}
#dead states
var i = {0,4,6,8,10,12,14,16,18,20,22,24,26,28,30,2}
#live states
var j = {1,5,7,9,11,13,15,17,19,21,23,25,27,29,31,3}
#2 from NE
var k = {8,9,16,17,24,25,2,3}
#2 from SE
var l = {14,15,16,17,30,31,2,3}
#2 from SW
var m = {26,27,28,29,30,31,2,3}
#2 from NW
var n = {20,21,24,25,28,29,2,3}
#1 from NE
var o = {4,5,6,7,12,13,14,15,20,21,22,23,28,29,30,31}
#1 from SE
var p = {6,7,8,9,10,11,12,13,22,23,24,25,26,27,28,29}
#1 from SW
var q = {10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}
#1 from NW
var r = {4,5,8,9,12,13,16,17,18,19,22,23,26,27,30,31}
# 0 from NE
var s = {0,1,10,11,18,19,26,27}
# 0 from SE
var t = {0,1,4,5,18,19,20,21}
# 0 from SW
var u = {0,1,4,5,6,7,8,9}
# 0 from NW
var v = {0,1,6,7,10,11,14,15}

# B2
# 2 from same secondary
#i,a,k,b,t,c,u,d,v,1
#i,a,s,b,l,c,u,d,v,1
#i,a,s,b,t,c,m,d,v,1
#i,a,s,b,t,c,u,d,n,1
# 1+1 from two different secondaries
#i,a,o,b,p,c,u,d,v,1
#i,a,o,b,t,c,q,d,v,1
#i,a,o,b,t,c,u,d,r,1
#i,a,s,b,p,c,q,d,v,1
#i,a,s,b,p,c,u,d,r,1
#i,a,s,b,t,c,q,d,r,1

# B3
# 2+1
i,a,o,b,l,c,u,d,v,1
i,a,k,b,p,c,u,d,v,1
i,a,o,b,t,c,m,d,v,1
i,a,k,b,t,c,q,d,v,1
i,a,o,b,t,c,u,d,n,1
i,a,k,b,t,c,u,d,r,1
i,a,s,b,p,c,m,d,v,1
i,a,s,b,l,c,q,d,v,1
i,a,s,b,p,c,u,d,n,1
i,a,s,b,l,c,u,d,r,1
i,a,s,b,t,c,q,d,n,1
i,a,s,b,t,c,m,d,r,1
# 1+1+1
i,a,o,b,p,c,q,d,v,1
i,a,o,b,p,c,u,d,r,1
i,a,o,b,t,c,q,d,r,1
i,a,s,b,p,c,q,d,r,1

# Extrude phase
# has orth neighbors in:
# N   E   S   W
0,0,a,0,b,0,c,0,d,0
1,0,a,0,b,0,c,0,d,1
0,1,a,0,b,0,c,0,d,4
1,1,a,0,b,0,c,0,d,5
0,0,a,1,b,0,c,0,d,6
1,0,a,1,b,0,c,0,d,7
0,1,a,1,b,0,c,0,d,8
1,1,a,1,b,0,c,0,d,9
0,0,a,0,b,1,c,0,d,10
1,0,a,0,b,1,c,0,d,11
0,1,a,0,b,1,c,0,d,12
1,1,a,0,b,1,c,0,d,13
0,0,a,1,b,1,c,0,d,14
1,0,a,1,b,1,c,0,d,15
0,1,a,1,b,1,c,0,d,16
1,1,a,1,b,1,c,0,d,17
0,0,a,0,b,0,c,1,d,18
1,0,a,0,b,0,c,1,d,19
0,1,a,0,b,0,c,1,d,20
1,1,a,0,b,0,c,1,d,21
0,0,a,1,b,0,c,1,d,22
1,0,a,1,b,0,c,1,d,23
0,1,a,1,b,0,c,1,d,24
1,1,a,1,b,0,c,1,d,25
0,0,a,0,b,1,c,1,d,26
1,0,a,0,b,1,c,1,d,27
0,1,a,0,b,1,c,1,d,28
1,1,a,0,b,1,c,1,d,29
0,0,a,1,b,1,c,1,d,30
1,0,a,1,b,1,c,1,d,31
0,1,a,1,b,1,c,1,d,2
1,1,a,1,b,1,c,1,d,3

# S0
j,a,s,b,t,c,u,d,v,1

# S1
j,a,o,b,t,c,u,d,v,1
j,a,s,b,p,c,u,d,v,1
j,a,s,b,t,c,q,d,v,1
j,a,s,b,t,c,u,d,r,1

# S2
# 2 from same secondary
j,a,k,b,t,c,u,d,v,1
j,a,s,b,l,c,u,d,v,1
j,a,s,b,t,c,m,d,v,1
j,a,s,b,t,c,u,d,n,1
# 1+1 from two different secondaries
j,a,o,b,p,c,u,d,v,1
j,a,o,b,t,c,q,d,v,1
j,a,o,b,t,c,u,d,r,1
j,a,s,b,p,c,q,d,v,1
j,a,s,b,p,c,u,d,r,1
j,a,s,b,t,c,q,d,r,1

# S3
# 2+1
j,a,o,b,l,c,u,d,v,1
j,a,k,b,p,c,u,d,v,1
j,a,o,b,t,c,m,d,v,1
j,a,k,b,t,c,q,d,v,1
j,a,o,b,t,c,u,d,n,1
j,a,k,b,t,c,u,d,r,1
j,a,s,b,p,c,m,d,v,1
j,a,s,b,l,c,q,d,v,1
j,a,s,b,p,c,u,d,n,1
j,a,s,b,l,c,u,d,r,1
j,a,s,b,t,c,q,d,n,1
j,a,s,b,t,c,m,d,r,1
# 1+1+1
j,a,o,b,p,b,q,d,v,1
j,a,o,b,p,b,u,d,r,1
j,a,o,b,t,b,q,d,r,1
j,a,s,b,p,b,q,d,r,1

# Death otherwise
i,a,b,c,d,e,f,g,h,0
j,a,b,c,d,e,f,g,h,0

And a knightlife.colors if you want to see something other than a mess of orange going on:

Code: Select all

color=0 	0	0	0
color=1 	0	255	0
color=2 	127	0	0
color=3 	0	255	255
color=4 	31	0	0
color=5 	0	191	63
color=6 	31	0	0
color=7 	0	191	63
color=8 	63	0	0
color=9 	0	191	127
color=10	31	0	0
color=11	0	191	63
color=12	63	0	0
color=13	0	191	127
color=14	63	0	0
color=15	0	191	127
color=16	95	0	0
color=17	0	255	191
color=18	31	0	0
color=19	0	191	63
color=20	63	0	0
color=21	0	191	127
color=22	63	0	0
color=31	0	191	127
color=24	95	0	0
color=25	0	255	191
color=26	63	0	0
color=27	0	191	127
color=28	95	0	0
color=29	0	255	191
color=30	95	0	0
color=31	0	255	191

Live cells are green, with a bluish tint depending on how many neighbors they're tracking during transition. Dead cells are similarly tinted red.

Three still lifes and a couple of p2 oscillators that work under B2/S2:

Code: Select all

x = 42, y = 32, rule = knightlife
17.A$4.A5.A$2.A5.A7.A.A$3.A7.A$.A7.A7.A4$40.A$12.A3.A4.A9.2A5.A$14.A
14.A$22.A16.A$14.A6.A2.A5.A10.A5$33.A$A8.A6.A8.A$3.A4.A$16.A8.A6.A$
26.A6.A4$21.A$9.A$8.A16.A2$12.A6.A$11.A$23.A!

The phoenices in the lower 2 rows, unsurprizingly, also work in B2/S.

Overall B2/whatever seems to tend towards exploding at 5c/3, using this engine:

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x = 3, y = 2, rule = knightlife
.A$A.A!

B3/S23 appears to stabilize quite fast to various tub and beehive analogues. B3/S123 also stabilizes to what appears to be a dotfield but is actually mostly made of "chain" still lifes. B3/S012 is somewhat denser in appearence but actually has more isolated cells (a straight line will comprise of these). B3/S0123 is the first rule that has any actual action going on, but still so little that I probably need to add B4 and S4 to the mix… still, here's the initial results anyway to play with.

Tried B3/D as well. Even this stabilizes quickly. B3Knight might really just be too weak a growth condition to support any particularly interesting 2-state totalistic rules; anything close to type 4 will probably just look like a fancy Diamoeba. OTOH, even B4 will be sufficient for a pattern to grow beyond its bounding box, so that's more space to explore…

Tropylium · Post by **Tropylium** » September 11th, 2012, 4:44 pm

Tropylium wrote:even B4 will be sufficient for a pattern to grow beyond its bounding box

But on the contrary! if we consider a bounding region with a knight-octagonal shape…

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......*......
....*...*....
..*.......*..
............*
.*.....
.......
*......

…then even B3 will actually be insufficient for escaping this area.

Seems like a dead end here, then

EricG · Post by **EricG** » September 11th, 2012, 8:52 pm

Wow, that's crazy! I can imagine how it might work, but I didn't even try to follow the details. Nice job!

But, a dead end? Many of your posts have been dedicated to coaxing/bludgeoning B2 into doing something interesting. So, there are B0 rules, Generations rules, Non-totalistic rules (Sans Domino, etc), Alternating rules, the Bx2 trick as a specific case of increasingly general 3 state rules, and surely more. There are no dead ends in CA, only increasingly elaborate elaborations!

So, with the big caveat that I don't understand your scheme, I tried Brian's Brain -- B2/S/C3, except I figured it would have to be implemented as C4 because of the two-stage nature of your rule. I don't know if I did it right, but spaceships emerged. They are very simple orthogonal spaceships, but there is a hint of a more elaborate spaceship that dies out in this rule, but might survive in a related rule.

I changed the following lines of your table at the top of the file:
n_states:34
var a = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33}
and otherwise left the variables alone. I commented out all but the #B2 section and the #Extrude phase section.
And I added, at the bottom of the file:
1,a,b,c,d,e,f,g,h,32
32,a,b,c,d,e,f,g,h,33
33,a,b,c,d,e,f,g,h,0
right before the existing lines:
i,a,b,c,d,e,f,g,h,0
j,a,b,c,d,e,f,g,h,0

=============

Edit: I found some interesting behavior after all. I'm labeling the rule with C3 so that the label is implementation independent. Here is a rake that starts out unstable. It fires off something that becomes a breeder. The original rake settles down (or at least, breeding is suppressed) while the breeder heads off and breeds:

Code: Select all

x = 11, y = 12, rule = Knightlife-B2_S_C3
6.A$5.3A$5.A.A$3.A5.A$3.A$10.pH$3.6A$A3.A$3.A2.A2$A4.pIA$2.pH3.pH!

Pretty double barreled rake:

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x = 31, y = 30, rule = Knightlife-B2_S_C3
15.A$13.5A2$12.2A3.2A$15.A$10.A4.A4.A$9.A.ApI2.pH2.pIA.A$11.pH.pI3.pI
.pH$12.pI.pI.pI.pI$10.A2.pI3.pI2.A$11.A.A3.A.A$14.pH.pH$15.pH6$13.A.A
.A$9.pH5.pI5.pH$11.A2.pI.pI2.A$8.A6.pI6.A$7.A3.ApI.pI.pI.pIA3.A$5.pH
3.pHApH7.pHApH3.pH$11.ApH5.pHA$5.pI6.A5.A6.pI$.ApH4.A3.A.ApI.pIA.A3.A
4.pHA$A2.pI5.pH5.pI5.pH5.pI2.A$.ApH12.A12.pHA$15.pI!

Asymmetrical single barrel rake:

Code: Select all

x = 19, y = 20, rule = Knightlife-B2_S_C3
14.A$10.A.4A$15.pH$11.A.A$10.2A.A$12.pHA$10.ApH.pI$9.A.A$6.A4.pHA$5.A
7.A$5.pH.pHA3.2A3.pH$6.pI.pI.pI4.pH$12.pI5.A$.ApH5.pI7.A$A2.pI3.pH3.A
2.pH$.ApH4.ApH4.A2.A$5.pI6.pHA.A2$5.pH3.pH$7.A!

And B23/S23/C3 looks more like the regular B2/S/C3 Generations rule -- growth with all kinds of ships and rakes swirling about. Some of the patterns remind me fronts on a weather map.

EricG · Post by **EricG** » September 12th, 2012, 10:09 am

Tropylium, I just realized the patterns I posted above have their rules mislabeled. I need to get the various patterns sorted out, according to their rules. I'm sorry about that.

Here's what I have so far, but there are more patterns to be sorted.

---- B2/S/C3

Seed for two backrakes:
x = 12, y = 6, rule = Knightlife-B2_S_C3
2$2.A.4A$6.A!

Triple rake:
x = 12, y = 28, rule = Knightlife-B2_S_C3
4.4A$5.2A2$.A.6A.A$3.A4.A$4.A2.A2$.A.2A2.2A.A3$2.A6.A3$A.A6.A.A3$A.A
6.A.A5$3.2A2.2A2$4.4A2$3.A4.A2$3.6A!

---- B2/S23/C3

Single barrel rake:
x = 15, y = 18, rule = Knightlife-B2_S23_C3
5.2A.A$4.A.2A$9.pH$7.A$.A4.3A$3.pI2.A$A3.pH$.4A3.pH$A$2.pI2$2.pI$.pH
3$7.A6.pH$9.pH$7.A!

Tropylium · Post by **Tropylium** » September 12th, 2012, 10:34 am

EricG wrote:Wow, that's crazy! I can imagine how it might work, but I didn't even try to follow the details. Nice job!

The "extrude" phase encodes into each cell what orthogonal neighbors they have. In the birth/survival phase, cells then react to their diagonal von Neumann neighborhood (considering that certain cell types count as two neighbors). Thus information flows like this:

Code: Select all

  +---+---+---+
  |   |   |   |
3 | O | O |   |
  |   |   |   |
  +---+---+---+
  |   |   |   |
2 |   |   |   |
  |   |   |   |
  +---+---+---+
  |   |   |   |
1 | O |   |   |
  |   |   |   |
  +---+---+---+
    A   B   C

  +---+---+---+
  |   |   |   | A3 = state 7: live with a neighbor to E
3 | O*|*O*|*  | B3 = state 23: live with neighbors to E, W
  |   |   |   | C3 = state 18: dead with a neighbor to W
  +---+---+---+
  | * | * |   | A2 = state 12: dead with neighbors to N, S
2 |   |   |   | B2 = state 4: dead with a neighbor to N
  | * |   |   |
  +---+---+---+
  |   |   |   | A1 = state 1: "plain" live (with no orthogonal neighbors)
1 | O |*  |   | B1 = state 18
  |   |   |   |
  +---+---+---+
    A   B   C
  
  +---+---+---+
  |   |   |   |
3 |   |   |   |
  |   |   |   |
  +---+---+---+
  |   |   |   |  C2 is born since it had:
2 |   |   | O |  - one NW neighbor (B3) that encodes one N or W neighbor (A3)
  |   |   |   |  - one SW neighbor (B1) that encodes one S or E neighbor (A1)
  +---+---+---+
  |   |   |   |
1 |   |   |   |
  |   |   |   |
  +---+---+---+
    A   B   C

EricG wrote:But, a dead end? Many of your posts have been dedicated to coaxing/bludgeoning B2 into doing something interesting. So, there are B0 rules, Generations rules, Non-totalistic rules (Sans Domino, etc), Alternating rules, the Bx2 trick as a specific case of increasingly general 3 state rules, and surely more. There are no dead ends in CA, only increasingly elaborate elaborations!

Sure, not a dead end for this neighborhood in general, just the totalistic B3 and B4 rules.

EricG wrote:So, with the big caveat that I don't understand your scheme, I tried Brian's Brain -- B2/S/C3, except I figured it would have to be implemented as C4 because of the two-stage nature of your rule. I don't know if I did it right, but spaceships emerged. They are very simple orthogonal spaceships, but there is a hint of a more elaborate spaceship that dies out in this rule, but might survive in a related rule.

So it seems. What you'd actually have to do to get an exact Knightan's Brain though would be to add not two, but sixteen states (so you can imagine getting this neighborhood included in the RuleTable format itself would make the job exploring 3+state Knight rules a lot easier). Your current implementation leaves the two dying states opaque to the process that tracks neighbors. A dying cell can thus block a birth in a diagonally adjacent cell:

Code: Select all

x = 10, y = 2, rule = Knightlife-B2_S_C3
pI$A.A4.A.A!

Eliminating this effect would be expected to increase the volatility…

Regardless, this does not come up in the small p3 spaceship at least.

(Also 5c/3 is indeed the fastest orthogonal speed possible: a spaceship's front corner can progress 2 cells while shrinking 1 cell in width, or progress 1 cell while increasing 2 cells in width.)

But, since adding extra states with exactness is a pain, let's try the SansDomino approach. This neighborhood has, just like Moore, 6 different B2 environments:

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x = 13, y = 23, rule = Knightlife
.A7.A.A$A$2.B7.B5$7.A$4.A$6.B4$3.A$8.A3.A$2.B7.B$A4$8.A$6.B$4.A!

Except here we have two environments that grow at the maximum speed; both are needed for the 5c/3 engine. So there will be 3 ways to tame down B2 without sacrificing growability. "SansDominoDiagonal" is the easiest to implement (eliminating the top left B2 environment), we just zap the part where a cell is born on the basis of only one temp-neighbor. Hence, knightlife-SDD.table will have just this:

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# B2
# 1+1 from two different secondaries
i,a,o,b,p,c,u,d,v,1
i,a,o,b,t,c,q,d,v,1
i,a,o,b,t,c,u,d,r,1
i,a,s,b,p,c,q,d,v,1
i,a,s,b,p,c,u,d,r,1
i,a,s,b,t,c,q,d,r,1

These rules still appear to be explosive, but much weaker at that. For example this seed in B2/S

Code: Select all

x = 12, y = 2, rule = Knightlife-SDD
A$.11A!

will settle into a p10 oscillator after 70 generations (140 tics; I'm counting generations as if the ×2 delay did not exist).

A small c/1 spaceship exists:

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x = 4, y = 3, rule = Knightlife-SDD
A$.A.A$A!

It is a phoenix, so a funny effect of this neighborhood can be showcased with it: all phoenices have a parity, in that they alternate between "black" and "white" squares just like a chess knight does. Thus we can overlay a "black" and a "white" spaceship in a few ways so that they remain uninteracting:

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x = 38, y = 20, rule = Knightlife-SDD
13.A22.A$14.A.A16.A3.A$3.A9.A22.A$3.2A.A6.A$3.2A.A7.A.A$3.A9.A6$16.A$
3.A9.A3.A$A2.2A8.A2.A$3.2A.A7.A.A$3.A9.A$23.A.A$24.A2$24.A!

The effect will be perfect in B2/S, but the previous four bi-spaceships and transparent collision also work in B2/S2.

Anyway, still a little too explosive to possibly support anything engineerable. Next up: Knightlife-SDO.

Tropylium · Post by **Tropylium** » September 12th, 2012, 11:55 am

Tropylium wrote:Next up: Knightlife-SDO.

This takes a bit more fine-tuning, so here's knightlife-SDO.table in its entirety:

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n_states:32
neighborhood:Moore
symmetries:none

var a = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31}
var b = {a}
var c = {a}
var d = {a}
var e = {a}
var f = {a}
var g = {a}
var h = {a}
#dead states
var i = {0,4,6,8,10,12,14,16,18,20,22,24,26,28,30,2}
#live states
var j = {1,5,7,9,11,13,15,17,19,21,23,25,27,29,31,3}
#2 from NE
var k = {8,9,16,17,24,25,2,3}
#2 from SE
var l = {14,15,16,17,30,31,2,3}
#2 from SW
var m = {26,27,28,29,30,31,2,3}
#2 from NW
var n = {20,21,24,25,28,29,2,3}
#1 from NE
var o = {4,5,6,7,12,13,14,15,20,21,22,23,28,29,30,31}
#1 from SE
var p = {6,7,8,9,10,11,12,13,22,23,24,25,26,27,28,29}
#1 from SW
var q = {10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}
#1 from NW
var r = {4,5,8,9,12,13,16,17,18,19,22,23,26,27,30,31}
# 0 from NE
var s = {0,1,10,11,18,19,26,27}
# 0 from SE
var t = {0,1,4,5,18,19,20,21}
# 0 from SW
var u = {0,1,4,5,6,7,8,9}
# 0 from NW
var v = {0,1,6,7,10,11,14,15}
# for SDO 
var oN = {4,5,12,13,20,21,28,29}
var oE = {6,7,14,15,22,23,30,31}
var pS = {10,11,12,13,26,27,28,29}
var pE = {6,7,8,9,22,23,24,25}
var qS = {10,11,12,13,14,15,16,17}
var qW = {18,19,20,21,22,23,24,25}
var rN = {4,5,8,9,12,13,16,17}
var rW = {18,19,22,23,26,27,30,31}


# B2
# 2 from same secondary
i,a,k,b,t,c,u,d,v,1
i,a,s,b,l,c,u,d,v,1
i,a,s,b,t,c,m,d,v,1
i,a,s,b,t,c,u,d,n,1
# 1+1 from two different secondaries without orthogonal 2c
i,a,oN,b,pE,c,u,d,v,1
i,a,oE,b,pS,c,u,d,v,1
i,a,oN,b,pS,c,u,d,v,1
i,a,s,b,pE,c,qS,d,v,1
i,a,s,b,pS,c,qW,d,v,1
i,a,s,b,pE,c,qW,d,v,1
i,a,s,b,t,c,qS,d,rW,1
i,a,s,b,t,c,qW,d,rN,1
i,a,s,b,t,c,qS,d,rN,1
i,a,oE,b,t,c,u,d,rN,1
i,a,oN,b,t,c,u,d,rW,1
i,a,oE,b,t,c,u,d,rW,1
i,a,o,b,t,c,q,d,v,1
i,a,s,b,p,c,u,d,r,1

# B3
# 2+1
#i,a,o,b,l,c,u,d,v,1
#i,a,k,b,p,c,u,d,v,1
#i,a,o,b,t,c,m,d,v,1
#i,a,k,b,t,c,q,d,v,1
#i,a,o,b,t,c,u,d,n,1
#i,a,k,b,t,c,u,d,r,1
#i,a,s,b,p,c,m,d,v,1
#i,a,s,b,l,c,q,d,v,1
#i,a,s,b,p,c,u,d,n,1
#i,a,s,b,l,c,u,d,r,1
#i,a,s,b,t,c,q,d,n,1
#i,a,s,b,t,c,m,d,r,1
# 1+1+1
#i,a,o,b,p,c,q,d,v,1
#i,a,o,b,p,c,u,d,r,1
#i,a,o,b,t,c,q,d,r,1
#i,a,s,b,p,c,q,d,r,1

# Extrude phase
# has orth neighbors in:
# N   E   S   W
0,0,a,0,b,0,c,0,d,0
1,0,a,0,b,0,c,0,d,1
0,1,a,0,b,0,c,0,d,4
1,1,a,0,b,0,c,0,d,5
0,0,a,1,b,0,c,0,d,6
1,0,a,1,b,0,c,0,d,7
0,1,a,1,b,0,c,0,d,8
1,1,a,1,b,0,c,0,d,9
0,0,a,0,b,1,c,0,d,10
1,0,a,0,b,1,c,0,d,11
0,1,a,0,b,1,c,0,d,12
1,1,a,0,b,1,c,0,d,13
0,0,a,1,b,1,c,0,d,14
1,0,a,1,b,1,c,0,d,15
0,1,a,1,b,1,c,0,d,16
1,1,a,1,b,1,c,0,d,17
0,0,a,0,b,0,c,1,d,18
1,0,a,0,b,0,c,1,d,19
0,1,a,0,b,0,c,1,d,20
1,1,a,0,b,0,c,1,d,21
0,0,a,1,b,0,c,1,d,22
1,0,a,1,b,0,c,1,d,23
0,1,a,1,b,0,c,1,d,24
1,1,a,1,b,0,c,1,d,25
0,0,a,0,b,1,c,1,d,26
1,0,a,0,b,1,c,1,d,27
0,1,a,0,b,1,c,1,d,28
1,1,a,0,b,1,c,1,d,29
0,0,a,1,b,1,c,1,d,30
1,0,a,1,b,1,c,1,d,31
0,1,a,1,b,1,c,1,d,2
1,1,a,1,b,1,c,1,d,3

# S0
j,a,s,b,t,c,u,d,v,1

# S1
#j,a,o,b,t,c,u,d,v,1
#j,a,s,b,p,c,u,d,v,1
#j,a,s,b,t,c,q,d,v,1
#j,a,s,b,t,c,u,d,r,1

# S2
# 2 from same secondary
#j,a,k,b,t,c,u,d,v,1
#j,a,s,b,l,c,u,d,v,1
#j,a,s,b,t,c,m,d,v,1
#j,a,s,b,t,c,u,d,n,1
# 1+1 from two different secondaries
#j,a,o,b,p,c,u,d,v,1
#j,a,o,b,t,c,q,d,v,1
#j,a,o,b,t,c,u,d,r,1
#j,a,s,b,p,c,q,d,v,1
#j,a,s,b,p,c,u,d,r,1
#j,a,s,b,t,c,q,d,r,1

# S3
# 2+1
#j,a,o,b,l,c,u,d,v,1
#j,a,k,b,p,c,u,d,v,1
#j,a,o,b,t,c,m,d,v,1
#j,a,k,b,t,c,q,d,v,1
#j,a,o,b,t,c,u,d,n,1
#j,a,k,b,t,c,u,d,r,1
#j,a,s,b,p,c,m,d,v,1
#j,a,s,b,l,c,q,d,v,1
#j,a,s,b,p,c,u,d,n,1
#j,a,s,b,l,c,u,d,r,1
#j,a,s,b,t,c,q,d,n,1
#j,a,s,b,t,c,m,d,r,1
# 1+1+1
#j,a,o,b,p,c,q,d,v,1
#j,a,o,b,p,c,u,d,r,1
#j,a,o,b,t,c,q,d,r,1
#j,a,s,b,p,c,q,d,r,1

# Death otherwise
i,a,b,c,d,e,f,g,h,0
j,a,b,c,d,e,f,g,h,0

Still a largely explosive rulespace chunk, seems like. Mostly makes a slow mess, but at least in B2/S0 there is a c/1 p16 dot puffer:

Code: Select all

x = 11, y = 14, rule = Knightlife-SDO
.A$A$3.A3.A.A$2.A7.A4$2.A2$2.A2$6.A.A2$4.A!

(The engine can also stretch growing chaos.)

ETA: Nothing else of interest turned up yet, so let's block both the "domino" environments. For this you can start with the previous table and again delete or comment-out the 4 lines after "# B2 # 2 from same secondary". Save this as knightlife-SDOD.table.

Initial scan results…

B2/S, /S0, /S2, /S3: quickly stabilizing
B2/S1: clouds smaller than about 1200 cells slowly shrink, larger than 1300 slowly grow
B2/S01(2,3): stabilizes into checkerboard raster shapes

B2/S02, /S12, /S023, /S123: exploding, smaller seeds stabilize into still lifes
B2/S03: slowly shrinks leaving sparse dots
B2/S13: clouds smaller than about 110 cells shrink, larger than 120 grow
B2/S23: slowly shrinks, holes will appear

B23/S: exploding, smaller seeds stabilize into oscillators

Nothing particularly promising here either (no spaceships, novel oscillators etc. sighted), but at least some of the rules have less predictable behavior. Maybe I'll need to amend the ruletable to handle B4 and S4.

Tropylium · Post by **Tropylium** » September 12th, 2012, 6:44 pm

Under the weakest B2 subtype, B2/S12 actually supports all sorts of funny oscillators and still lifes upon closer inspection:

Code: Select all

x = 124, y = 49, rule = Knightlife-SDOD
53.A3.A10.A3.A10.A3.A$54.3A12.3A12.3A$52.2A3.2A8.2A3.2A8.2A3.2A$50.A.
A5.A.A4.A.A.A3.A.A4.A.A.A.A.A.A4.A2.A7.A3.A$51.A2.A.A2.A6.A2.A2.A.A6.
A.A3.A.A6.2A9.A3.A$51.A7.A6.A7.A6.A7.A6.A10.A3.A$51.A2.A.A2.A6.A2.A2.
A.A6.A.A3.A.A6.A9.A3.A$50.A.A5.A.A4.A.A.A3.A.A4.A.A.A.A.A.A4.A.A4.A$
16.A2.A32.2A3.2A8.2A3.2A8.2A3.2A8.2A2.A$17.2A35.3A12.3A12.3A12.3A$12.
A3.A.A34.A3.A10.A3.A10.A3.A10.A3.A$15.A$13.A16.A$33.A2$108.A.A$5.A70.
A.A30.A$77.A31.2A$3.4A8.A2.A5.A3.A9.A35.2A3.2A7.2A.2A6.2A7.A.A$A.4A.A
5.A2.2A7.3A18.A16.A11.A3.A9.A.A19.A$.A32.A2.2A6.A7.A20.2A.A.2A7.A3.A
5.A2.A17.A3.A$5.A6.A2.A21.A7.2A8.A6.A11.A5.A7.A3.A15.A.A7.2A2.A$2.2A
9.2A9.A3.A4.A3.A7.2A5.A7.A.A.A9.2A.A.2A7.A3.A5.A2.A16.A2.2A$5.A9.A10.
A9.2A7.2A5.A10.A11.A3.A9.A.A19.A5.A3.A$3.A39.3A6.A.A6.A12.2A3.2A7.2A.
2A6.2A7.A.A$36.A14.A3.A7.A13.A31.2A$44.A31.A.A30.A$108.A.A$13.A$3.A7.
A.A.A8.A$2.A.A6.A10.A3.A$2.A.A5.A2.A6.A3.A3.A$3.A.A7.2A90.A10.A$2.A.A
6.A3.A60.A12.A13.A3.A6.A3.A$2.A.A34.A30.A10.2A4.2A4.2A.2A4.A5.A4.A5.A
$38.A.2A13.A8.A.A8.A.A10.A5.A.A6.2A.2A6.2A.2A$40.A15.2A7.A5.A9.2A4.2A
4.2A.2A7.A10.A$41.A14.A.A4.A.A10.A12.A25.A.A$24.A13.A.A.A14.A$23.A12.
A.A4.A.A$25.A11.A4.2A$22.A15.A.A.2A2.A21.A6.A5.2A10.2A.A$24.A14.A3.A
14.A10.A24.A$21.A15.A2.A.4A11.A2.A6.A6.A.A5.2A9.2A$57.A$39.2A.A2.A12.
2A$38.6A$37.A$42.A!

Spaceships would probably be findable, but I imagine they're going to be too slow to occur naturally.

EricG · Post by **EricG** » September 12th, 2012, 8:51 pm

This is a very interesting project, and thanks for the additional explanation also. I think I will try out Generations Knightlife on a homebrew program.

And a subject for a future post, inspired by your avatar: the 20 neighbor Tropylium-shaped neighborhood!

Might as well try the shape here too:
x = 7, y = 7, rule = Knightlife-SDOD
3.2A$.3A.A$A4.A$2A.W.2A$.A4.A$.A.3A$2.2A!

EricG · Post by **EricG** » September 13th, 2012, 6:57 pm

I have Knightlife and "the Tropylium neighborhood" rules working, with or without extra decay states.

You were right that B2/S/C3 is much more volatile than my incorrect version. C3 and C4 are both explosive, but C5 calms things down. Knightlife-B2/S2/C5 turns out to be a nice rule to watch on a torus. It has lots of orthogonal ships, with different speeds, a quite rare diagonal ship, growing spaceships, rakes, and a surprising oscillator that is basically a ship that fails and turns around repeatedly.) Given that I reported incorrect results earlier in this thread, I think skepticism is entirely justified, but I'm using a much more straightforward system.

For the Tropylium neighborhood, no spaceships or complicated oscillators to report, mostly just expanding or contracting chaos. Two state B3 rules explode, but two state B4 rules ad B5 rules alternately expand or die out according to the survival rule - for example B4/S45 explodes, B4/S5 contracts, B5/S456 explodes, while B5/S145 contracts, and B5/S1457 contracts more slowly. There may be a sweet spot in there somewhere. I'll have a look at Generations rules as well, but the lack of orderliness may be an issue.

I'll also look at simpler ring neighborhoods , say, the perimeters of Range 2, and Range 3.

I plan to share my program, as it is web-based, but it won't be immediate - needs a better interface. Someone else might want to just throw together a very simple CA program in the meantime.

Tropylium · Post by **Tropylium** » September 14th, 2012, 11:19 am

EricG wrote:For the Tropylium neighborhood, (…)

My current avatar has nothing to do with my username though… "tropylium shaped" would probably be a term best applied to a heptagonal (hyperbolic) neighborhood.

An isotropic but chiral neighborhood of that sort might actually be able to produce some interesting novel effects, but a 20-cell example is larger than needed & I suspect would just obscure details in the sheer size of the rulespace. The simplest nbh of the sort would be a "horned von Neumann":

Code: Select all

.*...
..*.*
.*O*.
*.*..
...*.

Interesting-sounding results on Knightlife+Generations though!

ralph4769 · Post by **ralph4769** » September 26th, 2012, 3:38 am

As I try to follow the program, I find them interesting and in which gives me eagerness to create mine.

bprentice · Post by **bprentice** » November 25th, 2012, 8:47 am

Recently I explored the chess knight neighborhood and found four rules that might be of interest here.

The first rule, Rule 001, supports a glider gun and numerous noisy puffers and orthogonal ships. Of particular interest is puffer P001.sqc which periodically generates copies of itself.

The second rule, Rule 002, is the most interesting in that it quickly generates many small knight ships and orthogonal ships from a world set to random states. It is easy to build knight puffers and larger knight ships from these small ships. The rule also has a replicator from which it is possible to build oscillators. From these oscillators I was able to build a knight ship gun. There is much more to explore in this rule.

Rule 003 generates a moving ribbon in a sea of expanding chaos and small oscillators.

Rule 004 simply generates an interesting display containing small knight ships from an initial random state.

Example patterns for each rule are in the file Patterns.zip here:

http://bprentice.webenet.net/Square%20Cell/

These patterns may be run on my Java Square Cell simulator which is included in "Square Cell.zip". This archive contains the Java source code and the executable file SquareCell.jar. "Java Square Cell.html", which is also included in the above directory, briefly tells how to use the simulator.

All of my Java CA Programs together with a large collection of patterns are archived in "Java CA Programs.zip" which can be downloaded here:

http://bprentice.webenet.net/Java%20Square%20Cell/

Brian Prentice

bprentice · Post by **bprentice** » November 26th, 2012, 1:50 am

I've added a fifth rule, Rule 005, to the archive Patterns.zip. This one is a variation on Rule 002, it also generates many small knight ships and orthogonal ships. In this rule, however, many of the small ships mark their paths with a sequence of still life patterns. Others erase such trails. The replicator in Rule 002 has changed to an irregular gun which can be used to construct both knight ship guns and orthogonal ship guns. I have included several examples of each type. Again there is much more to explore in this rule and I suspect there are other interesting variants still to be discovered.

Brian Prentice

bprentice · Post by **bprentice** » May 23rd, 2013, 11:49 am

I've added examples for two more rules, Rule 006 and Rule 007, to the archive Patterns.zip. These rules are related in that they both generate Knight Ships with two different speeds from a world set to random states. They also both produce many different oscillator threads with Knight slopes and Knight breeders which can easily be converted to large Knight Ships. I will probably add more examples from time to time.

As a difficult exercise, try to construct Knight Ship guns for each of these rules.

Brian Prentice

EricG · Post by **EricG** » May 23rd, 2013, 6:04 pm

Wow! Synchronicity! Rules 6 & 7 look rather similar to something I was playing with just a few days ago. I'm actually so surprised, I'm going to go ahead and post, but I apologize for not playing more with your rules before commenting.

One trick for dealing with explosive rules is to use Generations, but after that, my next avenue of approach has been to try the Bx2 trick that Edwardfanboy and ExtremeEnthusiast introduced to the forum here: viewtopic.php?f=11&t=949 and viewtopic.php?f=11&t=808 (I'm unclear on who invented the Bx2 trick, do I understand correctly that it originated with someone in Russia?)

So, for example, the Bx2 trick came in handy with various triangle-based rules: viewtopic.php?f=11&t=965 And of course, that was the thread that led Tropylium to start this one, so it is appropriate to try the Bx2 trick with knightlife rules.

Sure enough, Knightlife-B1x2/S yields interesting behavior. Unfortunately, it is an exploding rule, but rather like Rule 6 and Rule 7 above, it explodes into interesting patterns -- in this case, it explodes into ball-shaped knightships, breeders, a replicator, and so on. It is rather fun to watch. And unless there is an interesting two-state knightlife rule, B1x2/S may be the most simple rule interesting knightlife rule.

The B2x2 rules are quieter, and Knightlife-B2x2/S245678 is neat. If you scribble a random drawing, and then fill in some of the holes, it turns into stable blobs that are surrounded by a chaotic perimeter that unpredictably expands and retracts long tendrils. (Kind of like a scary carnivourous plant!) I saw something similar in Tri6Inner-B1x2_S3456 (see the triangular thread), although that rule was much less dynamic.

Ok, I'm trying to get the hang of how your Java programs work, Brian, so here's an attempt to translate into Square Cell's format:

A Knightship, an orthogonal ship, and an oscillator in B1x2/S:

Code: Select all

#Rule = Rule Table
#States = 3
#Counts = 9
#SW 0,0,1
#NW 0,1,0,1,0
#NW 1,0,0,0,1
#NW 0,0,0,0,0
#NW 1,0,0,0,1
#NW 0,1,0,1,0
#RT 0,1,0,0,0,0,0,0,0
#RT 0,2,0,0,0,0,0,0,0
#RT 0,0,0,0,0,0,0,0,0
#Rows = 81
#Columns = 68
#L 9.A.A$8.A3.A$12.A$8.BA2.AB$9.A$9.A3.A$10.A.A21$5.A.A$4.A.A$5.A3.A$.
#L 2AB.A4.A$2A6.A$10.A.A$AB.A7.A$.A.A.A5.2A$7.A3.A$2.B.B.B2.2A2.A$3.A2.
#L A.A2.A2.A2$6.AB3.A2.B$7.5A.A27$56.A.A2.A.A$55.A3.2B3.A2$53.A5.2A5.A
#L $52.A5.B2.B5.A2$52.A3.A6.A3.A$53.A.A8.A.A2$55.A.A4.A.A$54.A3.B2.B3.
#L A2$54.A3.A2.A3.A$55.A.B4.B.A

A replicator which moves orthogonally as a whole, but the components travel on a knightship trajectory:

Code: Select all

#Rule = Rule Table
#States = 3
#Counts = 9
#SW 0,0,1
#NW 0,1,0,1,0
#NW 1,0,0,0,1
#NW 0,0,0,0,0
#NW 1,0,0,0,1
#NW 0,1,0,1,0
#RT 0,1,0,0,0,0,0,0,0
#RT 0,2,0,0,0,0,0,0,0
#RT 0,0,0,0,0,0,0,0,0
#Rows = 8
#Columns = 8
#L 4.A.A$3.2B.2A$3.A3.A$.A5.B$B2.A2.2A$4.B.A$B3.A$.A.A

I don't know how to scribble or do a fill with Square Cell, so this next pattern isn't quite the same as what got me excited, but here's the flavor of the blob+tendril rule (you have to be patient and let it do its thing for a bit):

Code: Select all

#Rule = Rule Table
#States = 3
#Counts = 9
#SW 0,0,1
#NW 0,1,0,1,0
#NW 1,0,0,0,1
#NW 0,0,0,0,0
#NW 1,0,0,0,1
#NW 0,1,0,1,0
#RT 0,0,1,0,0,0,0,0,0
#RT 0,0,2,0,0,0,0,0,0
#RT 0,0,2,0,2,2,2,2,2
#Rows = 200
#Columns = 171
#L 7.A.B.3B.B$6.2B2.3B$8.7B$10.3B.B$8.2B.3B2.A$11.2B2.B.A$7.A2.3B2.B.B
#L 38.B$10.B.B2.B37.B.A.B$8.4B.2BAB.B.A34.BA.A$7.A.5B2.B.B29.B2.AB3.B5.
#L B$3.B3.B.B.5B.B3A18.A10.B2.6B7.A$5.B.B.5B.B.B18.A.B12.10B2.B5.B$3.A
#L .BA.3B.5B.B19.2B4.A4.14B2.B.A2.B$3.A2.7B3.B2.A15.2AB8.23BA2.A.A$4.B
#L .B.3B2.2B4.A13.A.B2A2B2.B.24B.B$2.BA5B2.B3.B16.B3.B3.B.25B.2B.B.BA$
#L A3.3B2.B5.B16.A.BA.35B.B$2.BA2.2B.B.B2.B2A13.2AB2.B.37BA$12.A.A18.3B
#L .34B.3B$5.A2.2A.A.A14.B2.3B2.37B2A$5.A.B22.B.A37B.3B$27.A.A3B.24B.8B
#L .5BA$29.BA2B.32B.3B3.A$30.BA3B.28B.3B3.B$28.A.AB3.B2.18B.4B2.3B.2B.
#L B2.A$34.5B.16B.2B2.3B2.B.A$33.BAB.4B.7B.4B.3B.B4.B2.A.2A$33.A.B.3B.
#L 11B.4B2.A.2B4.B$33.A.A.7B.2B2.BA2B2.2BA2.B2.BABA$36.B2.2B2.2B6.A2.B
#L A.BA4.A2.BA$38.B.A2B2.B4.BAB2.2A9.A.A.A$36.3AB.A27.A$37.B2.BA.B.B5.
#L A$38.A21$63.A$65.B$79.B.A$62.A.A.B.A7.A.A.A$22.A.A2.A17.B16.B.BA.A3.
#L A3.A3.ABAB17.A$19.A4.A.BA2.3B6.A6.B.B13.BAB2.BAB4.B2.B2A4.B4.A4.B2.
#L A.B3.A.A.B$20.A3BA6BA2.A2.BA6.B3.B.3B.B3.BA4.B2.3B.B.B4.4B3.2B3.AB2.
#L A5.2B.2A$20.B.2B3.B3.2B4.2B3.BA3.B4.B4.2B2.A2B2.3B4.B.B2.B.A2.B2.B.
#L B3.AB4.B3.A2B2.AB$18.B2.2B.7B.B.7B.A.2B3.7B2.3B3.3B.B.8B2.2B2.3B2.A
#L 2B2.3B.4B3.2B3.B$19.2B.22B.14B2.20B.3B2.3B2.3BA.3B.4B2.3B$18.B2.2B.
#L 7B.B.7B.A.2B3.7B2.3B3.3B.B.8B2.2B2.3B2.A2B2.3B.4B3.2B3.B$20.B.2B3.B
#L 3.2B4.2B3.BA3.B4.B4.2B2.A2B2.3B4.B.B2.B.A2.B2.B.B3.AB4.B3.A2B2.AB$20.
#L A3BA6BA2.A2.BA6.B3.B.3B.B3.BA4.B2.3B.B.B4.4B3.2B3.AB2.A5.2B.2A$19.A
#L 4.A.BA2.3B6.A6.B.B13.BAB2.BAB4.B2.B2A4.B4.A4.B2.A.B3.A.A.B$22.A.A2.
#L A17.B16.B.BA.A3.A3.A3.ABAB17.A$62.A.A.B.A7.A.A.A$79.B.A$65.B$63.A105.
#L B2$168.B.B2$169.B$140.B$142.B$141.B$44.B98.B2$43.B.B2$44.B21$42.A2.
#L A3.A$40.B.A4.BA$42.B3.B2.B$41.B.B2.A.B3.A$39.B.BA2.3B2.B2A$40.2A3B2.
#L 4B$40.3BA4B.B.BA$42.8B2.A$41.B2.3B.B.2B$43.8B2.BA$41.3B.B.6B.A.A$42.
#L B2.4B.5B$42.A.B.9BA$43.A2.9B$44.A9B.B2.A$43.2B2.8B$41.A.A.3B.3B.AB.
#L A$42.AB.B.4B.B$43.A.3B2.3B$44.BAB.3B$43.AB.2B$45.B.2BA$43.A5.B$46.B
#L 15$117.A3.A$115.B2.A3.A$48.A61.A.B4.BA.B$45.2A2.A2B.A12.A2.BA33.B.A
#L .B3.BA3.A3B4.B$46.A3.A.B.B7.2A4.B37.BA.3B2.BA2B3.B2.A$44.BA.2B.B.B.
#L 2BA3.A3.B2.A2BA36.3B.B.2B3.3B2.ABA$20.2A23.B2.3B2.B2.B.B3.2B2.2B3.2B
#L 32.BAB.4B2.4B.4B$18.2B3.B15.B2.2B.4B.3B2.B7.AB3.3B.B31.A.A4B2.2B3.3B
#L .A3B$11.A6.2BAB.A.B14.15B2.2B6.6B.B.A31.B3.2B.A2.2B3.4BA$3.A.B3AB3.
#L B2.2B.B3.B2.3BA8.BAB.B.12B2.A2.BAB.7B.A33.2B.AB.2BA2.AB.BA.BA$.A4.B
#L .B.AB2.B.2B2.3B.5B.B10.18B.B.2B.7B.B37.B3.A.A3.3B$2.B.3B.2B.B.4B.7B
#L .3BAB7.2B.16B3.B2.3B.5B.BAB45.A3.BA$.ABA5B.3B.5B.3B.3B3.B6.B2.20B.6B
#L .5B3.2B44.A$.BAB.6B.9B.4B.B11.2B.23B.5B.BA3B49.A$2.AB.4B.13B.3B.2B7.
#L ABA.20B.12B2.AB$4.3B.13B.6B11.B.B.27B.B.B.B$2AB.B.12B.5B.B.2B.AB7.B
#L .36B$2A5B.13B2.3B2.B.B7.A.33B.B$.3B.4B.9B.4B.3BA2B6.A3.B.28B.B.B.A$
#L A2.4B.7B.4B2.A.B2.2B8.A.3B.23B.2B.3B$A3B.A2B.3B.4B6.3B3.B7.A2B.23B.
#L 5B3.BA$4.B.A2.5B.B.B.ABA.A.B12.3B.21B.3B2.B.4B$2.A4.3B.B.B.B.B.B4.A
#L 13.A.B.24B.B2.B.B.A$3.A.2B3.4B2.AB23.15B.9B.ABA2.B$6.A3.B.2B.B2.A20.
#L A.B.B.B.3B2.6B2.2B9.A$11.5B23.B2.A3B4.3B3.B2.3B2.B$9.B.3BA22.A3.2B3.
#L 2B2.A.B.3B2.A.B$8.2A2B2.2A24.BA.2B2.A.2A.3AB.2A.A.AB$8.A.B.B31.A.A8.
#L 3A$8.B.B.2BA26.A.B3.A$8.A2.B2.AB28.A$5.3A.B.4B.B$5.B.B2.3B.B.B$5.10B
#L .A$3.A2.B.5B.2B.A$2.A.B2.3B.B.B.A$7.7B$4.A2BA2B.B.B.B$7.B.4B.B$4.2A
#L 4.B.B.B$7.B.A.2BA2.B$9.B.B.B$8.AB.B$9.AB.B.B$8.B.B.B$11.B$7.BA5B$6.
#L B2.4B3.A$7.AB.B.3BA$6.2A.4B.3B$9.B.B.2B$9.BAB.2B.B$8.A2.B3.B$10.BA3B
#L $9.A3BA$11.B3.A$7.B.3B.B.B

Brian, I admit I do have a secondary agenda: I noticed that all of your knightlife rules use five states. I'm hoping that if we find a really interesting knightlife rule, it will have three or at most four states, so that there is a hope of seeing it with Golly. If you use the most straightforeward approach, and subdivide Golly cells into four parts, so that emulating two states rules take 16 states, emulating five state rules will be out of reach for Golly, as it has a 256 state limit. I totally understand if you don't share this goal, but that's part of why I'm interested in the Bx2 trick.

In any case, I'm hoping there are other even more interesting Bx2 knightlife rules (or three state rules) to be found.

Edit: I wonder if blob+tendrils is a characteristic of Bx2 rules, regardless of neighborhood, or at least in many different kinds of neighborhoods.

bprentice · Post by **bprentice** » May 23rd, 2013, 9:15 pm

Eric,

The controls of Square Cell, Hexagonal Cell and Triangular Cell are essentially the same. The major difference being that Square Cell selection rotations are 90 degrees and the selection rotations for the other two simulators are 60 degrees.

A selection is created and cleared by clicking the display with the Control key depressed. The first click marks a corner of the selected area and the second click marks the opposite corner. A subsequent third click clears the selection.

If the mouse pointer is held over a button, a hint is displayed telling what it does. Several of these buttons manipulate the selection. One of these fills the selection with random states. Another button displays a dialog with parameters controlling how the random states are generated.

The state of a cell on the main display or in a dialog can be changed by clicking on it. This changes the state to the state selected in the Color Selector. Clicking a cell with the shift key depressed steps through all the possible states. The status bar displays the state number.

I have not felt the need for scribbling. I have found that patterns can be quickly constructed by making a few clicks on the display and then using the selector to manipulate them using the move, copy, rotate and flip buttons.

The selector has another nice feature. Selected cells do not participate when the simulation is run. This means that the selector can be used for temporary storage and more importantly for synchronizing parts of a pattern. For example a part of a pattern can be selected and the remaining part can be stepped before the selected part is repositioned.

You can use the Square Cell "test new rule button" or the N key to see if you can find an interesting 3 or 4 state rule suitable for Golly. Just continuously click until something interesting turns up. I will do the same tomorrow.

I look forward to seeing both of your interesting rules run on Golly.

Brian

bprentice · Post by **bprentice** » May 24th, 2013, 9:02 pm

Eric,

I tried Bx2 with this neighborhood:

.x...
.x.xx
..o..
xx.x.
...x.

and it also generated interesting results. Here are two examples from two different but related rules.
A Knight Puffer:

Code: Select all

#Rule = Rule Table
#States = 3
#Counts = 9
#SW 0,0,1
#NW 0,1,0,0,0
#NW 0,1,0,1,1
#NW 0,0,0,0,0
#NW 1,1,0,1,0
#NW 0,0,0,1,0
#RT 0,1,0,0,0,0,0,0,0
#RT 0,2,0,0,0,0,0,0,0
#RT 0,0,0,0,0,0,0,0,0
#Rows = 31
#Columns = 25
#L 5.A$.A3.A.BA$.A.A6.A2.A$3.B.2A3.A.A2.2A$2A4.AB$6.A2.2A2.A.A$2.2A.2A
#L 5.A2.A$5.A3.A$9.A.2A$3.A3.A$3.A.AB.A.AB$5.A.B.3A$2.2A2.B2.A$5.A.A$4.
#L BA.B.A$.A5.A.A.A$.B.2AB3.B2.3A$5.B.2A7.B$2A.A3.3A3.A2.B.2A$3.B2A5.B
#L 2.A$7.A.B7.B$6.BA3.BA4.A2.BA$8.B$11.A4.A.A$10.BA.A.B2.A3.2A$13.A$14.
#L 2A.A.B.2A$17.A2.2A2.B2$19.A.A2B$22.2A

and a Knight Ship:

Code: Select all

#Rule = Rule Table
#States = 3
#Counts = 9
#SW 0,0,1
#NW 0,1,0,0,0
#NW 0,1,0,1,1
#NW 0,0,0,0,0
#NW 1,1,0,1,0
#NW 0,0,0,1,0
#RT 0,1,0,0,0,0,0,0,0
#RT 0,2,0,0,0,0,0,0,0
#RT 0,0,1,2,2,2,2,2,2
#Rows = 8
#Columns = 6
#L .B$.A.2A2$A.2B$.2A2.A2$A.A2B$3.2A

Try each rule starting with the world set to random states. The second rule generates spikes whose sides are buzzing with Knight Ships. These rules are not fully symmetric, they only have rotational symmetry.

Brian

bprentice · Post by **bprentice** » May 26th, 2013, 8:04 pm

Eric,

I admit I do have a secondary agenda: I noticed that all of your knightlife rules use five states. I'm hoping that if we find a really interesting knightlife rule, it will have three or at most four states, so that there is a hope of seeing it with Golly.

I found a 3 state rule that is rich in both Knight and Orthogonal objects. Hopefully it will be suitable for Golly.

Here is an Orthogonal Gun:

Code: Select all

#Rule = Rule Table
#States = 3
#Counts = 9
#SW 0,1,0
#NW 0,1,0,1,0
#NW 1,0,0,0,1
#NW 0,0,0,0,0
#NW 1,0,0,0,1
#NW 0,1,0,1,0
#RT 0,2,0,0,0,0,0,1,0
#RT 0,2,0,0,0,0,0,0,1
#RT 0,1,0,0,0,0,0,0,0
#Rows = 66
#Columns = 49
#L 13.B.B17.B.B$12.B3.B15.B3.B$16.A.B11.B.A$12.B2.BA2.B9.B2.AB2.B$13.B
#L .A17.A.B$15.A3.B9.B3.A$16.B.B11.B.B2$9.B.B25.B.B$8.B3.B23.B3.B$12.A
#L .B19.B.A$8.B2.BA2.B17.B2.AB2.B$9.B.A25.A.B$11.A3.B17.B3.A$12.B.B19.
#L B.B2$5.B.B33.B.B$4.B3.B31.B3.B$8.A.B27.B.A$4.B2.BA2.B25.B2.AB2.B$5.
#L B.A33.A.B$7.A3.B25.B3.A$8.B.B27.B.B2$.B.B41.B.B$B3.B39.B3.B$4.A.B35.
#L B.A$B2.BA2.B33.B2.AB2.B$.B.A41.A.B$3.A3.B33.B3.A$4.B.B35.B.B5$4.B.B
#L 35.B.B$3.A3.B33.B3.A$.B.A41.A.B$B2.BA2.B33.B2.AB2.B$4.A.B35.B.A$B3.
#L B39.B3.B$.B.B41.B.B2$8.B.B27.B.B$7.A3.B25.B3.A$5.B.A33.A.B$4.B2.BA2.
#L B25.B2.AB2.B$8.A.B27.B.A$4.B3.B31.B3.B$5.B.B33.B.B2$12.B.B19.B.B$11.
#L A3.B17.B3.A$9.B.A25.A.B$8.B2.BA2.B17.B2.AB2.B$12.A.B19.B.A$8.B3.B23.
#L B3.B$9.B.B25.B.B2$16.B.B11.B.B$15.A3.B9.B3.A$13.B.A17.A.B$12.B2.BA2.
#L B9.B2.AB2.B$16.A.B11.B.A$12.B3.B15.B3.B$13.B.B17.B.B

and here is a Knight Gun:

Code: Select all

#Rule = Rule Table
#States = 3
#Counts = 9
#SW 0,1,0
#NW 0,1,0,1,0
#NW 1,0,0,0,1
#NW 0,0,0,0,0
#NW 1,0,0,0,1
#NW 0,1,0,1,0
#RT 0,2,0,0,0,0,0,1,0
#RT 0,2,0,0,0,0,0,0,1
#RT 0,1,0,0,0,0,0,0,0
#Rows = 61
#Columns = 95
#L 43.AB2A3.2ABA$42.BA2.2B.2B2.AB2$42.2B2.BA.AB2.2B$35.AB2A4.AB2A3.2AB
#L A4.2ABA$34.BA2.2B17.2B2.AB2$34.2B2.BA17.AB2.2B$35.AB2A19.2ABA8$11.A
#L B2A67.2ABA$10.BA2.2B65.2B2.AB2$10.2B2.BA65.AB2.2B$3.AB2A4.AB2A67.2A
#L BA4.2ABA$2.BA2.2B81.2B2.AB2$2.2B2.BA81.AB2.2B$3.AB2A83.2ABA12$.AB2A
#L 83.2ABA$2B2.BA81.AB2.2B2$BA2.2B81.2B2.AB$.AB2A4.AB2A67.2ABA4.2ABA$8.
#L 2B2.BA65.AB2.2B2$8.BA2.2B65.2B2.AB$9.AB2A67.2ABA8$33.AB2A19.2ABA$32.
#L 2B2.BA17.AB2.2B2$32.BA2.2B17.2B2.AB$33.AB2A4.AB2A3.2ABA4.2ABA$40.2B
#L 2.BA.AB2.2B2$40.BA2.2B.2B2.AB$41.AB2A3.2ABA

Brian

FWKnightship · Post by **FWKnightship** » August 19th, 2020, 5:44 am

bprentice wrote: ↑
August 17th, 2020, 11:27 pm
FWKnightship,

Try emulating this rule:

https://conwaylife.com/forums/viewtopic ... =967#p8067

Brian Prentice

Code: Select all

@RULE bprenticesrule-emulated
@TABLE
n_states:245
neighborhood:Moore
symmetries:none


var Da= {0,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82}
var Db=Da
var Dc=Da
var Dd=Da
var De=Da
var Df=Da
var Dg=Da
var Dh=Da
var Di=Da

var Aa= {83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163}
var Ab=Aa
var Ac=Aa
var Ad=Aa
var Ae=Aa
var Af=Aa
var Ag=Aa
var Ah=Aa
var Ai=Aa

var Ba= {164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244}
var Bb=Ba
var Bc=Ba
var Bd=Ba
var Be=Ba
var Bf=Ba
var Bg=Ba
var Bh=Ba
var Bi=Ba

var NE0= {0,3,4,5,6,7,8,9,10,20,21,22,23,24,25,26,27,28,56,57,58,59,60,61,62,63,64,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,101,102,103,104,105,106,107,108,109,137,138,139,140,141,142,143,144,145,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,182,183,184,185,186,187,188,189,190,218,219,220,221,222,223,224,225,226,236,237,238,239,240,241,242,243,244}
var SE0= {0,3,4,8,9,10,20,21,22,26,27,28,29,30,31,35,36,37,47,48,49,53,54,55,56,57,58,62,63,64,74,75,76,80,81,82,83,84,85,89,90,91,101,102,103,107,108,109,110,111,112,116,117,118,128,129,130,134,135,136,137,138,139,143,144,145,155,156,157,161,162,163,164,165,166,170,171,172,182,183,184,188,189,190,191,192,193,197,198,199,209,210,211,215,216,217,218,219,220,224,225,226,236,237,238,242,243,244}
var SW0= {0,4,8,10,11,13,17,19,20,22,26,28,29,31,35,37,38,40,44,46,47,49,53,55,56,58,62,64,65,67,71,73,74,76,80,82,83,85,89,91,92,94,98,100,101,103,107,109,110,112,116,118,119,121,125,127,128,130,134,136,137,139,143,145,146,148,152,154,155,157,161,163,164,166,170,172,173,175,179,181,182,184,188,190,191,193,197,199,200,202,206,208,209,211,215,217,218,220,224,226,227,229,233,235,236,238,242,244}
var NW0= {0,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,56,58,59,61,62,64,65,67,68,70,71,73,74,76,77,79,80,82,83,85,86,88,89,91,92,94,95,97,98,100,101,103,104,106,107,109,137,139,140,142,143,145,146,148,149,151,152,154,155,157,158,160,161,163,164,166,167,169,170,172,173,175,176,178,179,181,182,184,185,187,188,190,218,220,221,223,224,226,227,229,230,232,233,235,236,238,239,241,242,244}

var NE1= {11,12,13,14,15,16,17,18,19,29,30,31,32,33,34,35,36,37,47,48,49,50,51,52,53,54,55,65,66,67,68,69,70,71,72,73,92,93,94,95,96,97,98,99,100,110,111,112,113,114,115,116,117,118,128,129,130,131,132,133,134,135,136,146,147,148,149,150,151,152,153,154,173,174,175,176,177,178,179,180,181,191,192,193,194,195,196,197,198,199,209,210,211,212,213,214,215,216,217,227,228,229,230,231,232,233,234,235}
var SE1= {5,6,7,11,12,13,17,18,19,23,24,25,32,33,34,38,39,40,44,45,46,50,51,52,59,60,61,65,66,67,71,72,73,77,78,79,86,87,88,92,93,94,98,99,100,104,105,106,113,114,115,119,120,121,125,126,127,131,132,133,140,141,142,146,147,148,152,153,154,158,159,160,167,168,169,173,174,175,179,180,181,185,186,187,194,195,196,200,201,202,206,207,208,212,213,214,221,222,223,227,228,229,233,234,235,239,240,241}
var SW1= {3,5,7,9,12,14,16,18,21,23,25,27,30,32,34,36,39,41,43,45,48,50,52,54,57,59,61,63,66,68,70,72,75,77,79,81,84,86,88,90,93,95,97,99,102,104,106,108,111,113,115,117,120,122,124,126,129,131,133,135,138,140,142,144,147,149,151,153,156,158,160,162,165,167,169,171,174,176,178,180,183,185,187,189,192,194,196,198,201,203,205,207,210,212,214,216,219,221,223,225,228,230,232,234,237,239,241,243}
var NW1= {3,6,9,12,15,18,21,24,27,29,31,32,34,35,37,38,40,41,43,44,46,47,49,50,52,53,55,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99,102,105,108,110,112,113,115,116,118,119,121,122,124,125,127,128,130,131,133,134,136,138,141,144,147,150,153,156,159,162,165,168,171,174,177,180,183,186,189,191,193,194,196,197,199,200,202,203,205,206,208,209,211,212,214,215,217,219,222,225,228,231,234,237,240,243}

var NE2={38,39,40,41,42,43,44,45,46,119,120,121,122,123,124,125,126,127,200,201,202,203,204,205,206,207,208}
var SE2={14,15,16,41,42,43,68,69,70,95,96,97,122,123,124,149,150,151,176,177,178,203,204,205,230,231,232}
var SW2={6,15,24,33,42,51,60,69,78,87,96,105,114,123,132,141,150,159,168,177,186,195,204,213,222,231,240}
var NW2={30,33,36,39,42,45,48,51,54,111,114,117,120,123,126,129,132,135,192,195,198,201,204,207,210,213,216}



var all= {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244}
var bll=all
var cll=all
var dll=all
var ell=all
var fll=all
var gll=all
var hll=all
var ill=all


0,0,all,0,bll,0,cll,1,dll,3
0,0,all,0,bll,0,cll,2,dll,4
0,0,all,0,bll,1,cll,0,dll,5
0,0,all,0,bll,1,cll,1,dll,6
0,0,all,0,bll,1,cll,2,dll,7
0,0,all,0,bll,2,cll,0,dll,8
0,0,all,0,bll,2,cll,1,dll,9
0,0,all,0,bll,2,cll,2,dll,10
0,0,all,1,bll,0,cll,0,dll,11
0,0,all,1,bll,0,cll,1,dll,12
0,0,all,1,bll,0,cll,2,dll,13
0,0,all,1,bll,1,cll,0,dll,14
0,0,all,1,bll,1,cll,1,dll,15
0,0,all,1,bll,1,cll,2,dll,16
0,0,all,1,bll,2,cll,0,dll,17
0,0,all,1,bll,2,cll,1,dll,18
0,0,all,1,bll,2,cll,2,dll,19
0,0,all,2,bll,0,cll,0,dll,20
0,0,all,2,bll,0,cll,1,dll,21
0,0,all,2,bll,0,cll,2,dll,22
0,0,all,2,bll,1,cll,0,dll,23
0,0,all,2,bll,1,cll,1,dll,24
0,0,all,2,bll,1,cll,2,dll,25
0,0,all,2,bll,2,cll,0,dll,26
0,0,all,2,bll,2,cll,1,dll,27
0,0,all,2,bll,2,cll,2,dll,28
0,1,all,0,bll,0,cll,0,dll,29
0,1,all,0,bll,0,cll,1,dll,30
0,1,all,0,bll,0,cll,2,dll,31
0,1,all,0,bll,1,cll,0,dll,32
0,1,all,0,bll,1,cll,1,dll,33
0,1,all,0,bll,1,cll,2,dll,34
0,1,all,0,bll,2,cll,0,dll,35
0,1,all,0,bll,2,cll,1,dll,36
0,1,all,0,bll,2,cll,2,dll,37
0,1,all,1,bll,0,cll,0,dll,38
0,1,all,1,bll,0,cll,1,dll,39
0,1,all,1,bll,0,cll,2,dll,40
0,1,all,1,bll,1,cll,0,dll,41
0,1,all,1,bll,1,cll,1,dll,42
0,1,all,1,bll,1,cll,2,dll,43
0,1,all,1,bll,2,cll,0,dll,44
0,1,all,1,bll,2,cll,1,dll,45
0,1,all,1,bll,2,cll,2,dll,46
0,1,all,2,bll,0,cll,0,dll,47
0,1,all,2,bll,0,cll,1,dll,48
0,1,all,2,bll,0,cll,2,dll,49
0,1,all,2,bll,1,cll,0,dll,50
0,1,all,2,bll,1,cll,1,dll,51
0,1,all,2,bll,1,cll,2,dll,52
0,1,all,2,bll,2,cll,0,dll,53
0,1,all,2,bll,2,cll,1,dll,54
0,1,all,2,bll,2,cll,2,dll,55
0,2,all,0,bll,0,cll,0,dll,56
0,2,all,0,bll,0,cll,1,dll,57
0,2,all,0,bll,0,cll,2,dll,58
0,2,all,0,bll,1,cll,0,dll,59
0,2,all,0,bll,1,cll,1,dll,60
0,2,all,0,bll,1,cll,2,dll,61
0,2,all,0,bll,2,cll,0,dll,62
0,2,all,0,bll,2,cll,1,dll,63
0,2,all,0,bll,2,cll,2,dll,64
0,2,all,1,bll,0,cll,0,dll,65
0,2,all,1,bll,0,cll,1,dll,66
0,2,all,1,bll,0,cll,2,dll,67
0,2,all,1,bll,1,cll,0,dll,68
0,2,all,1,bll,1,cll,1,dll,69
0,2,all,1,bll,1,cll,2,dll,70
0,2,all,1,bll,2,cll,0,dll,71
0,2,all,1,bll,2,cll,1,dll,72
0,2,all,1,bll,2,cll,2,dll,73
0,2,all,2,bll,0,cll,0,dll,74
0,2,all,2,bll,0,cll,1,dll,75
0,2,all,2,bll,0,cll,2,dll,76
0,2,all,2,bll,1,cll,0,dll,77
0,2,all,2,bll,1,cll,1,dll,78
0,2,all,2,bll,1,cll,2,dll,79
0,2,all,2,bll,2,cll,0,dll,80
0,2,all,2,bll,2,cll,1,dll,81
0,2,all,2,bll,2,cll,2,dll,82
1,0,all,0,bll,0,cll,0,dll,83
1,0,all,0,bll,0,cll,1,dll,84
1,0,all,0,bll,0,cll,2,dll,85
1,0,all,0,bll,1,cll,0,dll,86
1,0,all,0,bll,1,cll,1,dll,87
1,0,all,0,bll,1,cll,2,dll,88
1,0,all,0,bll,2,cll,0,dll,89
1,0,all,0,bll,2,cll,1,dll,90
1,0,all,0,bll,2,cll,2,dll,91
1,0,all,1,bll,0,cll,0,dll,92
1,0,all,1,bll,0,cll,1,dll,93
1,0,all,1,bll,0,cll,2,dll,94
1,0,all,1,bll,1,cll,0,dll,95
1,0,all,1,bll,1,cll,1,dll,96
1,0,all,1,bll,1,cll,2,dll,97
1,0,all,1,bll,2,cll,0,dll,98
1,0,all,1,bll,2,cll,1,dll,99
1,0,all,1,bll,2,cll,2,dll,100
1,0,all,2,bll,0,cll,0,dll,101
1,0,all,2,bll,0,cll,1,dll,102
1,0,all,2,bll,0,cll,2,dll,103
1,0,all,2,bll,1,cll,0,dll,104
1,0,all,2,bll,1,cll,1,dll,105
1,0,all,2,bll,1,cll,2,dll,106
1,0,all,2,bll,2,cll,0,dll,107
1,0,all,2,bll,2,cll,1,dll,108
1,0,all,2,bll,2,cll,2,dll,109
1,1,all,0,bll,0,cll,0,dll,110
1,1,all,0,bll,0,cll,1,dll,111
1,1,all,0,bll,0,cll,2,dll,112
1,1,all,0,bll,1,cll,0,dll,113
1,1,all,0,bll,1,cll,1,dll,114
1,1,all,0,bll,1,cll,2,dll,115
1,1,all,0,bll,2,cll,0,dll,116
1,1,all,0,bll,2,cll,1,dll,117
1,1,all,0,bll,2,cll,2,dll,118
1,1,all,1,bll,0,cll,0,dll,119
1,1,all,1,bll,0,cll,1,dll,120
1,1,all,1,bll,0,cll,2,dll,121
1,1,all,1,bll,1,cll,0,dll,122
1,1,all,1,bll,1,cll,1,dll,123
1,1,all,1,bll,1,cll,2,dll,124
1,1,all,1,bll,2,cll,0,dll,125
1,1,all,1,bll,2,cll,1,dll,126
1,1,all,1,bll,2,cll,2,dll,127
1,1,all,2,bll,0,cll,0,dll,128
1,1,all,2,bll,0,cll,1,dll,129
1,1,all,2,bll,0,cll,2,dll,130
1,1,all,2,bll,1,cll,0,dll,131
1,1,all,2,bll,1,cll,1,dll,132
1,1,all,2,bll,1,cll,2,dll,133
1,1,all,2,bll,2,cll,0,dll,134
1,1,all,2,bll,2,cll,1,dll,135
1,1,all,2,bll,2,cll,2,dll,136
1,2,all,0,bll,0,cll,0,dll,137
1,2,all,0,bll,0,cll,1,dll,138
1,2,all,0,bll,0,cll,2,dll,139
1,2,all,0,bll,1,cll,0,dll,140
1,2,all,0,bll,1,cll,1,dll,141
1,2,all,0,bll,1,cll,2,dll,142
1,2,all,0,bll,2,cll,0,dll,143
1,2,all,0,bll,2,cll,1,dll,144
1,2,all,0,bll,2,cll,2,dll,145
1,2,all,1,bll,0,cll,0,dll,146
1,2,all,1,bll,0,cll,1,dll,147
1,2,all,1,bll,0,cll,2,dll,148
1,2,all,1,bll,1,cll,0,dll,149
1,2,all,1,bll,1,cll,1,dll,150
1,2,all,1,bll,1,cll,2,dll,151
1,2,all,1,bll,2,cll,0,dll,152
1,2,all,1,bll,2,cll,1,dll,153
1,2,all,1,bll,2,cll,2,dll,154
1,2,all,2,bll,0,cll,0,dll,155
1,2,all,2,bll,0,cll,1,dll,156
1,2,all,2,bll,0,cll,2,dll,157
1,2,all,2,bll,1,cll,0,dll,158
1,2,all,2,bll,1,cll,1,dll,159
1,2,all,2,bll,1,cll,2,dll,160
1,2,all,2,bll,2,cll,0,dll,161
1,2,all,2,bll,2,cll,1,dll,162
1,2,all,2,bll,2,cll,2,dll,163
2,0,all,0,bll,0,cll,0,dll,164
2,0,all,0,bll,0,cll,1,dll,165
2,0,all,0,bll,0,cll,2,dll,166
2,0,all,0,bll,1,cll,0,dll,167
2,0,all,0,bll,1,cll,1,dll,168
2,0,all,0,bll,1,cll,2,dll,169
2,0,all,0,bll,2,cll,0,dll,170
2,0,all,0,bll,2,cll,1,dll,171
2,0,all,0,bll,2,cll,2,dll,172
2,0,all,1,bll,0,cll,0,dll,173
2,0,all,1,bll,0,cll,1,dll,174
2,0,all,1,bll,0,cll,2,dll,175
2,0,all,1,bll,1,cll,0,dll,176
2,0,all,1,bll,1,cll,1,dll,177
2,0,all,1,bll,1,cll,2,dll,178
2,0,all,1,bll,2,cll,0,dll,179
2,0,all,1,bll,2,cll,1,dll,180
2,0,all,1,bll,2,cll,2,dll,181
2,0,all,2,bll,0,cll,0,dll,182
2,0,all,2,bll,0,cll,1,dll,183
2,0,all,2,bll,0,cll,2,dll,184
2,0,all,2,bll,1,cll,0,dll,185
2,0,all,2,bll,1,cll,1,dll,186
2,0,all,2,bll,1,cll,2,dll,187
2,0,all,2,bll,2,cll,0,dll,188
2,0,all,2,bll,2,cll,1,dll,189
2,0,all,2,bll,2,cll,2,dll,190
2,1,all,0,bll,0,cll,0,dll,191
2,1,all,0,bll,0,cll,1,dll,192
2,1,all,0,bll,0,cll,2,dll,193
2,1,all,0,bll,1,cll,0,dll,194
2,1,all,0,bll,1,cll,1,dll,195
2,1,all,0,bll,1,cll,2,dll,196
2,1,all,0,bll,2,cll,0,dll,197
2,1,all,0,bll,2,cll,1,dll,198
2,1,all,0,bll,2,cll,2,dll,199
2,1,all,1,bll,0,cll,0,dll,200
2,1,all,1,bll,0,cll,1,dll,201
2,1,all,1,bll,0,cll,2,dll,202
2,1,all,1,bll,1,cll,0,dll,203
2,1,all,1,bll,1,cll,1,dll,204
2,1,all,1,bll,1,cll,2,dll,205
2,1,all,1,bll,2,cll,0,dll,206
2,1,all,1,bll,2,cll,1,dll,207
2,1,all,1,bll,2,cll,2,dll,208
2,1,all,2,bll,0,cll,0,dll,209
2,1,all,2,bll,0,cll,1,dll,210
2,1,all,2,bll,0,cll,2,dll,211
2,1,all,2,bll,1,cll,0,dll,212
2,1,all,2,bll,1,cll,1,dll,213
2,1,all,2,bll,1,cll,2,dll,214
2,1,all,2,bll,2,cll,0,dll,215
2,1,all,2,bll,2,cll,1,dll,216
2,1,all,2,bll,2,cll,2,dll,217
2,2,all,0,bll,0,cll,0,dll,218
2,2,all,0,bll,0,cll,1,dll,219
2,2,all,0,bll,0,cll,2,dll,220
2,2,all,0,bll,1,cll,0,dll,221
2,2,all,0,bll,1,cll,1,dll,222
2,2,all,0,bll,1,cll,2,dll,223
2,2,all,0,bll,2,cll,0,dll,224
2,2,all,0,bll,2,cll,1,dll,225
2,2,all,0,bll,2,cll,2,dll,226
2,2,all,1,bll,0,cll,0,dll,227
2,2,all,1,bll,0,cll,1,dll,228
2,2,all,1,bll,0,cll,2,dll,229
2,2,all,1,bll,1,cll,0,dll,230
2,2,all,1,bll,1,cll,1,dll,231
2,2,all,1,bll,1,cll,2,dll,232
2,2,all,1,bll,2,cll,0,dll,233
2,2,all,1,bll,2,cll,1,dll,234
2,2,all,1,bll,2,cll,2,dll,235
2,2,all,2,bll,0,cll,0,dll,236
2,2,all,2,bll,0,cll,1,dll,237
2,2,all,2,bll,0,cll,2,dll,238
2,2,all,2,bll,1,cll,0,dll,239
2,2,all,2,bll,1,cll,1,dll,240
2,2,all,2,bll,1,cll,2,dll,241
2,2,all,2,bll,2,cll,0,dll,242
2,2,all,2,bll,2,cll,1,dll,243
2,2,all,2,bll,2,cll,2,dll,244

Da,all,NE0,bll,SE0,cll,SW0,dll,NW1,2
Aa,all,NE0,bll,SE0,cll,SW0,dll,NW1,2
Ba,all,NE0,bll,SE0,cll,SW0,dll,NW1,1
Da,all,NE0,bll,SE0,cll,SW1,dll,NW0,2
Aa,all,NE0,bll,SE0,cll,SW1,dll,NW0,2
Ba,all,NE0,bll,SE0,cll,SW1,dll,NW0,1
Da,all,NE0,bll,SE1,cll,SW0,dll,NW0,2
Aa,all,NE0,bll,SE1,cll,SW0,dll,NW0,2
Ba,all,NE0,bll,SE1,cll,SW0,dll,NW0,1
Da,all,NE1,bll,SE0,cll,SW0,dll,NW0,2
Aa,all,NE1,bll,SE0,cll,SW0,dll,NW0,2
Ba,all,NE1,bll,SE0,cll,SW0,dll,NW0,1
Da,all,NE1,bll,SE2,cll,SW2,dll,NW2,1
Da,all,NE2,bll,SE1,cll,SW2,dll,NW2,1
Da,all,NE2,bll,SE2,cll,SW1,dll,NW2,1
Da,all,NE2,bll,SE2,cll,SW2,dll,NW1,1
Aa,all,NE2,bll,SE2,cll,SW2,dll,NW2,1

all,bll,cll,dll,ell,fll,gll,hll,ill,0

Code: Select all

x = 99, y = 63, rule = bprenticesrule-emulated
47.ABA.ABA$46.BA.B.B.AB$43.AB2A7.2ABA$42.BA5.B.B5.AB$39.AB2A4.ABA.ABA
4.2ABA$38.BA6.BA5.AB6.AB$35.AB2A4.AB2A7.2ABA4.2ABA$34.BA6.BA13.AB6.AB
$39.AB2A15.2ABA$34.2B2.BA21.AB2.2B$35.AB2A23.2ABA6$15.AB2A63.2ABA$14.
BA2.2B61.2B2.AB$11.AB2A71.2ABA$10.BA6.BA61.AB6.AB$7.AB2A4.AB2A63.2ABA
4.2ABA$6.BA6.BA69.AB6.AB$3.AB2A4.AB2A71.2ABA4.2ABA$2.BA6.BA77.AB6.AB$
7.AB2A79.2ABA$2.2B2.BA85.AB2.2B$3.AB2A87.2ABA10$.AB2A87.2ABA$2B2.BA
85.AB2.2B$5.AB2A79.2ABA$BA6.BA77.AB6.AB$.AB2A4.AB2A71.2ABA4.2ABA$4.BA
6.BA69.AB6.AB$5.AB2A4.AB2A63.2ABA4.2ABA$8.BA6.BA61.AB6.AB$9.AB2A71.2A
BA$12.BA2.2B61.2B2.AB$13.AB2A63.2ABA6$33.AB2A23.2ABA$32.2B2.BA21.AB2.
2B$37.AB2A15.2ABA$32.BA6.BA13.AB6.AB$33.AB2A4.AB2A7.2ABA4.2ABA$36.BA
6.BA5.AB6.AB$37.AB2A4.ABA.ABA4.2ABA$40.BA5.B.B5.AB$41.AB2A7.2ABA$44.B
A.B.B.AB$45.ABA.ABA!
[[ STEP 2 ]]

Code: Select all

x = 49, y = 66, rule = bprenticesrule-emulated
13.B.B17.B.B$12.B3.B15.B3.B$16.A.B11.B.A$12.B2.BA2.B9.B2.AB2.B$13.B.A
17.A.B$15.A3.B9.B3.A$16.B.B11.B.B2$9.B.B25.B.B$8.B3.B23.B3.B$12.A.B
19.B.A$8.B2.BA2.B17.B2.AB2.B$9.B.A25.A.B$11.A3.B17.B3.A$12.B.B19.B.B
2$5.B.B33.B.B$4.B3.B31.B3.B$8.A.B27.B.A$4.B2.BA2.B25.B2.AB2.B$5.B.A
33.A.B$7.A3.B25.B3.A$8.B.B27.B.B2$.B.B41.B.B$B3.B39.B3.B$4.A.B35.B.A$
B2.BA2.B33.B2.AB2.B$.B.A41.A.B$3.A3.B33.B3.A$4.B.B35.B.B5$4.B.B35.B.B
$3.A3.B33.B3.A$.B.A41.A.B$B2.BA2.B33.B2.AB2.B$4.A.B35.B.A$B3.B39.B3.B
$.B.B41.B.B2$8.B.B27.B.B$7.A3.B25.B3.A$5.B.A33.A.B$4.B2.BA2.B25.B2.AB
2.B$8.A.B27.B.A$4.B3.B31.B3.B$5.B.B33.B.B2$12.B.B19.B.B$11.A3.B17.B3.
A$9.B.A25.A.B$8.B2.BA2.B17.B2.AB2.B$12.A.B19.B.A$8.B3.B23.B3.B$9.B.B
25.B.B2$16.B.B11.B.B$15.A3.B9.B3.A$13.B.A17.A.B$12.B2.BA2.B9.B2.AB2.B
$16.A.B11.B.A$12.B3.B15.B3.B$13.B.B17.B.B!
[[ STEP 2 ]]

Code: Select all

x = 103, y = 152, rule = bprenticesrule-emulated
48.B.2B.B24.4B14.4B$47.B2.2A2.B22.2A2.2B12.2B2.2A$11.B.B.B.B$10.2B.A
4.B8.B.A17.B2.2B2.B21.B7.B8.B7.B$10.B3.B11.2B.3B.B14.B.2A.B21.2A5.A2.
B6.B2.A5.2A$10.A7.B7.A7.B$10.2B.AB11.B5.B42.B3.3B.2B8.2B.3B3.B$11.A.
2B3.B7.BA5.2B40.BA2B5.3B4.3B5.2BAB$27.B.B.B.B$14.B3.B10.B3.B41.B6.B2.
2B4.2B2.B6.B$15.B.B12.A.B43.A6.2AB6.B2A6.A2$78.B3.B12.B3.B$79.A.B14.B
.A3$8.2B.B.B3.3B.2B$8.B2.B.B5.B2.B$8.B2.3B3.3B2.B.3B53.B.B12.B.B$8.B
4.B.B.B4.B.B54.A3.B10.B3.A$8.2B3.B.B.3B.2B.3B$79.B5.B6.B5.B$6.23B51.A
5.A4.A5.A$48.B.2B.B$16.B.B28.B2.2A2.B27.B2.3B2.3B2.B$16.B.B64.A2B2.2B
2.2BA$16.3B28.B2.AB2.A$18.B32.B.B30.B3.2B3.B$18.B28.B3.A33.B.B2.B.B2$
47.B3.B$48.A.B6$4.B.B14.B.A$3.A3.B12.B3.A58.B.3B$.B.A14.B.A62.B3.B$B
2.2B2.B9.B2.AB4.A56.B.3B.3B$4.A.B14.A3.A.A19.B.B2.B.B28.B.B3.B$B3.B
12.B3.2B3.A19.B3.2A3.B27.B.3B.3B$.A.B14.B.A2.A3.B$22.A.A21.B.B2.A3.A
25.13B$23.A.B26.B.B$48.B3.A32.B.3B$47.B3.B33.B3.B$5.2B.3B3.3B.2B65.B.
3B$5.B2.B7.B2.B31.B.A31.B.B$5.B2.3B3.3B2.B.3B61.B.3B$5.B2.B.B.B3.B2.B
.B27.B3.B$5.2B.3B.B.3B.2B.3B26.A.B2$3.23B2$13.3B$13.B$13.3B$13.B.B$
13.3B$48.3B$48.B.B$48.3B.3B$48.B.B.B$48.3B.3B2$46.11B2$50.3B$50.B.B$
50.3B$50.B.B$2.B.B16.B.B26.3B$.2B.2B14.A3.B$.A3.B12.B.A$.A3.B11.B2.BA
2.B$.BA.2B15.B.A$2.B.A12.B3.B$18.A.B$20.B.B$19.A3.A2$19.B3.B$20.B.B4$
5.2B.3B3.B.B.2B$5.B2.B.B3.B.B2.B$5.B2.3B3.3B2.B.3B$5.B2.B.B.B3.B2.B.B
$5.2B.3B.B3.B.2B.3B2$3.23B$54.3B$13.3B40.B$13.B.B38.3B7.B.A9.B.B11.A.
B$13.3B38.B8.B2.2BA6.B2.BAB8.B2.A2B$13.B.B38.3B8.B3.B7.B3.A9.B3.B$13.
3B47.B3.B7.B3.B9.B3.B$64.3B2.B6.3B2.B8.3B2.B$66.B.B9.B.B11.B.B7$12.B.
A$11.2B.AB$11.B5.A49.A.B$11.B2.BA2.B47.B3.A11.A.B12.B.A$11.AB.2B38.B.
B24.B3.B10.B3.A$12.B5.B35.B.B9.B3.B$10.B.B2.B.B36.3B9.2A2B11.2B.AB9.A
2B2.B$9.B3.B42.B8.B3.A11.2A.2B8.B2.A2B$56.B$9.B3.B51.B3.B11.B3.B8.B3.
B$10.B.B53.B.B13.B.B10.B.A4$4.2B.B.3B3.3B.2B$4.B2.B3.B3.B4.B$4.B2.B.
3B3.3B2.B.3B$4.B2.B.B3.B.B.B2.B.B$4.2B.B.3B.B.3B.2B.3B2$2.25B27.3B9.B
.B$54.B10.B2.2BA8.B.A$11.3B.B.B36.3B10.B3.B6.B2.A2B$13.B.B.B36.B.B8.B
3.B10.B3.B$11.3B.3B36.3B9.2BA2.B6.B3.B$11.B5.B50.B.B8.3B2.B$11.3B3.B
63.B.B10$54.3B9.B5.B9.3BA$54.B.B8.B.B3.A.A7.2B2.AB$54.3B12.B.B$54.B.B
8.B.BA2.BAB7.2B2.BA$54.3B9.B5.B9.A3B$68.B3.B$69.B.B!
[[ STEP 2 ]]

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