Rule request thread

[Citation needed]

Are there any isotropic range-1 two-state rules with small glider reflectors/duplicators with short repeat time?
"Investigator" rules are also welcome.

[confocaloid]

Are there any isotropic range-1 two-state rules with small glider reflectors/duplicators with short repeat time? [...]

• https://github.com/yujh-yujh/gliderduplicatordb
• viewtopic.php?f=11&t=4759
• viewtopic.php?f=11&t=5158
• viewtopic.php?f=11&t=5162
• viewtopic.php?f=11&t=5606

[islptng]

Ignorance, but based on BasiKnight instead of Life.
Thanks.

Also a challenge: 5-state vN construction universal.

[b-engine]

Ignorance, but based on BasiKnight instead of Life.
Thanks.

This is the handwritten ruletable of B2e3air4ijwz/S12-in3k4r5i:

Code: Select all

#R BasiKnight
! 
[[ RANDOMIZE ]]

@RULE BasiKnight
@TABLE
n_states:2
neighborhood:Moore 
symmetries:rotate4reflect
var a={0,1}
var a1=a
var a2=a
var a3=a
var a4=a
var a5=a
var a6=a
var a7=a
var a8=a

0,1,0,1,0,0,0,0,0,1
0,1,1,1,0,0,0,0,0,1
0,0,1,1,1,0,0,0,0,1
0,1,1,0,0,1,0,0,0,1
0,1,1,0,1,1,0,0,0,1
0,1,0,1,0,1,1,0,0,1
0,1,1,0,0,0,1,1,0,1
0,1,1,0,0,1,1,0,0,1
1,1,0,0,0,0,0,0,0,1
1,0,1,0,0,0,0,0,0,1
1,1,1,0,0,0,0,0,0,1
1,1,0,1,0,0,0,0,0,1
1,0,1,0,1,0,0,0,0,1
1,1,0,0,1,0,0,0,0,1
1,1,0,1,0,0,1,0,0,1
1,1,1,1,0,1,0,0,0,1
1,1,1,1,1,1,0,0,0,1


a,a1,a2,a3,a4,a5,a6,a7,a8,0

[LuveelVoom]

The rules described in these discord conversations:
https://discord.com/channels/3579222555 ... 3285567599
(For the first one, can it have n>6 or so?)

Also, a rule that is life except gliders move at normal speed and the rest of life only updates every other tick (doublespeedgliderlife)

[confocaloid]

The rules described in these discord conversations:

Please crosspost all discussion relevant to the request, so that people who aren't on Discord will be able to contribute.

In general, avoid assuming that everyone is willing or able to read stuff that's hidden behind a login wall. viewtopic.php?f=3&t=5906&start=25

[LuveelVoom]

The rules described in these discord conversations:

Please crosspost all discussion relevant to the request, so that people who aren't on Discord will be able to contribute.

In general, avoid assuming that everyone is willing or able to read stuff that's hidden behind a login wall. viewtopic.php?f=3&t=5906&start=25

[H. H. P. M. P. Cole]

Ignorance, but based on BasiKnight instead of Life.
Thanks.

[...]

Here you go (based on b-engine's ruletable for ordinary BasiKnight):

Code: Select all

x = 64, y = 64, rule = IgnoranceBasiKnight
!
[[ RANDOMIZE ]]
@RULE IgnoranceBasiKnight
@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect
var a={0,1,2}
var a1=a
var a2=a
var a3=a
var a4=a
var a5=a
var a6=a
var a7=a
var a8=a
var b={0,1}
var b1=b
var b2=b
var b3=b
var b4=b
var b5=b
var b6=b
var b7=b
var b8=b
var c={0,2}
var c1=c
var c2=c
var c3=c
var c4=c
var c5=c
var c6=c
var c7=c
var c8=c
0,1,c2,1,c4,c5,c6,c7,c8,1
0,1,1,1,c4,c5,c6,c7,c8,1
0,c1,1,1,1,c5,c6,c7,c8,1
0,1,1,c3,c4,1,c6,c7,c8,1
0,1,1,c3,1,1,c6,c7,c8,1
0,1,c2,1,c4,1,1,c7,c8,1
0,1,1,c2,c3,c4,1,1,c8,1
0,1,1,c3,c4,1,1,c7,c8,1
1,1,c2,c3,c4,c5,c6,c7,c8,1
1,c1,1,c3,c4,c5,c6,c7,c8,1
1,1,1,c3,c4,c5,c6,c7,c8,1
1,1,c2,1,c4,c5,c6,c7,c8,1
1,c1,1,c3,1,c5,c6,c7,c8,1
1,1,c2,c3,1,c5,c6,c7,c8,1
1,1,c2,1,c4,c5,1,c7,c8,1
1,1,1,1,c5,1,c6,c7,c8,1
1,1,1,1,1,1,c6,c7,c8,1
0,2,b2,2,b4,b5,b6,b7,b8,2
0,2,2,2,b4,b5,b6,b7,b8,2
0,b1,2,2,2,b5,b6,b7,b8,2
0,2,2,b3,b4,2,b6,b7,b8,2
0,2,2,b3,2,2,b6,b7,b8,2
0,2,b2,2,b4,2,2,b7,b8,2
0,2,2,b2,b3,b4,2,2,b8,2
0,2,2,b3,b4,2,2,b7,b8,2
2,2,b2,b3,b4,b5,b6,b7,b8,2
2,b1,2,b3,b4,b5,b6,b7,b8,2
2,2,2,b3,b4,b5,b6,b7,b8,2
2,2,b2,2,b4,b5,b6,b7,b8,2
2,b1,2,b3,2,b5,b6,b7,b8,2
2,2,b2,b3,2,b5,b6,b7,b8,2
2,2,b2,2,b4,b5,2,b7,b8,2
2,2,2,2,b5,2,b6,b7,b8,2
2,2,2,2,2,2,b6,b7,b8,2
a,a1,a2,a3,a4,a5,a6,a7,a8,0
@COLORS
1 255 150 0
2 0 92 255

[Conway's-C4]

WireWorld but there is a second type of wire can move like B2/S23, leading to "electrons" (spaceships that can carry signals)

[pifricted]

WireWorld but there is a second type of wire can move like B2/S23, leading to "electrons" (spaceships that can carry signals)

Move like this?

Code: Select all

x = 4, y = 3, rule = B2/S23
b2o2$o2bo!

Code: Select all

#ruletable for test
x = 20, y = 4, rule = WireAndB2S23Wire
A19C$19.C$19.C$18.2C!
@RULE WireAndB2S23Wire
@TABLE
n_states:7
neighborhood:Moore
symmetries:permute
var a={0,1,2,3,4,5,6}
var s=a
var d=a
var f=a
var g=a
var h=a
var j=a
var k=a
var wh1={1,4}
var wh2=wh1
var wh3=wh1
var wh4=wh1
var bg1={0,3,6}
var bg2=bg1
var bg3=bg1
var bg4=bg1
var bg5=bg1
var bg6=bg1
var bg7=bg1
#WireWorld
3,wh1,bg1,bg2,bg3,bg4,bg5,bg6,bg7,1
3,wh1,wh2,bg1,bg2,bg3,bg4,bg5,bg6,1
1,a,s,d,f,g,h,j,k,2
2,a,s,d,f,g,h,j,k,3
#What is the singal like?
#6,wh1,bg1,bg2,bg3,bg4,bg5,bg6,bg7,4
#6,wh1,wh2,bg1,bg2,bg3,bg4,bg5,bg6,4
4,a,s,d,f,g,h,j,k,5
5,a,s,d,f,g,h,j,k,6

[Conway's-C4]

WireWorld but there is a second type of wire can move like B2/S23, leading to "electrons" (spaceships that can carry signals)

Move like this?

Code: Select all

x = 4, y = 3, rule = B2/S23
b2o2$o2bo!

Code: Select all

#ruletable for test
x = 20, y = 4, rule = WireAndB2S23Wire
A19C$19.C$19.C$18.2C!
@RULE WireAndB2S23Wire
@TABLE
n_states:7
neighborhood:Moore
symmetries:permute
var a={0,1,2,3,4,5,6}
var s=a
var d=a
var f=a
var g=a
var h=a
var j=a
var k=a
var wh1={1,4}
var wh2=wh1
var wh3=wh1
var wh4=wh1
var bg1={0,3,6}
var bg2=bg1
var bg3=bg1
var bg4=bg1
var bg5=bg1
var bg6=bg1
var bg7=bg1
#WireWorld
3,wh1,bg1,bg2,bg3,bg4,bg5,bg6,bg7,1
3,wh1,wh2,bg1,bg2,bg3,bg4,bg5,bg6,1
1,a,s,d,f,g,h,j,k,2
2,a,s,d,f,g,h,j,k,3
#What is the singal like?
#6,wh1,bg1,bg2,bg3,bg4,bg5,bg6,bg7,4
#6,wh1,wh2,bg1,bg2,bg3,bg4,bg5,bg6,4
4,a,s,d,f,g,h,j,k,5
5,a,s,d,f,g,h,j,k,6

Whoops, typo. I meant B3/S23 but whatever I'll try to utilize it anyways

[pifricted]

Maybe you can also look up Hybridizing Life and WireWorld.

I'll edit the post when I finish the ruletable.

Edit:

Code: Select all

x = 45, y = 28, rule = WireAndB3S23Wire
19.26E$19.26E$19.26E$19.26E$19.26E$19.8ED17E$19.7ED2ED15E$19.7ED2ED15E
$19.9ED6E3D7E$19.26E$19.26E$19.26E$19.26E$19.26E$9.2C8.26E$8.C2.C7.26E
$.7C.AB8.26E$2C17.15ED4ED5E$C18.13E2DE4DE2D3E$C10.8C15ED4ED5E$C9.2C7.
26E$C2.2C2.2C.C8.26E$4C.2C.3C6.2C2ED23E$.C.2C2.2C5.3C.CE3D22E$.C11.2C
2.2C2ED23E$.2C9.2C5.26E$2.7C.3C$8.3C!
@RULE WireAndB3S23Wire
@TABLE
n_states:6
neighborhood:Moore
symmetries:permute
var a={0,1,2,3,4,5}
var s=a
var d=a
var f=a
var g=a
var h=a
var j=a
var k=a
var wh1={1,4}
var wh2=wh1
var wh3=wh1
var wh4=wh1
var bg1={0,2,3,5}
var bg2=bg1
var bg3=bg1
var bg4=bg1
var bg5=bg1
var bg6=bg1
var bg7=bg1
#WireWorld
3,wh1,bg1,bg2,bg3,bg4,bg5,bg6,bg7,1
3,wh1,wh2,bg1,bg2,bg3,bg4,bg5,bg6,1
1,a,s,d,f,g,h,j,k,2
2,a,s,d,f,g,h,j,k,3
#B3/S23
5,wh1,wh2,wh3,bg1,bg2,bg3,bg4,bg5,4
4,wh1,wh2,bg1,bg2,bg3,bg4,bg5,bg6,4
4,wh1,wh2,wh3,bg2,bg3,bg4,bg5,bg6,4
4,a,s,d,f,g,h,j,k,5
@COLORS
0  48  48  48   dark gray
1   0 128 255   light blue
2 255 255 255   white
3 255 128   0   orange
4 100 255 100   mint
5 100 100 100   grey

[LittleLWSS]

I thinks for colorful-life.

If the different colors are neighbours, both of them will die.
White act as normal GoL.
Gray is Day and Night.
Red is t-HighLife.
Blue is LongLife.
Green is Justfriends.
Cyan is Morley.
Magenta is t-DryLife.
Yellow is Seed.
Deep Green is Persian Rug.
Maroon Red is "B34z/S236c".
Navy Blue is "B3-ky4jy5cr/S2-in3-aeky4cnrt5a6ekn".
Salmon Red is MYRTLElife.
Mint Green is LeapLife.
Periwinkle Blue is PedestrianLife.

Can anyone implement this?

[hotcrystal0]

OverheatLife, but dead cells naturally “cool down”. (state 100 becomes 98, which becomes 96, and so on until it becomes state 0). Call the rule OverheatCoolLife.

[PiSpaceships]

I need an INT rule with the following properties:
-I consists of spaceship-looking structures like in StellarRace (B2e3-a4-ai/S2-a34-ai); (treat StellarRace as a base and gradually modify)
-It has Pi Spaceship from my signature, which means it's between B2e3i/S2ce3rq and B2-ac3-a4-i5-y67c8/S01c2-a34-i5678;
-It is stable, with lots of spaceships and block-laying puffers.

I found one but I forgot it... I only remember that I possibly removed B4 and next allowed 4 configurations for B3 or B4; but remember that I could misremember something.

Please find this rule because I really want it to be found...

edit: Fixed 2nd conditon rulespace.
edit2: it is no longer restricted to have wanderers.

[hotcrystal0]

OverheatLife, but dead cells naturally “cool down”. (state 100 becomes 98, which becomes 96, and so on until it becomes state 0). Call the rule OverheatCoolLife.

I did this one myself:

Code: Select all

x = 0, y = 0, rule = OverheatCoolLife
!

@RULE OverheatCoolLife

@TABLE
n_states:103
neighborhood:Moore
symmetries:permute

var a1 = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 102}
var a2 = a1
var a3 = a1
var a4 = a1
var a5 = a1
var a6 = a1
var a7 = a1
var a8 = a1

var d0 = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100}
var d1 = d0
var d2 = d0
var d3 = d0
var d4 = d0
var d5 = d0
var d6 = d0
var d7 = d0
var d8 = d0

var x1 = {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}
var x2 = x1
var x3 = x1
var x4 = x1
var x5 = x1
var x6 = x1
var x7 = x1
var x8 = x1

0, a1, a2, a3, d1, d2, d3, d4, d5, 1  
2, a1, a2, a3, d1, d2, d3, d4, d5, 3  
4, a1, a2, a3, d1, d2, d3, d4, d5, 5  
6, a1, a2, a3, d1, d2, d3, d4, d5, 7  
8, a1, a2, a3, d1, d2, d3, d4, d5, 9  
10, a1, a2, a3, d1, d2, d3, d4, d5,11  
12, a1, a2, a3, d1, d2, d3, d4, d5,13  
14, a1, a2, a3, d1, d2, d3, d4, d5,15  
16, a1, a2, a3, d1, d2, d3, d4, d5,17  
18, a1, a2, a3, d1, d2, d3, d4, d5,19  
20, a1, a2, a3, d1, d2, d3, d4, d5,21  
22, a1, a2, a3, d1, d2, d3, d4, d5,23  
24, a1, a2, a3, d1, d2, d3, d4, d5,25  
26, a1, a2, a3, d1, d2, d3, d4, d5,27  
28, a1, a2, a3, d1, d2, d3, d4, d5,29  
30, a1, a2, a3, d1, d2, d3, d4, d5,31  
32, a1, a2, a3, d1, d2, d3, d4, d5,33  
34, a1, a2, a3, d1, d2, d3, d4, d5,35  
36, a1, a2, a3, d1, d2, d3, d4, d5,37  
38, a1, a2, a3, d1, d2, d3, d4, d5,39  
40, a1, a2, a3, d1, d2, d3, d4, d5,41  
42, a1, a2, a3, d1, d2, d3, d4, d5,43  
44, a1, a2, a3, d1, d2, d3, d4, d5,45  
46, a1, a2, a3, d1, d2, d3, d4, d5,47  
48, a1, a2, a3, d1, d2, d3, d4, d5,49  
50, a1, a2, a3, d1, d2, d3, d4, d5,51  
52, a1, a2, a3, d1, d2, d3, d4, d5,53  
54, a1, a2, a3, d1, d2, d3, d4, d5,55  
56, a1, a2, a3, d1, d2, d3, d4, d5,57  
58, a1, a2, a3, d1, d2, d3, d4, d5,59  
60, a1, a2, a3, d1, d2, d3, d4, d5,61  
62, a1, a2, a3, d1, d2, d3, d4, d5,63  
64, a1, a2, a3, d1, d2, d3, d4, d5,65  
66, a1, a2, a3, d1, d2, d3, d4, d5,67  
68, a1, a2, a3, d1, d2, d3, d4, d5,69  
70, a1, a2, a3, d1, d2, d3, d4, d5,71  
72, a1, a2, a3, d1, d2, d3, d4, d5,73  
74, a1, a2, a3, d1, d2, d3, d4, d5,75  
76, a1, a2, a3, d1, d2, d3, d4, d5,77  
78, a1, a2, a3, d1, d2, d3, d4, d5,79  
80, a1, a2, a3, d1, d2, d3, d4, d5,81  
82, a1, a2, a3, d1, d2, d3, d4, d5,83  
84, a1, a2, a3, d1, d2, d3, d4, d5,85  
86, a1, a2, a3, d1, d2, d3, d4, d5,87  
88, a1, a2, a3, d1, d2, d3, d4, d5,89  
90, a1, a2, a3, d1, d2, d3, d4, d5,91  
92, a1, a2, a3, d1, d2, d3, d4, d5,93  
94, a1, a2, a3, d1, d2, d3, d4, d5,95  
96, a1, a2, a3, d1, d2, d3, d4, d5,97  
98, a1, a2, a3, d1, d2, d3, d4, d5,99  
100, a1, a2, a3, d1, d2, d3, d4, d5,101 

101, 102, x1, x2, x3, x4, x5, x6, x7, 1

101, 100, 100, 100, x3, x4, x5, x6, x7, 101

d1, 102, x1, x2, x3, x4, x5, x6, x7, 0
102, d1, d2, d3, d4, d5, d6, d7, d8, 2 
102, a1, a2, d3, d4, d5, d6, d7, d8, 1 
102, a1, a2, a3, d4, d5, d6, d7, d8, 1 
102, a1, d2, d3, d4, d5, d6, d7, d8, 2 
102, a1, a2, a3, a4, d5, d6, d7, d8, 2 
102, a1, a2, a3, a4, a5, d6, d7, d8, 2 
102, a1, a2, a3, a4, a5, a6, d7, d8, 2 
102, a1, a2, a3, a4, a5, a6, a7, d8, 2 
102, a1, a2, a3, a4, a5, a6, a7, a8, 2 

1, d1, d2, d3, d4, d5, d6, d7, d8, 2 
1, a1, d2, d3, d4, d5, d6, d7, d8, 2 
1, a1, a2, a3, a4, d5, d6, d7, d8, 2 
1, a1, a2, a3, a4, a5, d6, d7, d8, 2 
1, a1, a2, a3, a4, a5, a6, d7, d8, 2 
1, a1, a2, a3, a4, a5, a6, a7, d8, 2 
1, a1, a2, a3, a4, a5, a6, a7, a8, 2 
3, d1, d2, d3, d4, d5, d6, d7, d8, 4 
3, a1, d2, d3, d4, d5, d6, d7, d8, 4 
3, a1, a2, a3, a4, d5, d6, d7, d8, 4 
3, a1, a2, a3, a4, a5, d6, d7, d8, 4 
3, a1, a2, a3, a4, a5, a6, d7, d8, 4 
3, a1, a2, a3, a4, a5, a6, a7, d8, 4 
3, a1, a2, a3, a4, a5, a6, a7, a8, 4 
5, d1, d2, d3, d4, d5, d6, d7, d8, 6 
5, a1, d2, d3, d4, d5, d6, d7, d8, 6 
5, a1, a2, a3, a4, d5, d6, d7, d8, 6 
5, a1, a2, a3, a4, a5, d6, d7, d8, 6 
5, a1, a2, a3, a4, a5, a6, d7, d8, 6 
5, a1, a2, a3, a4, a5, a6, a7, d8, 6 
5, a1, a2, a3, a4, a5, a6, a7, a8, 6 
7, d1, d2, d3, d4, d5, d6, d7, d8, 8 
7, a1, d2, d3, d4, d5, d6, d7, d8, 8 
7, a1, a2, a3, a4, d5, d6, d7, d8, 8 
7, a1, a2, a3, a4, a5, d6, d7, d8, 8 
7, a1, a2, a3, a4, a5, a6, d7, d8, 8 
7, a1, a2, a3, a4, a5, a6, a7, d8, 8 
7, a1, a2, a3, a4, a5, a6, a7, a8, 8 
9, d1, d2, d3, d4, d5, d6, d7, d8, 10 
9, a1, d2, d3, d4, d5, d6, d7, d8, 10 
9, a1, a2, a3, a4, d5, d6, d7, d8, 10 
9, a1, a2, a3, a4, a5, d6, d7, d8, 10 
9, a1, a2, a3, a4, a5, a6, d7, d8, 10 
9, a1, a2, a3, a4, a5, a6, a7, d8, 10 
9, a1, a2, a3, a4, a5, a6, a7, a8, 10 
11, d1, d2, d3, d4, d5, d6, d7, d8, 12 
11, a1, d2, d3, d4, d5, d6, d7, d8, 12 
11, a1, a2, a3, a4, d5, d6, d7, d8, 12 
11, a1, a2, a3, a4, a5, d6, d7, d8, 12 
11, a1, a2, a3, a4, a5, a6, d7, d8, 12 
11, a1, a2, a3, a4, a5, a6, a7, d8, 12 
11, a1, a2, a3, a4, a5, a6, a7, a8, 12 
13, d1, d2, d3, d4, d5, d6, d7, d8, 14 
13, a1, d2, d3, d4, d5, d6, d7, d8, 14 
13, a1, a2, a3, a4, d5, d6, d7, d8, 14 
13, a1, a2, a3, a4, a5, d6, d7, d8, 14 
13, a1, a2, a3, a4, a5, a6, d7, d8, 14 
13, a1, a2, a3, a4, a5, a6, a7, d8, 14 
13, a1, a2, a3, a4, a5, a6, a7, a8, 14 
15, d1, d2, d3, d4, d5, d6, d7, d8, 16 
15, a1, d2, d3, d4, d5, d6, d7, d8, 16 
15, a1, a2, a3, a4, d5, d6, d7, d8, 16 
15, a1, a2, a3, a4, a5, d6, d7, d8, 16 
15, a1, a2, a3, a4, a5, a6, d7, d8, 16 
15, a1, a2, a3, a4, a5, a6, a7, d8, 16 
15, a1, a2, a3, a4, a5, a6, a7, a8, 16 
17, d1, d2, d3, d4, d5, d6, d7, d8, 18 
17, a1, d2, d3, d4, d5, d6, d7, d8, 18 
17, a1, a2, a3, a4, d5, d6, d7, d8, 18 
17, a1, a2, a3, a4, a5, d6, d7, d8, 18 
17, a1, a2, a3, a4, a5, a6, d7, d8, 18 
17, a1, a2, a3, a4, a5, a6, a7, d8, 18 
17, a1, a2, a3, a4, a5, a6, a7, a8, 18 
19, d1, d2, d3, d4, d5, d6, d7, d8, 20 
19, a1, d2, d3, d4, d5, d6, d7, d8, 20 
19, a1, a2, a3, a4, d5, d6, d7, d8, 20 
19, a1, a2, a3, a4, a5, d6, d7, d8, 20 
19, a1, a2, a3, a4, a5, a6, d7, d8, 20 
19, a1, a2, a3, a4, a5, a6, a7, d8, 20 
19, a1, a2, a3, a4, a5, a6, a7, a8, 20 
21, d1, d2, d3, d4, d5, d6, d7, d8, 22 
21, a1, d2, d3, d4, d5, d6, d7, d8, 22 
21, a1, a2, a3, a4, d5, d6, d7, d8, 22 
21, a1, a2, a3, a4, a5, d6, d7, d8, 22 
21, a1, a2, a3, a4, a5, a6, d7, d8, 22 
21, a1, a2, a3, a4, a5, a6, a7, d8, 22 
21, a1, a2, a3, a4, a5, a6, a7, a8, 22 
23, d1, d2, d3, d4, d5, d6, d7, d8, 24 
23, a1, d2, d3, d4, d5, d6, d7, d8, 24 
23, a1, a2, a3, a4, d5, d6, d7, d8, 24 
23, a1, a2, a3, a4, a5, d6, d7, d8, 24 
23, a1, a2, a3, a4, a5, a6, d7, d8, 24 
23, a1, a2, a3, a4, a5, a6, a7, d8, 24 
23, a1, a2, a3, a4, a5, a6, a7, a8, 24 
25, d1, d2, d3, d4, d5, d6, d7, d8, 26 
25, a1, d2, d3, d4, d5, d6, d7, d8, 26 
25, a1, a2, a3, a4, d5, d6, d7, d8, 26 
25, a1, a2, a3, a4, a5, d6, d7, d8, 26 
25, a1, a2, a3, a4, a5, a6, d7, d8, 26 
25, a1, a2, a3, a4, a5, a6, a7, d8, 26 
25, a1, a2, a3, a4, a5, a6, a7, a8, 26 
27, d1, d2, d3, d4, d5, d6, d7, d8, 28 
27, a1, d2, d3, d4, d5, d6, d7, d8, 28 
27, a1, a2, a3, a4, d5, d6, d7, d8, 28 
27, a1, a2, a3, a4, a5, d6, d7, d8, 28 
27, a1, a2, a3, a4, a5, a6, d7, d8, 28 
27, a1, a2, a3, a4, a5, a6, a7, d8, 28 
27, a1, a2, a3, a4, a5, a6, a7, a8, 28 
29, d1, d2, d3, d4, d5, d6, d7, d8, 30 
29, a1, d2, d3, d4, d5, d6, d7, d8, 30 
29, a1, a2, a3, a4, d5, d6, d7, d8, 30 
29, a1, a2, a3, a4, a5, d6, d7, d8, 30 
29, a1, a2, a3, a4, a5, a6, d7, d8, 30 
29, a1, a2, a3, a4, a5, a6, a7, d8, 30 
29, a1, a2, a3, a4, a5, a6, a7, a8, 30 
31, d1, d2, d3, d4, d5, d6, d7, d8, 32 
31, a1, d2, d3, d4, d5, d6, d7, d8, 32 
31, a1, a2, a3, a4, d5, d6, d7, d8, 32 
31, a1, a2, a3, a4, a5, d6, d7, d8, 32 
31, a1, a2, a3, a4, a5, a6, d7, d8, 32 
31, a1, a2, a3, a4, a5, a6, a7, d8, 32 
31, a1, a2, a3, a4, a5, a6, a7, a8, 32 
33, d1, d2, d3, d4, d5, d6, d7, d8, 34 
33, a1, d2, d3, d4, d5, d6, d7, d8, 34 
33, a1, a2, a3, a4, d5, d6, d7, d8, 34 
33, a1, a2, a3, a4, a5, d6, d7, d8, 34 
33, a1, a2, a3, a4, a5, a6, d7, d8, 34 
33, a1, a2, a3, a4, a5, a6, a7, d8, 34 
33, a1, a2, a3, a4, a5, a6, a7, a8, 34 
35, d1, d2, d3, d4, d5, d6, d7, d8, 36 
35, a1, d2, d3, d4, d5, d6, d7, d8, 36 
35, a1, a2, a3, a4, d5, d6, d7, d8, 36 
35, a1, a2, a3, a4, a5, d6, d7, d8, 36 
35, a1, a2, a3, a4, a5, a6, d7, d8, 36 
35, a1, a2, a3, a4, a5, a6, a7, d8, 36 
35, a1, a2, a3, a4, a5, a6, a7, a8, 36 
37, d1, d2, d3, d4, d5, d6, d7, d8, 38 
37, a1, d2, d3, d4, d5, d6, d7, d8, 38 
37, a1, a2, a3, a4, d5, d6, d7, d8, 38 
37, a1, a2, a3, a4, a5, d6, d7, d8, 38 
37, a1, a2, a3, a4, a5, a6, d7, d8, 38 
37, a1, a2, a3, a4, a5, a6, a7, d8, 38 
37, a1, a2, a3, a4, a5, a6, a7, a8, 38 
39, d1, d2, d3, d4, d5, d6, d7, d8, 40 
39, a1, d2, d3, d4, d5, d6, d7, d8, 40 
39, a1, a2, a3, a4, d5, d6, d7, d8, 40 
39, a1, a2, a3, a4, a5, d6, d7, d8, 40 
39, a1, a2, a3, a4, a5, a6, d7, d8, 40 
39, a1, a2, a3, a4, a5, a6, a7, d8, 40 
39, a1, a2, a3, a4, a5, a6, a7, a8, 40 
41, d1, d2, d3, d4, d5, d6, d7, d8, 42 
41, a1, d2, d3, d4, d5, d6, d7, d8, 42 
41, a1, a2, a3, a4, d5, d6, d7, d8, 42 
41, a1, a2, a3, a4, a5, d6, d7, d8, 42 
41, a1, a2, a3, a4, a5, a6, d7, d8, 42 
41, a1, a2, a3, a4, a5, a6, a7, d8, 42 
41, a1, a2, a3, a4, a5, a6, a7, a8, 42 
43, d1, d2, d3, d4, d5, d6, d7, d8, 44 
43, a1, d2, d3, d4, d5, d6, d7, d8, 44 
43, a1, a2, a3, a4, d5, d6, d7, d8, 44 
43, a1, a2, a3, a4, a5, d6, d7, d8, 44 
43, a1, a2, a3, a4, a5, a6, d7, d8, 44 
43, a1, a2, a3, a4, a5, a6, a7, d8, 44 
43, a1, a2, a3, a4, a5, a6, a7, a8, 44 
45, d1, d2, d3, d4, d5, d6, d7, d8, 46 
45, a1, d2, d3, d4, d5, d6, d7, d8, 46 
45, a1, a2, a3, a4, d5, d6, d7, d8, 46 
45, a1, a2, a3, a4, a5, d6, d7, d8, 46 
45, a1, a2, a3, a4, a5, a6, d7, d8, 46 
45, a1, a2, a3, a4, a5, a6, a7, d8, 46 
45, a1, a2, a3, a4, a5, a6, a7, a8, 46 
47, d1, d2, d3, d4, d5, d6, d7, d8, 48 
47, a1, d2, d3, d4, d5, d6, d7, d8, 48 
47, a1, a2, a3, a4, d5, d6, d7, d8, 48 
47, a1, a2, a3, a4, a5, d6, d7, d8, 48 
47, a1, a2, a3, a4, a5, a6, d7, d8, 48 
47, a1, a2, a3, a4, a5, a6, a7, d8, 48 
47, a1, a2, a3, a4, a5, a6, a7, a8, 48 
49, d1, d2, d3, d4, d5, d6, d7, d8, 50 
49, a1, d2, d3, d4, d5, d6, d7, d8, 50 
49, a1, a2, a3, a4, d5, d6, d7, d8, 50 
49, a1, a2, a3, a4, a5, d6, d7, d8, 50 
49, a1, a2, a3, a4, a5, a6, d7, d8, 50 
49, a1, a2, a3, a4, a5, a6, a7, d8, 50 
49, a1, a2, a3, a4, a5, a6, a7, a8, 50 
51, d1, d2, d3, d4, d5, d6, d7, d8, 52 
51, a1, d2, d3, d4, d5, d6, d7, d8, 52 
51, a1, a2, a3, a4, d5, d6, d7, d8, 52 
51, a1, a2, a3, a4, a5, d6, d7, d8, 52 
51, a1, a2, a3, a4, a5, a6, d7, d8, 52 
51, a1, a2, a3, a4, a5, a6, a7, d8, 52 
51, a1, a2, a3, a4, a5, a6, a7, a8, 52 
53, d1, d2, d3, d4, d5, d6, d7, d8, 54 
53, a1, d2, d3, d4, d5, d6, d7, d8, 54 
53, a1, a2, a3, a4, d5, d6, d7, d8, 54 
53, a1, a2, a3, a4, a5, d6, d7, d8, 54 
53, a1, a2, a3, a4, a5, a6, d7, d8, 54 
53, a1, a2, a3, a4, a5, a6, a7, d8, 54 
53, a1, a2, a3, a4, a5, a6, a7, a8, 54 
55, d1, d2, d3, d4, d5, d6, d7, d8, 56 
55, a1, d2, d3, d4, d5, d6, d7, d8, 56 
55, a1, a2, a3, a4, d5, d6, d7, d8, 56 
55, a1, a2, a3, a4, a5, d6, d7, d8, 56 
55, a1, a2, a3, a4, a5, a6, d7, d8, 56 
55, a1, a2, a3, a4, a5, a6, a7, d8, 56 
55, a1, a2, a3, a4, a5, a6, a7, a8, 56 
57, d1, d2, d3, d4, d5, d6, d7, d8, 58 
57, a1, d2, d3, d4, d5, d6, d7, d8, 58 
57, a1, a2, a3, a4, d5, d6, d7, d8, 58 
57, a1, a2, a3, a4, a5, d6, d7, d8, 58 
57, a1, a2, a3, a4, a5, a6, d7, d8, 58 
57, a1, a2, a3, a4, a5, a6, a7, d8, 58 
57, a1, a2, a3, a4, a5, a6, a7, a8, 58 
59, d1, d2, d3, d4, d5, d6, d7, d8, 60 
59, a1, d2, d3, d4, d5, d6, d7, d8, 60 
59, a1, a2, a3, a4, d5, d6, d7, d8, 60 
59, a1, a2, a3, a4, a5, d6, d7, d8, 60 
59, a1, a2, a3, a4, a5, a6, d7, d8, 60 
59, a1, a2, a3, a4, a5, a6, a7, d8, 60 
59, a1, a2, a3, a4, a5, a6, a7, a8, 60 
61, d1, d2, d3, d4, d5, d6, d7, d8, 62 
61, a1, d2, d3, d4, d5, d6, d7, d8, 62 
61, a1, a2, a3, a4, d5, d6, d7, d8, 62 
61, a1, a2, a3, a4, a5, d6, d7, d8, 62 
61, a1, a2, a3, a4, a5, a6, d7, d8, 62 
61, a1, a2, a3, a4, a5, a6, a7, d8, 62 
61, a1, a2, a3, a4, a5, a6, a7, a8, 62 
63, d1, d2, d3, d4, d5, d6, d7, d8, 64 
63, a1, d2, d3, d4, d5, d6, d7, d8, 64 
63, a1, a2, a3, a4, d5, d6, d7, d8, 64 
63, a1, a2, a3, a4, a5, d6, d7, d8, 64 
63, a1, a2, a3, a4, a5, a6, d7, d8, 64 
63, a1, a2, a3, a4, a5, a6, a7, d8, 64 
63, a1, a2, a3, a4, a5, a6, a7, a8, 64 
65, d1, d2, d3, d4, d5, d6, d7, d8, 66 
65, a1, d2, d3, d4, d5, d6, d7, d8, 66 
65, a1, a2, a3, a4, d5, d6, d7, d8, 66 
65, a1, a2, a3, a4, a5, d6, d7, d8, 66 
65, a1, a2, a3, a4, a5, a6, d7, d8, 66 
65, a1, a2, a3, a4, a5, a6, a7, d8, 66 
65, a1, a2, a3, a4, a5, a6, a7, a8, 66 
67, d1, d2, d3, d4, d5, d6, d7, d8, 68 
67, a1, d2, d3, d4, d5, d6, d7, d8, 68 
67, a1, a2, a3, a4, d5, d6, d7, d8, 68 
67, a1, a2, a3, a4, a5, d6, d7, d8, 68 
67, a1, a2, a3, a4, a5, a6, d7, d8, 68 
67, a1, a2, a3, a4, a5, a6, a7, d8, 68 
67, a1, a2, a3, a4, a5, a6, a7, a8, 68 
69, d1, d2, d3, d4, d5, d6, d7, d8, 70 
69, a1, d2, d3, d4, d5, d6, d7, d8, 70 
69, a1, a2, a3, a4, d5, d6, d7, d8, 70 
69, a1, a2, a3, a4, a5, d6, d7, d8, 70 
69, a1, a2, a3, a4, a5, a6, d7, d8, 70 
69, a1, a2, a3, a4, a5, a6, a7, d8, 70 
69, a1, a2, a3, a4, a5, a6, a7, a8, 70 
71, d1, d2, d3, d4, d5, d6, d7, d8, 72 
71, a1, d2, d3, d4, d5, d6, d7, d8, 72 
71, a1, a2, a3, a4, d5, d6, d7, d8, 72 
71, a1, a2, a3, a4, a5, d6, d7, d8, 72 
71, a1, a2, a3, a4, a5, a6, d7, d8, 72 
71, a1, a2, a3, a4, a5, a6, a7, d8, 72 
71, a1, a2, a3, a4, a5, a6, a7, a8, 72 
73, d1, d2, d3, d4, d5, d6, d7, d8, 74 
73, a1, d2, d3, d4, d5, d6, d7, d8, 74 
73, a1, a2, a3, a4, d5, d6, d7, d8, 74 
73, a1, a2, a3, a4, a5, d6, d7, d8, 74 
73, a1, a2, a3, a4, a5, a6, d7, d8, 74 
73, a1, a2, a3, a4, a5, a6, a7, d8, 74 
73, a1, a2, a3, a4, a5, a6, a7, a8, 74 
75, d1, d2, d3, d4, d5, d6, d7, d8, 76 
75, a1, d2, d3, d4, d5, d6, d7, d8, 76 
75, a1, a2, a3, a4, d5, d6, d7, d8, 76 
75, a1, a2, a3, a4, a5, d6, d7, d8, 76 
75, a1, a2, a3, a4, a5, a6, d7, d8, 76 
75, a1, a2, a3, a4, a5, a6, a7, d8, 76 
75, a1, a2, a3, a4, a5, a6, a7, a8, 76 
77, d1, d2, d3, d4, d5, d6, d7, d8, 78 
77, a1, d2, d3, d4, d5, d6, d7, d8, 78 
77, a1, a2, a3, a4, d5, d6, d7, d8, 78 
77, a1, a2, a3, a4, a5, d6, d7, d8, 78 
77, a1, a2, a3, a4, a5, a6, d7, d8, 78 
77, a1, a2, a3, a4, a5, a6, a7, d8, 78 
77, a1, a2, a3, a4, a5, a6, a7, a8, 78 
79, d1, d2, d3, d4, d5, d6, d7, d8, 80 
79, a1, d2, d3, d4, d5, d6, d7, d8, 80 
79, a1, a2, a3, a4, d5, d6, d7, d8, 80 
79, a1, a2, a3, a4, a5, d6, d7, d8, 80 
79, a1, a2, a3, a4, a5, a6, d7, d8, 80 
79, a1, a2, a3, a4, a5, a6, a7, d8, 80 
79, a1, a2, a3, a4, a5, a6, a7, a8, 80 
81, d1, d2, d3, d4, d5, d6, d7, d8, 82 
81, a1, d2, d3, d4, d5, d6, d7, d8, 82 
81, a1, a2, a3, a4, d5, d6, d7, d8, 82 
81, a1, a2, a3, a4, a5, d6, d7, d8, 82 
81, a1, a2, a3, a4, a5, a6, d7, d8, 82 
81, a1, a2, a3, a4, a5, a6, a7, d8, 82 
81, a1, a2, a3, a4, a5, a6, a7, a8, 82 
83, d1, d2, d3, d4, d5, d6, d7, d8, 84 
83, a1, d2, d3, d4, d5, d6, d7, d8, 84 
83, a1, a2, a3, a4, d5, d6, d7, d8, 84 
83, a1, a2, a3, a4, a5, d6, d7, d8, 84 
83, a1, a2, a3, a4, a5, a6, d7, d8, 84 
83, a1, a2, a3, a4, a5, a6, a7, d8, 84 
83, a1, a2, a3, a4, a5, a6, a7, a8, 84 
85, d1, d2, d3, d4, d5, d6, d7, d8, 86 
85, a1, d2, d3, d4, d5, d6, d7, d8, 86 
85, a1, a2, a3, a4, d5, d6, d7, d8, 86 
85, a1, a2, a3, a4, a5, d6, d7, d8, 86 
85, a1, a2, a3, a4, a5, a6, d7, d8, 86 
85, a1, a2, a3, a4, a5, a6, a7, d8, 86 
85, a1, a2, a3, a4, a5, a6, a7, a8, 86 
87, d1, d2, d3, d4, d5, d6, d7, d8, 88 
87, a1, d2, d3, d4, d5, d6, d7, d8, 88 
87, a1, a2, a3, a4, d5, d6, d7, d8, 88 
87, a1, a2, a3, a4, a5, d6, d7, d8, 88 
87, a1, a2, a3, a4, a5, a6, d7, d8, 88 
87, a1, a2, a3, a4, a5, a6, a7, d8, 88 
87, a1, a2, a3, a4, a5, a6, a7, a8, 88 
89, d1, d2, d3, d4, d5, d6, d7, d8, 90 
89, a1, d2, d3, d4, d5, d6, d7, d8, 90 
89, a1, a2, a3, a4, d5, d6, d7, d8, 90 
89, a1, a2, a3, a4, a5, d6, d7, d8, 90 
89, a1, a2, a3, a4, a5, a6, d7, d8, 90 
89, a1, a2, a3, a4, a5, a6, a7, d8, 90 
89, a1, a2, a3, a4, a5, a6, a7, a8, 90 
91, d1, d2, d3, d4, d5, d6, d7, d8, 92 
91, a1, d2, d3, d4, d5, d6, d7, d8, 92 
91, a1, a2, a3, a4, d5, d6, d7, d8, 92 
91, a1, a2, a3, a4, a5, d6, d7, d8, 92 
91, a1, a2, a3, a4, a5, a6, d7, d8, 92 
91, a1, a2, a3, a4, a5, a6, a7, d8, 92 
91, a1, a2, a3, a4, a5, a6, a7, a8, 92 
93, d1, d2, d3, d4, d5, d6, d7, d8, 94 
93, a1, d2, d3, d4, d5, d6, d7, d8, 94 
93, a1, a2, a3, a4, d5, d6, d7, d8, 94 
93, a1, a2, a3, a4, a5, d6, d7, d8, 94 
93, a1, a2, a3, a4, a5, a6, d7, d8, 94 
93, a1, a2, a3, a4, a5, a6, a7, d8, 94 
93, a1, a2, a3, a4, a5, a6, a7, a8, 94 
95, d1, d2, d3, d4, d5, d6, d7, d8, 96 
95, a1, d2, d3, d4, d5, d6, d7, d8, 96 
95, a1, a2, a3, a4, d5, d6, d7, d8, 96 
95, a1, a2, a3, a4, a5, d6, d7, d8, 96 
95, a1, a2, a3, a4, a5, a6, d7, d8, 96 
95, a1, a2, a3, a4, a5, a6, a7, d8, 96 
95, a1, a2, a3, a4, a5, a6, a7, a8, 96 
97, d1, d2, d3, d4, d5, d6, d7, d8, 98 
97, a1, d2, d3, d4, d5, d6, d7, d8, 98 
97, a1, a2, a3, a4, d5, d6, d7, d8, 98 
97, a1, a2, a3, a4, a5, d6, d7, d8, 98 
97, a1, a2, a3, a4, a5, a6, d7, d8, 98 
97, a1, a2, a3, a4, a5, a6, a7, d8, 98 
97, a1, a2, a3, a4, a5, a6, a7, a8, 98 
99, d1, d2, d3, d4, d5, d6, d7, d8, 100
99, a1, d2, d3, d4, d5, d6, d7, d8, 100
99, a1, a2, a3, a4, d5, d6, d7, d8, 100
99, a1, a2, a3, a4, a5, d6, d7, d8, 100
99, a1, a2, a3, a4, a5, a6, d7, d8, 100
99, a1, a2, a3, a4, a5, a6, a7, d8, 100
99, a1, a2, a3, a4, a5, a6, a7, a8, 100
101, d1, d2, d3, d4, d5, d6, d7, d8, 102
101, a1, d2, d3, d4, d5, d6, d7, d8, 102
101, a1, a2, a3, a4, d5, d6, d7, d8, 102
101, a1, a2, a3, a4, a5, d6, d7, d8, 102
101, a1, a2, a3, a4, a5, a6, d7, d8, 102
101, a1, a2, a3, a4, a5, a6, a7, d8, 102
101, a1, a2, a3, a4, a5, a6, a7, a8, 102

100,x1,d6,d7,d5,d4,d3,d2,d1,98
98,x1,d6,d7,d5,d4,d3,d2,d1,96
96,x1,d6,d7,d5,d4,d3,d2,d1,94
94,x1,d6,d7,d5,d4,d3,d2,d1,92
92,x1,d6,d7,d5,d4,d3,d2,d1,90
90,x1,d6,d7,d5,d4,d3,d2,d1,88
88,x1,d6,d7,d5,d4,d3,d2,d1,86
86,x1,d6,d7,d5,d4,d3,d2,d1,84
84,x1,d6,d7,d5,d4,d3,d2,d1,82
82,x1,d6,d7,d5,d4,d3,d2,d1,80
80,x1,d6,d7,d5,d4,d3,d2,d1,78
78,x1,d6,d7,d5,d4,d3,d2,d1,76
76,x1,d6,d7,d5,d4,d3,d2,d1,74
74,x1,d6,d7,d5,d4,d3,d2,d1,72
72,x1,d6,d7,d5,d4,d3,d2,d1,70
70,x1,d6,d7,d5,d4,d3,d2,d1,68
68,x1,d6,d7,d5,d4,d3,d2,d1,66
66,x1,d6,d7,d5,d4,d3,d2,d1,64
64,x1,d6,d7,d5,d4,d3,d2,d1,62
62,x1,d6,d7,d5,d4,d3,d2,d1,60
60,x1,d6,d7,d5,d4,d3,d2,d1,58
58,x1,d6,d7,d5,d4,d3,d2,d1,56
56,x1,d6,d7,d5,d4,d3,d2,d1,54
54,x1,d6,d7,d5,d4,d3,d2,d1,52
52,x1,d6,d7,d5,d4,d3,d2,d1,50
50,x1,d6,d7,d5,d4,d3,d2,d1,48
48,x1,d6,d7,d5,d4,d3,d2,d1,46
46,x1,d6,d7,d5,d4,d3,d2,d1,44
44,x1,d6,d7,d5,d4,d3,d2,d1,42
42,x1,d6,d7,d5,d4,d3,d2,d1,40
40,x1,d6,d7,d5,d4,d3,d2,d1 38
38,x1,d6,d7,d5,d4,d3,d2,d1,36
36,x1,d6,d7,d5,d4,d3,d2,d1,34
34,x1,d6,d7,d5,d4,d3,d2,d1,32
32,x1,d6,d7,d5,d4,d3,d2,d1,30
30,x1,d6,d7,d5,d4,d3,d2,d1,28
28,x1,d6,d7,d5,d4,d3,d2,d1,26
26,x1,d6,d7,d5,d4,d3,d2,d1,24
24,x1,d6,d7,d5,d4,d3,d2,d1,22
22,x1,d6,d7,d5,d4,d3,d2,d1,20
20,x1,d6,d7,d5,d4,d3,d2,d1,18
18,x1,d6,d7,d5,d4,d3,d2,d1,16
16,x1,d6,d7,d5,d4,d3,d2,d1,14
14,x1,d6,d7,d5,d4,d3,d2,d1,12
12,x1,d6,d7,d5,d4,d3,d2,d1,10
10,x1,d6,d7,d5,d4,d3,d2,d1,8
8,x1,d6,d7,d5,d4,d3,d2,d1,6
6,x1,d6,d7,d5,d4,d3,d2,d1,4
4,x1,d6,d7,d5,d4,d3,d2,d1,2
2,x1,d6,d7,d5,d4,d3,d2,d1,0

@COLORS

0 0 0 0
1 0 255 255
2 1 49 49
3 5 250 250
4 2 48 48
5 10 245 245
6 3 47 47
7 15 240 240
8 4 46 46
9 20 235 235
10 5 45 45
11 25 230 230
12 6 44 44
13 30 225 225
14 7 43 43
15 35 220 220
16 8 42 42
17 40 215 215
18 9 41 41
19 45 210 210
20 10 40 40
21 50 205 205
22 11 39 39
23 55 200 200
24 12 38 38
25 60 195 195
26 13 37 37
27 65 190 190
28 14 36 36
29 70 185 185
30 15 35 35
31 75 180 180
32 16 34 34
33 80 175 175
34 17 33 33
35 85 170 170
36 18 32 32
37 90 165 165
38 19 31 31
39 95 160 160
40 20 30 30
41 100 155 155
42 21 29 29
43 105 150 150
44 22 28 28
45 110 145 145
46 23 27 27
47 115 140 140 
48 24 26 26
49 120 135 135
50 25 25 25
51 125 130 130
52 26 24 24
53 130 125 125
54 27 23 23
55 135 120 120
56 28 22 22
57 140 115 115
58 29 21 21
59 145 110 110
60 30 20 20
61 150 105 105
62 31 19 19
63 155 100 100
64 32 18 18
65 160 95 95
66 33 17 17
67 165 90 90
68 34 16 16
69 170 85 85
70 35 15 15
71 175 80 80
72 36 14 14
73 180 75 75
74 37 13 13
75 185 70 70
76 38 12 12
77 190 65 65
78 39 11 11
79 195 60 60
80 40 10 10
81 200 55 55
82 41 9 9 
83 205 50 50
84 42 8 8
85 210 45 45
86 43 7 7
87 215 40 40
88 44 6 6 
89 220 35 35
90 45 5 5
91 225 30 30
92 46 4 4
93 230 25 25
94 47 3 3
95 235 20 20
96 48 2 2 
97 240 15 15
98 49 1 1 
99 245 10 10
100 50 0 0
101 250 5 5
102 0 255 255

[CARuler]

Repilcator??????

Code: Select all

x = 4, y = 3, rule = OverheatCoolLife
2.A$.3A$2A!

[b-engine]

Repilcator??????

Code: Select all

x = 4, y = 3, rule = OverheatCoolLife
2.A$.3A$2A!

That should be a dirty replicator.

[hotcrystal0]

Twin bees shuttle eventually breaks, but not after over 1000 generations:

Code: Select all

x = 29, y = 11, rule = OverheatCoolLife
17.2A$17.A.A$19.A$17.3A4$17.3A$2A17.A7.2A$2A15.A.A7.2A$17.2A!

[confocaloid]

-It has both spaceships present on my signature, which means it's between B2e3ei/S2cen3inq4a and B2-ac3-a4-i5-y67c8/S2-a3-a4-eir5-a678;

I get a different space (between B2e3ei/S2cen3iqr4a and B2-ac3-a4-i5-y67c8/S02-a34-ir5-ac678):

Code: Select all

#C 2^76 = 75557863725914323419136
#C required birth conditions: B2e3ei
#C required survival conditions: S2cen3iqr4a
#C optional birth conditions: B2ikn3cjknqry4acejknqrtwyz5aceijknqr67c8
#C optional survival conditions: S02ik3acejkny4cejknqtwyz5eijknqry678
#C disabled birth conditions: B012ac3a4i5y7e
#C disabled survival conditions: S12a4ir5ac
x = 9, y = 4, rule = B2e3ei/S2-a34a
7bo$3o3b3o$obo4b2o$obo5bo!

In particular, to enter this space starting from B2e3-a4-ai/S2-a34-ai (which you mentioned), it's at least necessary to add the survival condition S4a and to remove the survival condition S4r:

Code: Select all

x = 9, y = 4, rule = B2e3-a4-ai/S2-a34-ir
7bo$3o3b3o$obo4b2o$obo5bo!

Code: Select all

x = 1, y = 1, rule = B2e3-a4-ai/S2-a34-ir
o!
#C [[ RANDOMIZE RANDWIDTH 64 RANDHEIGHT 48 RANDFILL 25 ]]

That much was relatively easy; however, after that there are still lots of possibilities based on what you wrote (there are 10 available subconditions of B3 and 13 available subconditions of B4; B3e, B3i are required, B3a, B4i are disabled, the remaining 19 are optional and there are several thousands of ways to choose which four out of those; if only subconditions of B4 were changed then there are 12 optional subconditions and several hundreds of ways to choose which four out of those to readd after removing B4 entirely).

I tried several tweaks without any good heuristic, and I did not see any block-laying puffers in soups.

So I guess people might have some difficulty rediscovering that particular ruleset, unless there are some additional details to limit the search space.

I need an INT rule with the following properties:
-I consists of spaceship-looking structures like in StellarRace (B2e3-a4-ai/S2-a34-ai); (treat StellarRace as a base and gradually modify)
-It has both spaceships present on my signature, which means it's between B2e3ei/S2cen3inq4a and B2-ac3-a4-i5-y67c8/S2-a3-a4-eir5-a678;
-It is stable, with lots of spaceships and block-laying puffers.

I found one but I forgot it... :? I only remember that I possibly removed B4 and next allowed 4 configurations for B3 or B4; but remember that I could misremember something.

Please find this rule because I really want it to be found...

[dvgrn]

(there are 10 available subconditions of B3 and 13 available subconditions of B4; B3e, B3i are required, B3a, B4i are disabled, the remaining 19 are optional and there are several thousands of ways to choose which four out of those; if only subconditions of B4 were changed then there are 12 optional subconditions and several hundreds of ways to choose which four out of those to readd after removing B4 entirely).

This is the kind of problem where a helper script can be really handy. For example, below is a script that helped me look quickly through the 330 options for adding four four-neighbor isotropic bits to "B2e3-a4cejk/S2-a34-ir", out of this list:

bits = ["c","e","j","k","n","q","r","t","w","y","z"]

Maybe I should have included "a" also, but I'll leave that for someone else to try -- it's an easy adjustment to the script. EDIT Nah, I tried that. 165 ( = 11 choose 3 ) rules contained "a", and they all showed up at the beginning of the new enumeration. Every single one of those rules looked about the same level of "highly explosive". Maybe I had a reason for leaving the "a" out of the list after all.

In the 330-rule space I looked at, I think only twenty or so rules were anything other than "obviously explosive". The best series started at this rule, which is "barely stable". Several of the rules out of the next twenty in the enumeration are "almost immediately stable".

Code: Select all

x = 257, y = 7, rule = B2e3-a4jknw/S2-a34-ir
o2bob3o2bo4b3obob2ob2ob4obo2b2obo5bo4b2o3b2o2b2o3bo5b5obobo4b2o2bo2b8o
2b4o3bob3o5bo2bo4bob4ob3o2b2obobo2bo3bob3obobo2bo2bo2b3obo5bobobo3b2o
67bo$3bob2o2b2ob5obobob2ob2o3bo2bo2bob3o2b2o2bobob2obobo3b2o2bo3b2o2b
7ob2o2bob2o3b2obob2obo2b4obobobo5bo2bobo3bo4bob3o2bo2bob3obob3obob2o2b
o6b2ob3ob2ob3o4bo2bo58b3o3b3o$o3b4ob5ob2o6b2o4bobo3b4obob2o2bo2bobob2o
bo5b3obo2bobo2b10ob2o2bob2obo2bo2b3obob5ob2o2bo2bobo2bob2o3b2o2bo2bob
2obob2obobo2b3obo3b2o2b3ob3o4b3o2b2obo60bobo4b2o$3bob3o4b2obo2b3o3bob
2ob4obobo12b4o2bobobo4bobo9bo2b3ob5o5b3o7b5o6bo3bob2ob2obobo4b4ob2o3b
3o2b2ob2obo2bo2bo2b2o2bob3obo2bo3bo64bobo5bo$b2obo3bo2bo2bo2bobobo2b2o
b2ob2o3b4o2bo2bob4ob2ob2ob2ob3obo2bob2o3bobo2bo2b4ob5o5bob4o2b3o2bobob
5o4b2ob2o4bo2bo2bobobo2b2ob2o2b2ob2o6bo2b4o4b2o2b3o2b2obo$2o2bo2b2ob2o
2bob5o5b5ob4o3b2o2bo2b2o2bo5bo2b5ob4o2bobob5o4bobo2bobob2ob2ob2obo4bo
3b7obo3b2obob2obo2b2o2bobo4bo2b3obo2bo5bo3b4o3b2ob5o2bo3bo$2o4b2obo2bo
2b2o2b2obo2bo2b3o3b5o2bobobob3ob3ob2o2bob3ob6o2b2o2bob2o2bob2o3bo6b2ob
o2bob4o4bo3b2ob2o3bo5bobob3ob2obob7o4bo4b2o2b2ob4obo2bo3b2o3b2o!

Here's the code I used:

Code: Select all

import golly as g
import itertools

bits = ["c","e","j","k","n","q","r","t","w","y","z"]

# enumerate all sets of four of these bits
combinations = list(itertools.combinations(bits, 4))
numcombos = len(combinations)

# look and see which combination is in the current rule
current_rule = g.getrule()
found = 0
count = 0
while not found:
  fourbits = ''.join(combinations[count])
  if current_rule.find("4" + fourbits + "/")>0:
    found = 1
  count += 1
  if count == numcombos:
    if found == 1:
      g.exit("You're at the end of the search space. The beginning was at B2e3-a4cejk/S2-a34-ir.")
    else:
      g.exit("Your test pattern isn't in the search space. To start at the beginning of the enumerated space, set a soup's rule to B2e3-a4cejk/S2-a34-ir.")

nextfourbits = ''.join(combinations[count])
g.setrule(current_rule.replace("4" + fourbits + "/", "4" + nextfourbits + "/"))

g.show("Found " + fourbits + " at count=" + str(count)+ ", replaced with " + nextfourbits)

Here's how I could inspect 330 rules exhaustively in just a few minutes, looking for block puffers -- about two seconds per explosive rule, and longer for the ones that weren't explosive but there weren't many of those.

• First, figure out an appropriate sized soup. I did a long flat rectangle of 50% fill, plus the two test spaceships but those always work in this search space.
• Turn up the step size to taste -- 2^4 or 2^6 or so, maybe.
• Assign a keyboard shortcut to the script in Golly.
• Set the rule to "B2e3-a4cejk/S2-a34-ir" to start at the beginning of the search space.
• Hit the keyboard shortcut -- I use the backtick key (`) because it's easy to find quickly.
• Every time you run the script, you move to the next rule. Hit [Enter] to test that rule.
• As soon as you see the soup growing fast, hit the Z key -- that's an uncontrolled explosion, and for this search task we don't want those.
• Repeat until you find what you want, or reach the end of the search space.

The rule I liked best in the space was probably this one, which stabilizes fairly quickly, allows "long pi spaceships" as well as pi spaceships... but beehives are replicators:

Code: Select all

x = 31, y = 59, rule = B2e3-a4jkqw/S2-a34-ir
o5b4o2b4o4bob2obo4bo$b4o2bo3b3obo2bob3o2b3ob2o$o2bob2obob2ob2ob3obobob
3o3bo$o2b2ob2o2bo2bobo5b2obob3obo$bo4bo2bo2b5o2bo6bo$ob3ob2o5b4o2b2o3b
o3b2o$3o2bo2bo2bo4b4ob3ob3ob2o$2obo4b3ob2ob3o4b3ob4o$3o2b4o2bob3obobob
2o2bo4bo$o3b2o2bob6o5b2obo3b3o$2b2o3bob2o5bo7bo2bo$2bobobo5b3ob12o$4ob
ob4ob2o7b2obob5o$2obo2b5ob2ob2obo2b8o$2o3b2ob3ob3obo2bobobob6o$2b2ob2o
2b2o2b3obo2bobo2b2o2bo$o2b4o2b3o2bob4o2bo3bob2o$2ob2o2b3obob2obob2ob2o
bobob3o$b2obo3bo2bobo2bob2o2b3o2bob2o$2o4b2o3b2ob5o7b5o$2o2bo2bo2bob3o
5bob4o2b3o$b3ob3o3bobob8obo3bobo$4ob2o2b3obobobo2bo2b4obo$6obo3bobob4o
bo2b7o$3o4b2o3bob4o2b2o2bobobobo$2b7o3b3obo4bobo2bo2bo$b3o2bobo2bob2o
2b2o2bo2bobo2bo$o2bo2b2ob4o2b4obobob3ob2o28$13bo$12bobo$12bobo$13bo!

[CARuler]

a wickstrencher found in the Investigator version

Code: Select all

x = 9, y = 1, rule = B2e3-a4-ai/S2-a34Investigator
9Q!

[PiSpaceships]

I get a different space (between B2e3ei/S2cen3iqr4a and B2-ac3-a4-i5-y67c8/S02-a34-ir5-ac678):

Code: Select all

rulespace and pattern from my signature

I fixed it and removed the requirement to have the second spaceship from my signature because I was no longer sure did this rule have it.

I tried several tweaks without any good heuristic, and I did not see any block-laying puffers in soups.
So I guess people might have some difficulty rediscovering that particular ruleset, unless there are some additional details to limit the search space.

Today I found two rules which are closer to what I try to find.
In B2e3ceiq4-i/S2-a34-ai random soups stabilize quickly but create a lot of blinker puffers before it happens.

Code: Select all

x=0, y=0, rule=B2e3ceiq4-i/S2-a34-ai
!
#C [[ RANDOMIZE RANDWIDTH 500 RANDHEIGHT 500 ]]

In B2e3ceiq4-i5a/S2-a34-ai5a behaviour of random soups is very close to what I want, but unfortunely it has no puffers in them.

Code: Select all

x=0, y=0, rule=B2e3ceiq4-i5a/S2-a34-ai5a
!
#C [[ RANDOMIZE RANDWIDTH 250 RANDHEIGHT 250 ]]

I need an INT rule with the following properties:
-I consists of spaceship-looking structures like in StellarRace (B2e3-a4-ai/S2-a34-ai); (treat StellarRace as a base and gradually modify)
-It has Pi Spaceship from my signature, which means it's between B2e3i/S2ce3rq and B2-ac3-a4-i5-y67c8/S01c2-a34-i5678;
-It is stable, with lots of spaceships and block-laying puffers.

I found one but I forgot it... I only remember that I possibly removed B4 and next allowed 4 configurations for B3 or B4; but remember that I could misremember something.

Please find this rule because I really want it to be found...

[hotcrystal0]

Edit: call the rule SumLife5.
A rule with 6 states (5 alive states) that behaves identically to CGoL, however when a cell is born it's born with the state number equal to the sum of the cell states that birthed it (mod 5, except 0 mod 5 corresponds to state 5, so for example states 2, 4, and 5 birth state 1).

[confocaloid]

I fixed it and removed the requirement to have the second spaceship from my signature because I was no longer sure did this rule have it.

Unfortunately removing constraints is likely to make the problem harder (more possibilities to explore). You might consider trying to rediscover it yourself, or just looking for other CA with similar properties.