ConwayLife.com

Posted: **September 3rd, 2017, 10:26 pm**

BlinkerSpawn wrote:For the most part it's just a binary counter.

It is. Once the counter overflows, the tick moves up a slot, and the process starts again... all the way until the end of the line is reached. Then the ship moves one cell.

Posted: **September 4th, 2017, 3:05 pm**

Saka wrote:Lemme join in with my own rule, it's 7 states and it's based on a binary counter and it's not very slow, colors added for easy viewing:

Code: Select all

@RULE BinSlow

@TABLE
n_states:7
neighborhood:vonNeumann
symmetries:none
var a={0,1,2,3,4,5,6}
var b=a
var c=a
var d=a
#IMPORTANT
a,b,c,5,d,4
1,b,c,6,d,6

0,a,b,c,1,2
2,a,b,c,1,3
2,a,b,c,3,3
0,a,b,c,3,2
3,a,b,c,d,0
4,2,0,0,4,5
5,a,b,c,d,0
4,1,5,b,c,6
4,a,5,b,c,5
6,1,b,c,d,0
6,a,4,b,c,4
0,a,b,6,c,1

@COLORS
0 48 48 48
1 255 0 0
2 0 255 0
3 0 230 0
4 0 108 255
5 0 178 255
6 0 255 255

Example:

Code: Select all

x = 23, y = 21, rule = BinSlow
5.3D$5.D.D6.A$5.3D6.3D$5.D.D$5.3D4$3.3D.3D$5.D.D$3.3D.3D4.A$5.D3.D4.
6D$3.3D.3D4$3D.3D.3D$2.D.D.D.D.D3.A$3D.D.D.3D3.9D$D3.D.D3.D$3D.3D.3D!

bounding box x*2 : period = 3*2^(x-3)+2x-1 , speed = c/period

ANOTHER RATE ( exponential, base=(1+sqrt(5))/2 )

Code: Select all

@RULE FibonacciSpeed
@TABLE
n_states:4
neighborhood:Moore
symmetries:none
var a={1,2,3}
var b={a}
var c={0,1,2,3}
var d={1,2}
var e={0,3}
2,0,0,1,0,0,0,e,0,3
3,0,0,d,0,0,0,0,0,1
1,0,0,2,0,0,0,e,0,3
1,0,0,3,0,0,0,0,0,2
1,0,0,1,0,0,0,3,0,2
3,0,0,d,0,0,0,1,0,1
1,0,0,0,0,0,0,3,0,2
2,0,0,0,0,0,0,3,0,0
0,0,0,0,0,2,3,0,0,3
0,0,0,1,0,2,0,0,0,3
0,0,0,d,0,3,0,0,0,1
0,0,0,2,0,1,e,0,0,3
0,0,0,3,0,1,0,0,0,2
0,0,0,1,0,1,3,0,0,2
0,0,0,1,0,2,3,0,0,3
0,0,0,d,0,3,1,0,0,1
0,0,0,a,0,1,2,0,0,1
0,0,0,1,0,2,1,0,0,2
0,0,0,a,0,1,1,0,0,1
a,0,b,0,0,0,0,c,0,0
3,0,0,0,0,0,1,0,0,1
1,0,0,1,0,0,3,0,0,2
2,0,0,1,0,0,3,0,0,3
3,0,0,d,0,0,1,0,0,1
1,0,0,2,0,0,3,0,0,3

length N : period = (N+3)rd Fibonacci number , speed = c/period

EXAMPLE
N=20 (c/28657 predecessor)

Code: Select all

x = 20, y = 1, rule = FibonacciSpeed
B19A!

(c/28657 itself)

Code: Select all

x = 20, y = 1, rule = FibonacciSpeed
AB2ACB14A!

Posted: **September 12th, 2017, 9:02 am**

Idea: Use LCMs! I'm writing a program to calculate the LCM of primes.

Posted: **September 12th, 2017, 10:44 am**

You could use the idea here to make a 1-cell spaceship with some massive but provably finite speed. Like, counting up to graham's number and then moving one cell. This thread is actually what gave me the idea for that thread.

Posted: **September 12th, 2017, 12:48 pm**

Saka wrote:Idea: Use LCMs! I'm writing a program to calculate the LCM of primes.

What is LCM?

Posted: **September 12th, 2017, 2:16 pm**

gameoflifemaniac wrote:What is LCM?

Least common multiple. You could've looked this up; going through Wikipedia's disambiguation page, the phrase "Least common multiple" should stand out as being the only one that would pertain to this kind of thing.

Posted: **September 12th, 2017, 7:37 pm**

gameoflifemaniac wrote:
Saka wrote:Idea: Use LCMs! I'm writing a program to calculate the LCM of primes.
What is LCM?

A person who is "like 3rd grade middle school" in maths and someone who "memorized 250 digits of pi and understands infinite sums and integrals" should know what an LCM is.

Posted: **September 13th, 2017, 11:46 am**

Saka wrote:
gameoflifemaniac wrote:
Saka wrote:Idea: Use LCMs! I'm writing a program to calculate the LCM of primes.
What is LCM?
A person who is "like 3rd grade middle school" in maths and someone who "memorized 250 digits of pi and understands infinite sums and integrals" should know what an LCM is.

Sok pinter ini orangnya

Sorry. I just could not recognize this! Maybe, if you would write this with lowercase letters, I would probably know what you're talking about.

Posted: **September 27th, 2017, 12:19 am**

Tetrationally slow ships:
(NOTE: If you installed this rule before this message was here, update! The previous version has a bug where some ships don't work!)

Code: Select all

@RULE Tesserun
Idea: Use vertically stacked binary counters
When a counter finishes, it lengthens and increments the next counter
When the last counter finishes, all lengths reset and the ship advances
0 empty
1 normal backbone
2 counter off
3 counter on
4 counter action
5 counter finish
6 increment backbone
7 unstable backbone
8 collapse backbone
9 waiting backbone
10 eater
11 eater report

@TABLE
n_states:12
neighborhood:Moore
symmetries:none
var a1={0,1,2,3,4,5,6,7,8,9,10,11}
var a2=a1
var a3=a1
var a4=a1
var a5=a1
var a6=a1
var a7=a1
var a8=a1
var any=a1
var any2=a1
var value={0,1,2,3,4,6,7}
var value2={0,1,2,3,4,6,7}
var valuen={1,2,3,4}
var valuex={0,1,2,3,4,5,6,7}
var bit={2,3,4}
var nonzero={1,2,3,4,5,6,7,8,9,10,11}
var backbone={1,6,7}
#counter
##create action
2,a1,a2,value,0,0,a4,backbone,a5,4 #inter row
2,a1,a2,value,a3,a4,6,backbone,a5,4 #inter row
##action moves
4,a1,a2,valuen,a3,a4,a5,value2,a6,2
3,a1,a2,valuen,a3,a4,a5,4,a6,4
##action finishes
2,a1,a2,value,a3,a4,a5,4,a6,3
##action transforms
3,a1,a2,0,a3,a4,a5,4,a6,5
###special case
4,a1,a2,0,a3,a4,a5,value,a6,5
##extend
0,a1,a2,any,a3,a4,a5,5,a6,2
##completion moves
5,a1,a2,value,a3,a4,a5,valuen,a6,2
bit,a1,a2,5,a3,a4,a5,value2,a6,5
##completion finishes
1,a1,a2,5,a3,a4,a5,any,a6,6
##backbone resets
6,backbone,a2,value,a3,a4,a5,any,a6,1
#advancement
##destablilize
6,0,a2,value,a3,a4,a5,any,a6,7
##collapse
7,a1,a2,5,a3,a4,a5,any,a6,8
##propagate collapse
1,8,a2,valuex,a3,a4,a5,any,a6,8
##send eater
8,a1,a2,valuex,a3,a4,a5,any,a6,9
valuex,a1,a2,value,a3,a4,a5,8,a6,10
##eater eats
10,a1,a2,valuex,a3,a4,a5,any,a6,0
valuex,a1,a2,valuen,a3,a4,a5,10,a6,10
##eater reports
valuex,a1,a2,0,a3,a4,a5,10,a6,11
##report moves
11,a1,a2,any,a3,a4,a5,any,a6,0
0,a1,a2,11,a3,a4,a5,0,a6,11
##report bonds
0,a1,a2,11,a3,a4,a5,9,a6,5
9,a1,a2,5,a3,a4,a5,any,a6,0
##prepare counter
5,a1,a2,0,a3,a4,nonzero,9,a6,9
##activate
5,a1,a2,0,a3,a4,0,9,a6,1
##propagate activation
9,a1,a2,any,a3,1,a5,any2,a6,1
@COLORS

0 0 0 0
1 255 0 0
2 0 255 0
3 0 0 255
4 255 255 0
5 255 0 255
6 0 255 255
7 255 255 255
8 127 0 0
9 0 127 0
10 0 0 127
11 127 127 0
12 127 0 127
13 0 127 127
14 127 127 127
15 127 255 0
16 255 127 0
17 127 0 255
18 255 0 127
19 0 127 255
20 0 255 127
21 127 255 255
22 255 127 255
23 255 255 127
24 255 127 127
25 127 255 127
26 127 127 255

Code: Select all

x = 2, y = 4, rule = Tesserun
AB$AB$AB$AB!

Speed ~ c/2^127

Posted: **September 27th, 2017, 10:29 am**

fluffykitty wrote:Tetrationally slow ships:

Code: Select all

@RULE Tesserun
Idea: Use vertically stacked binary counters
When a counter finishes, it lengthens and increments the next counter
When the last counter finishes, all lengths reset and the ship advances
0 empty
1 normal backbone
2 counter off
3 counter on
4 counter action
5 counter finish
6 increment backbone
7 unstable backbone
8 collapse backbone
9 waiting backbone
10 eater
11 eater report

@TABLE
n_states:12
neighborhood:Moore
symmetries:none
var a1={0,1,2,3,4,5,6,7,8,9,10,11}
var a2=a1
var a3=a1
var a4=a1
var a5=a1
var a6=a1
var a7=a1
var a8=a1
var any=a1
var any2=a1
var value={0,1,2,3,4,6,7}
var value2={0,1,2,3,4,6,7}
var valuen={1,2,3,4}
var valuex={0,1,2,3,4,5,6,7}
var bit={2,3,4}
var nonzero={1,2,3,4,5,6,7,8,9,10,11}
var backbone={1,6,7}
#counter
##create action
2,a1,a2,value,0,0,a4,backbone,a5,4 #inter row
2,a1,a2,value,a3,a4,6,backbone,a5,4 #inter row
##action moves
4,a1,a2,valuen,a3,a4,a5,value2,a6,2
3,a1,a2,valuen,a3,a4,a5,4,a6,4
##action finishes
2,a1,a2,value,a3,a4,a5,4,a6,3
##action transforms
3,a1,a2,0,a3,a4,a5,4,a6,5
###special case
4,a1,a2,0,a3,a4,a5,value,a6,5
##extend
0,a1,a2,any,a3,a4,a5,5,a6,2
##completion moves
5,a1,a2,value,a3,a4,a5,valuen,a6,2
bit,a1,a2,5,a3,a4,a5,value2,a6,5
##completion finishes
1,a1,a2,5,a3,a4,a5,any,a6,6
##backbone resets
6,backbone,a2,value,a3,a4,a5,any,a6,1
#advancement
##destablilize
6,0,a2,value,a3,a4,a5,any,a6,7
##collapse
7,a1,a2,5,a3,a4,a5,any,a6,8
##propagate collapse
1,8,a2,valuex,a3,a4,a5,any,a6,8
##send eater
8,a1,a2,valuex,a3,a4,a5,any,a6,9
valuex,a1,a2,value,a3,a4,a5,8,a6,10
##eater eats
10,a1,a2,valuex,a3,a4,a5,any,a6,0
valuex,a1,a2,valuen,a3,a4,a5,10,a6,10
##eater reports
valuex,a1,a2,0,a3,a4,a5,10,a6,11
##report moves
11,a1,a2,any,a3,a4,a5,any,a6,0
0,a1,a2,11,a3,a4,a5,0,a6,11
##report bonds
0,a1,a2,11,a3,a4,a5,9,a6,5
9,a1,a2,5,a3,a4,a5,any,a6,0
##prepare counter
5,a1,a2,0,a3,a4,nonzero,9,a6,9
##activate
5,a1,a2,0,a3,a4,0,9,a6,1
##propagate activation
9,a1,a2,any,a3,1,a5,any2,a6,1
@COLORS

0 0 0 0
1 255 0 0
2 0 255 0
3 0 0 255
4 255 255 0
5 255 0 255
6 0 255 255
7 255 255 255
8 127 0 0
9 0 127 0
10 0 0 127
11 127 127 0
12 127 0 127
13 0 127 127
14 127 127 127
15 127 255 0
16 255 127 0
17 127 0 255
18 255 0 127
19 0 127 255
20 0 255 127
21 127 255 255
22 255 127 255
23 255 255 127
24 255 127 127
25 127 255 127
26 127 127 255

Code: Select all

x = 2, y = 4, rule = Tesserun
AB$AB$AB$AB!

Speed ~ c/2^127

This is something we're all waiting for.
By the way, what's the formula for the spaceships speed?

Posted: **September 27th, 2017, 12:13 pm**

Haven't bothered to figure it out. It would probably be much more complicated than any previous rule due to various offsets.

Posted: **September 27th, 2017, 2:42 pm**

Since my last post i've been working on this problem, and I think I've figured it out.

Code: Select all

a(1)=3
a(n)=a(n-1)+2^n+2n-2 
b(1)=2
b(n)=2^b(n-1)-1
c(1,m)=a(m)
c(n,2)=a(b(n))
c(n,m)=c(n-1,2^m-1)
d(1)=0
d(n)=2b(n-1)+d(n-1)
f(n)=c(n,2)+d(n)+n-1+2b(n)+2

The height 4 spaceship has speed c/340282366920938463463374607431768227739 (c/3e38)

My notes: (a=∑,b=¬,c=∏,d=∆,n-1=∫,2b+2=Ω)

Code: Select all

Height 1 c/15
Height 2 c/34
Height 3 c/325
Height 4 c/340282366920938463463374607431768227739
Height 5 ~c/2^2^127

Extension times (Blank-Blank):
Length 1 3 (exceptional)
Length 2 6 (2^n+2n-2)
Length 3 12
Length 4 22
Length 5 40
Length 6 74
Length 7 140
Length 8 270
Increments required (Blank-Blank):
Length 1: 1 (2^n)
Length 2: 2
Length 3: 4
Time after last increment (State 6 below-Backbone activation):
Length 2: 4 (2n-2)
Length 3: 6
Total time after last increment (State 6 bottom-State 8 top):
Height 1: 0 (∆n)
Height 2: 4
Height 3: 10
Collapse propagation: (State 8 top-State 8 bottom):
Height 1: 0 (n-1)
Height 2: 1
Clearing time (State 8-State 1+2):
Length 4: 8 (2n)
Length 5: 10
∑n=n extensions of bottom
∑0=0
∑1=3
∑n=∑(n-1)+2^n+2n-2
∏n,m=m extensions of nth layer from length 1
∏1,m=∑m
∏n,m=∏n-1,(2^m-1)
¬n=Length of layer n (1=top layer):
¬1=2
¬n=2^(¬n-1)-1
∆n=Increment propagation time bottom to top with n layers (final increment)
∆1=0
∆n=2¬(n-1)+∆(n-1)
∫n=Collapse propagation time with n layers
∫n=n-1
Ωn=Clearing time for bottom layer with n layers
Ωn=2¬n+2

Height 1: ∏1,2+∆1+∫1+Ω1=15
∏1,2=∑2=3+6=9
∆1=0
∫1=0
Ω1=2¬1+2=2*2+2=6
Height 2: ∏2,2+∆2+∫2+Ω2=34
∏2,2=∏1,3=∑3=3+6+12=21
∆2=2¬1+∆1=2¬1=4
∫2=1
Ω2=2¬2=2*3+2=8
Height 3: ∏3,2+∆3+∫3+Ω3=325
∏3,2=∏2,3=∏1,7=∑7=3+6+12+22+40+74+140=297
∆3=2(¬2+¬1)=2(3+2)=2*5=10
∫3=2
Ω3=2¬3=2*7+2=16
Height 4: ∏4,2+∆4+∫4+Ω4=340282366920938463463374607431768227739
∏4,2=∏3,3=∏2,7=∏1,127=∑127=3+6+12+22+40+...+170141183460469231731687303715884105980=340282366920938463463374607431768227456
∆4=2(¬3+¬2+¬1)=2(7+3+2)=2*12=24
∫4=3
Ω4=2¬4=2*127+2=256

Posted: **October 11th, 2017, 10:22 am**

Idea:
1. A dot creates a c/2 dot moving left and spawns a binary counter that counts to the left.
2. Once the counter hits a certain point (noted by a dot), it starts counting down (If possible) and is moved 1 cell to the right.
3. After countdown has finished, the counter is turned into a c/1 dot moving left and a dot marking the position, but 1 cell to the right.
4. Once the c/1 dot catches the c/2 dot, it turns into a c/1 dot.
5. The c/1 dot moves to the right until it hits the binary counter marker (See #3).
6. Repeat.

This would be REALLY slowm

Posted: **October 11th, 2017, 3:32 pm**

i want a speed at which an onion grows
EDIT: sorry for the short post, btw. It's just that I really want the speed of an onion in ca... don't judge me.

Posted: **October 11th, 2017, 7:00 pm**

83bismuth38 wrote:i want a speed at which an onion grows
EDIT: sorry for the short post, btw. It's just that I really want the speed of an onion in ca... don't judge me.

Few problems with this:
1. What onion? There are tons of onions out there, mind you. Sometimes Alliums are counted as onions and schizobasis intricata is called a vining onion so what onion?
2. Defini grow. The roots getting longer? The bulb grtting taller? The leaves getting taller? The olant getting taller in general?

Posted: **October 11th, 2017, 8:39 pm**

Saka wrote:
83bismuth38 wrote:i want a speed at which an onion grows
EDIT: sorry for the short post, btw. It's just that I really want the speed of an onion in ca... don't judge me.
Few problems with this:
1. What onion? There are tons of onions out there, mind you. Sometimes Alliums are counted as onions and schizobasis intricata is called a vining onion so what onion?
2. Defini grow. The roots getting longer? The bulb grtting taller? The leaves getting taller? The olant getting taller in general?

the growth at which bread grows on an onion ring.

Posted: **October 12th, 2017, 2:35 am**

Saka wrote:Sometimes Alliums are counted as onions

Aren't onions part of the Allium genus?

Posted: **October 12th, 2017, 2:40 am**

muzik wrote:
Saka wrote:Sometimes Alliums are counted as onions
Aren't onions part of the Allium subspecies?

Allium is a genus.
It has more than 500 species.

Posted: **October 26th, 2017, 1:21 pm**

83bismuth38 wrote:
Saka wrote:
83bismuth38 wrote:i want a speed at which an onion grows
EDIT: sorry for the short post, btw. It's just that I really want the speed of an onion in ca... don't judge me.
Few problems with this:
1. What onion? There are tons of onions out there, mind you. Sometimes Alliums are counted as onions and schizobasis intricata is called a vining onion so what onion?
2. Defini grow. The roots getting longer? The bulb grtting taller? The leaves getting taller? The olant getting taller in general?
the growth at which bread grows on an onion ring.

Code: Select all

x=1,y=1,rule=S0
o

Posted: **October 26th, 2017, 1:39 pm**

Saka wrote:Idea:
1. A dot creates a c/2 dot moving left and spawns a binary counter that counts to the left.
2. Once the counter hits a certain point (noted by a dot), it starts counting down (If possible) and is moved 1 cell to the right.
3. After countdown has finished, the counter is turned into a c/1 dot moving left and a dot marking the position, but 1 cell to the right.
4. Once the c/1 dot catches the c/2 dot, it turns into a c/1 dot.
5. The c/1 dot moves to the right until it hits the binary counter marker (See #3).
6. Repeat.

This would be REALLY slow

Probably no slower than exponential in size. I've made a rule which is doubly tetrationally slow in size.

Posted: **August 15th, 2018, 7:31 pm**

DISCLAIMER: This is not my work, all I did was translate it to Golly format.

The original work done is here.

I have translated the Turing machine for Knuth's up-arrow notation on that page into @RULE format, so it runs in Golly:

Code: Select all

@RULE KnuthArrows

@TABLE

n_states:41
neighborhood:Moore
symmetries:none

var all0 = {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}
var all1 = {all0}
var all2 = {all0}
var all3 = {all0}
var all4 = {all0}
var all5 = {all0}
var all6 = {all0}
var all7 = {all0}
var all8 = {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}

var onoff0 = {0,1,2,3}
var onoff1 = {0,1,2,3}
var onoff2 = {0,1,2,3}
var onoff3 = {0,1,2,3}

0,0,0,0,onoff0,onoff1,1,4,0,4

0,0,0,0,onoff0,onoff1,0,4,0,5

0,0,0,0,onoff0,onoff1,1,5,0,4

0,0,0,5,0,onoff0,onoff1,0,0,6

0,0,0,6,0,onoff0,onoff1,0,0,6

0,0,0,6,1,onoff0,onoff1,0,0,7

0,7,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,7,0,8

0,0,0,7,1,onoff0,onoff1,0,0,10

1,8,0,onoff0,0,0,0,onoff1,0,0
0,0,0,8,1,onoff0,onoff1,0,0,8

0,8,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,8,0,9

0,9,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,9,0,5

0,0,0,10,1,onoff0,onoff1,0,0,10

0,10,0,onoff0,0,0,0,onoff1,0,1
0,0,0,10,0,onoff0,onoff1,0,0,11

#halt

1,11,0,onoff0,0,0,0,onoff1,0,0
0,0,0,11,1,onoff0,onoff1,0,0,12

0,0,0,0,onoff0,onoff1,1,12,0,13

0,12,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,12,0,37

0,0,0,0,onoff0,onoff1,0,13,0,14

1,14,0,onoff0,0,0,0,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,14,0,15

1,15,0,onoff0,0,0,0,onoff1,0,0
0,0,0,15,1,onoff0,onoff1,0,0,16

0,0,0,16,0,onoff0,onoff1,0,0,17

0,0,0,17,0,onoff0,onoff1,0,0,17

1,17,0,onoff0,0,0,0,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,17,0,18

0,18,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,18,0,19

0,0,0,0,onoff0,onoff1,1,19,0,19

0,0,0,0,onoff0,onoff1,0,19,0,20

0,0,0,0,onoff0,onoff1,1,20,0,20

0,20,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,20,0,21

1,21,0,onoff0,0,0,0,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,21,0,22

0,0,0,0,onoff0,onoff1,0,21,0,21

0,0,0,0,onoff0,onoff1,1,22,0,22

0,22,0,onoff0,0,0,0,onoff1,0,1
0,0,0,22,0,onoff0,onoff1,0,0,23

0,0,0,23,1,onoff0,onoff1,0,0,23

0,0,0,23,0,onoff0,onoff1,0,0,24

0,0,0,24,1,onoff0,onoff1,0,0,24

0,0,0,24,0,onoff0,onoff1,0,0,25

0,0,0,25,1,onoff0,onoff1,0,0,25

0,0,0,25,0,onoff0,onoff1,0,0,26

0,0,0,0,onoff0,onoff1,0,26,0,27

0,0,0,0,onoff0,onoff1,1,26,0,17

0,27,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,27,0,28

0,0,0,0,onoff0,onoff1,1,28,0,28

0,28,0,onoff0,0,0,0,onoff1,0,1
0,0,0,28,0,onoff0,onoff1,0,0,29

1,29,0,onoff0,0,0,0,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,29,0,30

0,0,0,0,onoff0,onoff1,1,30,0,31

1,31,0,onoff0,0,0,0,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,31,0,32

0,0,0,0,onoff0,onoff1,1,32,0,32

0,32,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,32,0,33

0,0,0,0,onoff0,onoff1,1,33,0,34

1,34,0,onoff0,0,0,0,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,34,0,35

0,0,0,0,onoff0,onoff1,0,34,0,36

0,35,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,35,0,36

0,0,0,0,onoff0,onoff1,1,35,0,35

0,36,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,36,0,6

0,37,0,onoff0,0,0,0,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,37,0,38

0,0,0,0,onoff0,onoff1,1,38,0,38

0,0,0,38,0,onoff0,onoff1,0,0,39

1,39,0,onoff0,0,0,0,onoff1,0,0
0,0,0,39,1,onoff0,onoff1,0,0,40

1,40,0,onoff0,0,0,0,onoff1,0,0
0,0,0,40,1,onoff0,onoff1,0,0,6


all8, all1, all2, all3, all4, all5, all6, all7, all0, 0

The format of input is described on the linked page, but essentially, putting a state 4 cell above a row of input, like the pattern below, with a single dot, then n dots, then another m dots will calculate 2^^...^^(m+1) (with n - 2 arrows) :

Code: Select all

x = 13, y = 2, rule = KnuthArrows
D$A.3A.7A!

I am posting here because this might allow much, much slower ships then tetrationally slow ones. There are other machines on that page that may also be for use to make even more ridiculous speeds. All we need to figure out from here is how to restore the initial pattern, but shifted. Again this is not my work or idea (apart from using it to make spaceships), I just translated the language of the Turing machine into @RULE format.

Posted: **August 15th, 2018, 9:55 pm**

Nice! Interestingly, that page you linked actually references work by one of this forum's users, Adam Goucher.

Posted: **August 15th, 2018, 10:08 pm**

77topaz wrote:Interestingly, that page you linked actually references work by one of this forum's users, Adam Goucher.

Yeah, and the author of the page is LittlePeng9, or otherwise known as Wojowu, who used to be on these forums. At least, I am fairly certain they are one and the same.

Posted: **September 2nd, 2018, 12:16 pm**

Finally, here is the ruletable:

Code: Select all

@RULE KnuthArrows

@TABLE

n_states:47
neighborhood:Moore
symmetries:none

var all0 = {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}
var all1 = {all0}
var all2 = {all0}
var all3 = {all0}
var all4 = {all0}
var all5 = {all0}
var all6 = {all0}
var all7 = {all0}
var all8 = {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}

var onoff0 = {0,1,2,3}
var onoff1 = {0,1,2,3}
var onoff2 = {0,1,2,3}
var onoff3 = {0,1,2,3}

0,0,0,0,onoff0,onoff1,1,4,0,4

0,0,0,0,onoff0,onoff1,0,4,0,5

0,0,0,0,onoff0,onoff1,1,5,0,4

0,0,0,5,0,onoff0,onoff1,0,0,6

0,0,0,6,0,onoff0,onoff1,0,0,6

0,0,0,6,1,onoff0,onoff1,0,0,7

0,7,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,7,0,8

0,0,0,7,1,onoff0,onoff1,0,0,10

1,8,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,8,1,onoff0,onoff1,0,0,8

0,8,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,8,0,9

0,9,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,9,0,5

0,0,0,10,1,onoff0,onoff1,0,0,10

0,10,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,10,0,onoff0,onoff1,0,0,11

11,all0,all1,all2,all3,0,all4,all5,all6,41
0,41,0,1,0,0,0,0,0,41
0,41,1,0,0,0,0,0,0,42
0,1,all0,0,all1,1,all3,42,all4,43
0,1,all0,0,all1,1,all3,43,all4,43
0,1,all0,0,all1,all2,all3,42,all4,42
0,1,all0,0,all1,all2,all3,43,all4,42
1,all0,all1,all2,all3,42,all4,all5,all6,0
1,42,all0,all1,all2,all3,all4,all5,all6,0

0,0,0,0,0,0,0,42,1,44
0,0,0,44,0,0,0,0,0,44
0,0,0,44,0,0,1,0,1,45
0,1,onoff0,45,onoff0,1,1,0,1,45
0,0,onoff0,45,onoff0,0,1,0,1,45
0,1,onoff0,45,onoff0,1,0,0,0,45

0,0,1,45,1,0,0,0,0,46
0,0,0,1,0,0,46,0,0,46
0,0,0,0,0,1,46,0,0,4

0,0,0,all0,all1,45,0,onoff0,0,onoff0
1,0,0,all0,all1,45,0,onoff0,0,onoff0

0,45,0,all0,0,0,0,onoff0,0,onoff0
1,45,0,all0,0,0,0,onoff0,0,onoff0

#0,0,0,0,onoff0,1,onoff1,41,0,41


#1,0,0,1,0,onoff0,onoff1,onoff2,41,0

#1,0,0,0,0,0,0,0,41,42
#0,42,0,0,0,0,0,0,0,43
#0,43,0,0,0,0,0,0,0,44
#0,onoff0,onoff1,44,0,0,0,0,onoff2,44

1,11,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,11,1,onoff0,onoff1,0,0,12

0,0,0,0,onoff0,onoff1,1,12,0,13

0,12,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,12,0,37

0,0,0,0,onoff0,onoff1,0,13,0,14

1,14,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,14,0,15

1,15,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,15,1,onoff0,onoff1,0,0,16

0,0,0,16,0,onoff0,onoff1,0,0,17

0,0,0,17,0,onoff0,onoff1,0,0,17

1,17,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,17,0,18

0,18,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,18,0,19

0,0,0,0,onoff0,onoff1,1,19,0,19

0,0,0,0,onoff0,onoff1,0,19,0,20

0,0,0,0,onoff0,onoff1,1,20,0,20

0,20,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,20,0,21

1,21,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,21,0,22

0,0,0,0,onoff0,onoff1,0,21,0,21

0,0,0,0,onoff0,onoff1,1,22,0,22

0,22,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,22,0,onoff0,onoff1,0,0,23

0,0,0,23,1,onoff0,onoff1,0,0,23

0,0,0,23,0,onoff0,onoff1,0,0,24

0,0,0,24,1,onoff0,onoff1,0,0,24

0,0,0,24,0,onoff0,onoff1,0,0,25

0,0,0,25,1,onoff0,onoff1,0,0,25

0,0,0,25,0,onoff0,onoff1,0,0,26

0,0,0,0,onoff0,onoff1,0,26,0,27

0,0,0,0,onoff0,onoff1,1,26,0,17

0,27,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,27,0,28

0,0,0,0,onoff0,onoff1,1,28,0,28

0,28,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,28,0,onoff0,onoff1,0,0,29

1,29,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,29,0,30

0,0,0,0,onoff0,onoff1,1,30,0,31

1,31,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,31,0,32

0,0,0,0,onoff0,onoff1,1,32,0,32

0,32,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,32,0,33

0,0,0,0,onoff0,onoff1,1,33,0,34

1,34,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,0,onoff0,onoff1,1,34,0,35

0,0,0,0,onoff0,onoff1,0,34,0,36

0,35,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,35,0,36

0,0,0,0,onoff0,onoff1,1,35,0,35

0,36,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,36,0,6

0,37,0,onoff0,all0,all1,all2,onoff1,0,1
0,0,0,0,onoff0,onoff1,0,37,0,38

0,0,0,0,onoff0,onoff1,1,38,0,38

0,0,0,38,0,onoff0,onoff1,0,0,39

1,39,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,39,1,onoff0,onoff1,0,0,40

1,40,0,onoff0,all0,all1,all2,onoff1,0,0
0,0,0,40,1,onoff0,onoff1,0,0,6


all8, all1, all2, all3, all4, all5, all6, all7, all0, 0

This allows ships in the form of thew following, where it functions like the example in my previous ruletable post, except there is a copy two rows down.:

Code: Select all

x = 14, y = 4, rule = KnuthArrows
D$A.3A.8A2$A.3A.8A!

This method allows for some extraordinarily slow ships. A small one like this has a speed slower than C/5,500,000,000:

Code: Select all

x = 10, y = 4, rule = KnuthArrows
D$A.4A.3A2$A.4A.3A!

Posted: **September 4th, 2018, 10:16 am**

AforAmpere wrote:Finally, here is the ruletable:
Code: Select all
ruletable

How slow are the spaceships now?
And this spaceship:

Code: Select all

x = 14, y = 4, rule = KnuthArrows
D$A.3A.8A2$A.3A.8A!

has the speed c/364852.

ConwayLife.com

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