Real Life Speeds

[Hdjensofjfnen]

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.

[AbhpzTa]

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!

[Saka]

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

[blah]

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.

[gameoflifemaniac]

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

What is LCM?

[blah]

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.

[Saka]

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.

[gameoflifemaniac]

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.

[fluffykitty]

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

[gameoflifemaniac]

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?

[fluffykitty]

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

[fluffykitty]

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

[Saka]

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

[83bismuth38]

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.

[Saka]

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?

[83bismuth38]

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.

[muzik]

Sometimes Alliums are counted as onions

Aren't onions part of the Allium genus?

[Saka]

Sometimes Alliums are counted as onions

Aren't onions part of the Allium subspecies?

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

[fluffykitty]

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

[fluffykitty]

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.

[AforAmpere]

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.

[77topaz]

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

[AforAmpere]

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.

[AforAmpere]

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!

[gameoflifemaniac]

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.