## Real Life Speeds

For discussion of other cellular automata.
AforAmpere
Posts: 1077
Joined: July 1st, 2016, 3:58 pm

### Re: Real Life Speeds

gameoflifemaniac wrote: How slow are the spaceships now?
For a pattern like this, with n cells in the top middle area:

Code: Select all

``````x = 13, y = 4, rule = KnuthArrows
D\$A.8A.2A2\$A.8A.2A!
``````
The speed is approximately C/2^^^^^...^^3 with n-2 arrows.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

gameoflifemaniac
Posts: 852
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Real Life Speeds

AforAmpere wrote:
gameoflifemaniac wrote: How slow are the spaceships now?
For a pattern like this, with n cells in the top middle area:

Code: Select all

``````x = 13, y = 4, rule = KnuthArrows
D\$A.8A.2A2\$A.8A.2A!
``````
The speed is approximately C/2^^^^^...^^3 with n-2 arrows.
Ahh, so for 1 cell, then n cells, then m cells, it's asymptotic to c/2^^^^^...^^m+1 with n-2 arrows.
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac
Posts: 852
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Real Life Speeds

What will be the next step in how slow the spaceships will be?
One big dirty Oro. Yeeeeeeeeee...

AforAmpere
Posts: 1077
Joined: July 1st, 2016, 3:58 pm

### Re: Real Life Speeds

gameoflifemaniac wrote:What will be the next step in how slow the spaceships will be?
Well, first off, try doing some research yourself if you are really that desperate. Second, I am not sure what the next step is. Some of the other Turing machines on the page I referenced are able to calculate much larger values, so if you want to port them into Golly, you might be able to create slower ships.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

gameoflifemaniac
Posts: 852
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Real Life Speeds

fluffykitty wrote:I've made a rule which is doubly tetrationally slow in size.
Where is it? I saw your tetrational rule, but not your double tetrational rule!
One big dirty Oro. Yeeeeeeeeee...

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Real Life Speeds

Saka, earlier in this thread, 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 slowm
I made a rule based on that idea, with a few small changes.

Code: Select all

``````@RULE ChaseShip
********************************
**** COMPILED FROM NUTSHELL ****
****         v0.5.7         ****
********************************
1 -> c/2 going left, counter going right
counter hits stop, stop -> stop explode, counts erased
when counter eraser meets counter, counter moves 1 to right
se -> c/1 going left above, move to right 1 cell, change to state 0
when c/1 meets c/2, c/2 -> c/1 going right, c/1 going left disappears
when c/1 going right meets startmarker, startmarker -> start

0: vaccuum
1: start
2: left c2 1
3: left c2 2
4: binary counter
5: binary 1
6: binary thing
7: counter stop
8: stop explode
9: count eraser
10: startmarker
11: c/1 left
12: c/1 right
13: death

@TABLE
neighborhood: vonNeumann
symmetries: none
n_states: 14

var any.0 = {0,1,2,3,4,5,6,7,8,9,10,11,12,13}
var any.1 = any.0
var any.2 = any.0
var any.3 = any.0
var live.0 = {1,2,3,4,5,6,7,8,9,10,11,12,13}
var _a0.0 = {2,3}
var _b0.0 = {0,5,6}
var _c0.0 = {0,1,2,3,4,5,7,8,9,10,11,12,13}

0, any.0, 1, any.1, any.2, 2
1, any.0, any.1, any.2, any.3, 4
0, any.0, 11, _a0.0, any.1, 5
_a0.0, 5, any.0, any.1, any.2, 12
0, 11, any.0, any.1, 3, 12
0, 5, any.0, any.1, 2, 13
live.0, any.0, 13, any.1, any.2, 13
live.0, any.0, any.1, 13, any.2, 13
13, any.0, any.1, any.2, any.3, 0
2, any.0, any.1, any.2, any.3, 3
3, any.0, any.1, any.2, any.3, 0
0, any.0, 3, any.1, any.2, 2
_b0.0, any.0, 9, any.1, any.2, 9
9, any.0, any.1, any.2, 4, 10
9, any.0, any.1, any.2, _c0.0, 0
4, any.0, 9, any.1, any.2, 0
0, any.0, any.1, any.2, 4, 5
5, any.0, any.1, any.2, 4, 6
5, any.0, any.1, any.2, 6, 6
6, any.0, any.1, any.2, any.3, 0
0, any.0, any.1, any.2, 6, 5
7, any.0, any.1, any.2, 6, 8
0, any.0, any.1, 8, any.2, 11
0, any.0, any.1, any.2, 8, 7
8, any.0, any.1, any.2, any.3, 9
0, any.0, 11, any.1, any.2, 11
11, any.0, any.1, any.2, any.3, 0
0, any.0, any.1, any.2, 12, 12
12, any.0, any.1, any.2, any.3, 0
10, any.0, any.1, any.2, 12, 1
``````
The c/2 photon turning around is a bit wonky because it uses the vonNeumann neighborhood.
Example ship (c/178o):

Code: Select all

``````x = 7, y = 1, rule = ChaseShip
A5.G!
``````
It isn't that slow, but the minimum population is the same for every speed (besides c/2 and c/1, technically).
Fastest possible ship with the same format:
c/19o

Code: Select all

``````x = 3, y = 1, rule = ChaseShip
A.G!
``````
(Speeds c/2o and c/1o are also possible, but they aren't that fun.)

EDIT: Can anyone figure out the formula for the period?
EDIT2:
Dani found it:
6*l+2^(l-3)+2^l-8
where l is the width of the ship
Last edited by Saka on April 14th, 2019, 4:30 am, edited 2 times in total.
Airy Clave White It Nay

Code: Select all

``````x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5b
o2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!
``````
(Check gen 2)

dani
Posts: 982
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA
Contact:

### Re: Real Life Speeds

I like that rule. This ship goes at speed c/301990048, which is the closest to 1 m/s (0.992722972 m/s) I could get:

Code: Select all

``````x = 28, y = 1, rule = ChaseShip
A26.G!
``````
moose#0915

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Real Life Speeds

This is interesting, as you can see by the graph, the periods of the ships start to skyrocket at around width 45 (according to the function in the original rule post)
Attachments
psgsn.png (12.9 KiB) Viewed 3937 times
Airy Clave White It Nay

Code: Select all

``````x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5b
o2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!
``````
(Check gen 2)

Moosey
Posts: 3051
Joined: January 27th, 2019, 5:54 pm
Location: A house, or perhaps the OCA board. Or [click to not expand]
Contact:

### Re: Real Life Speeds

How large must the fourth ship be?

Code: Select all

``````x = 21, y = 3, rule = ChaseShip
A.G\$A8.G\$A19.G!
``````
I feel we have a fast-growing function, though it won’t grow VERY fast.
I am a prolific creator of many rather pathetic googological functions

My CA rules can be found here

Also, the tree game
Bill Watterson once wrote: "How do soldiers killing each other solve the world's problems?"

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Real Life Speeds

Moosey wrote:How large must the fourth ship be?

Code: Select all

``````x = 21, y = 3, rule = ChaseShip
A.G\$A8.G\$A19.G!
``````
I feel we have a fast-growing function, though it won’t grow VERY fast.
What do you mean?
Also, I just posted the function for the period in the post for the rule.
Airy Clave White It Nay

Code: Select all

``````x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5b
o2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!
``````
(Check gen 2)

Moosey
Posts: 3051
Joined: January 27th, 2019, 5:54 pm
Location: A house, or perhaps the OCA board. Or [click to not expand]
Contact:

### Re: Real Life Speeds

Saka wrote:
Moosey wrote:How large must the fourth ship be?

Code: Select all

``````x = 21, y = 3, rule = ChaseShip
A.G\$A8.G\$A19.G!
``````
I feel we have a fast-growing function, though it won’t grow VERY fast.
What do you mean?
Also, I just posted the function for the period in the post for the rule.
How large must the fourth ship in that line be so that it won’t be destroyed and stopped by the previous one?
I am a prolific creator of many rather pathetic googological functions

My CA rules can be found here

Also, the tree game
Bill Watterson once wrote: "How do soldiers killing each other solve the world's problems?"

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Real Life Speeds

I've made an even slower version of the rule:

Code: Select all

``````@RULE ChaseShipBin
********************************
**** COMPILED FROM NUTSHELL ****
****         v0.5.7         ****
********************************

0: vaccuum
1: start
2: left c2 1
3: left c2 2
4: binary counter
5: binary 1
6: binary thing
7: counter stop
8: stop explode
9: count eraser
10: startmarker
11: c/1 left
12: reactivator
13: death
14: complete count eraser

@TABLE
neighborhood: vonNeumann
symmetries: none
n_states: 15

var any.0 = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14}
var any.1 = any.0
var any.2 = any.0
var any.3 = any.0
var _a0.0 = {2,3}
var _b0.0 = {1,2,3,5,6,7,8,9,10,11,12,13,14}
var _c0.0 = {0,5,6}
var _d0.0 = {0,1,2,3,4,5,7,8,9,10,11,12,13,14}

0, any.0, 1, any.1, any.2, 2
1, any.0, any.1, any.2, any.3, 4
0, any.0, 11, _a0.0, any.1, 5
_a0.0, 5, any.0, any.1, any.2, 12
0, 11, any.0, any.1, 3, 4
0, 5, any.0, any.1, 2, 13
_b0.0, any.0, 13, any.1, any.2, 13
_b0.0, any.0, any.1, 13, any.2, 13
13, any.0, any.1, any.2, any.3, 0
2, any.0, any.1, any.2, any.3, 3
3, any.0, any.1, any.2, any.3, 0
0, any.0, 3, any.1, any.2, 2
_c0.0, any.0, 9, any.1, any.2, 9
9, any.0, any.1, any.2, 4, 10
9, any.0, any.1, any.2, _d0.0, 0
4, any.0, 9, any.1, any.2, 0
14, any.0, 1, any.1, any.2, 2
14, any.0, any.1, any.2, any.3, 0
4, any.0, 14, any.1, any.2, 12
6, any.0, 10, any.1, any.2, 14
any.0, any.1, 14, any.2, any.3, 14
0, any.0, any.1, any.2, 4, 5
5, any.0, any.1, any.2, 4, 6
5, any.0, any.1, any.2, 6, 6
6, any.0, any.1, any.2, any.3, 0
0, any.0, any.1, any.2, 6, 5
7, any.0, any.1, any.2, 6, 8
0, any.0, any.1, 8, any.2, 11
0, any.0, any.1, any.2, 8, 7
8, any.0, any.1, any.2, any.3, 9
0, any.0, 11, any.1, any.2, 11
11, any.0, any.1, any.2, any.3, 0
0, any.0, any.1, any.2, 12, 12
12, any.0, any.1, any.2, any.3, 0
10, any.0, any.1, any.2, 12, 1
6, any.0, 10, any.1, any.2, 14
``````
In this version, instead of creating a photon "reactivator", it uses another binary counter, and once the binary counter reaches the ship, it creates a photon that erases the counter and bounces back and reactivates the ship. This keeps the constant population at 2 and makes it slower as well.
Fastest: c/76o

Code: Select all

``````x = 3, y = 1, rule = ChaseShipBin
A.G!
``````
The width 4 ship has speed c/1589o and the width 5 ship is a c/393309o. I've calculated that the period for the width 6 ship is around 6 442 451 107, give or take at most 2.
I have yet to find the formula for the speed.
Airy Clave White It Nay

Code: Select all

``````x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5b
o2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!
``````
(Check gen 2)

PkmnQ
Posts: 817
Joined: September 24th, 2018, 6:35 am
Location: Server antipode

### Re: Real Life Speeds

I'm in the middle of making a rule for a new ship. I've created half of the process, and I'm taking a break for my mind.
(![]+[])[+!![]]+(![]+[])[!![]+!![]]+(!![]+[])[!![]+!![]+!![]]+(!![]+[])[+!![]]+(!![]+[])[+[]]

AforAmpere
Posts: 1077
Joined: July 1st, 2016, 3:58 pm

### Re: Real Life Speeds

For Saka's newest rule, for a gap of n, the period is equal to:

Code: Select all

``3 * 2^(3 * 2^(n-1) + 2n - 1) + 15 * 2^(n - 1) + 10n +3``
A gap of 100 has a period with more digits than could be stored on Earth.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

PkmnQ
Posts: 817
Joined: September 24th, 2018, 6:35 am
Location: Server antipode

### Re: Real Life Speeds

I've completed my rule!

Code: Select all

``````@RULE Track

@TABLE
n_states:18
neighborhood:vonNeumann
symmetries:none

#State 0: Nothing
#State 1: Front
#State 2: Initialized Puffer
#State 3: Puffer 1
#State 4: Puffer 2
#State 5: Track
#State 6: Counter
#State 7: Counted
#State 8: Returning
#State 9: Sending
#State 10: Waiting
#State 11: Signal Front
#State 12: Moving
#State 13: Signal Back
#State 14: Recount
#State 15: Recounted
#State 16: Uninitialized Puffer
#State 17: Forgotten Cell

var a={0,1}
var b={0,5}
var c={6,7}
var d={0,10}
var e={0,10,16}
var f={2,3,4}
var g={16,17}
var h={14,15}
var i={5,17}
var j={8,15}
var k={0,14,15,17}
var l={0,15,16}

#Puffing
2,0,0,0,0,0
0,0,2,0,0,3
3,0,b,0,0,5
0,0,3,0,0,4
4,0,b,0,0,5
0,0,4,0,0,6

#Counting
5,0,5,0,c,7
5,0,0,0,c,8

#Returning
8,0,0,0,c,17
17,0,0,0,8,0
8,0,i,0,c,5
7,0,8,0,c,8
6,0,8,0,0,9

#Sending
9,0,5,0,0,10
0,0,9,0,a,11

#SignalF
0,0,11,0,a,11
11,0,d,0,a,0
1,0,11,0,0,12

#Moving
12,0,0,0,0,13
0,0,12,0,0,1

#SignalP
0,0,e,0,13,13
13,0,e,0,a,0
10,0,5,0,13,3

#Hit
0,0,f,0,1,14

#Recounting
5,0,b,0,h,15
0,0,0,0,15,16

#Untrailing
15,0,g,0,h,17
17,0,l,0,k,0
14,0,17,0,1,13

#Initializing
16,0,0,0,13,2``````
To make a spaceship, you make a state 1, and then a gap (choose how long), then a state 2.

I don’t know the function for the speeds. At first, it looks like it doesn’t get slower than c/26 but then it matches up, and continues to slow down.
(![]+[])[+!![]]+(![]+[])[!![]+!![]]+(!![]+[])[!![]+!![]+!![]]+(!![]+[])[+!![]]+(!![]+[])[+[]]