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### Re: Real Life Speeds

Posted: September 4th, 2018, 4:43 pm
gameoflifemaniac wrote:How slow are the spaceships now?

For a pattern like this, with n cells in the top middle area:
`x = 13, y = 4, rule = KnuthArrowsD\$A.8A.2A2\$A.8A.2A!`

The speed is approximately C/2^^^^^...^^3 with n-2 arrows.

### Re: Real Life Speeds

Posted: September 5th, 2018, 1:54 am
AforAmpere wrote:
gameoflifemaniac wrote:How slow are the spaceships now?

For a pattern like this, with n cells in the top middle area:
`x = 13, y = 4, rule = KnuthArrowsD\$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.

### Re: Real Life Speeds

Posted: September 12th, 2018, 11:50 am
What will be the next step in how slow the spaceships will be?

### Re: Real Life Speeds

Posted: September 12th, 2018, 11:58 am
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.

### Re: Real Life Speeds

Posted: September 15th, 2018, 3:20 am
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!

### Re: Real Life Speeds

Posted: April 14th, 2019, 2:04 am
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.
`@RULE ChaseShip************************************ COMPILED FROM NUTSHELL ********         v0.5.7         ************************************1 -> c/2 going left, counter going rightcounter hits stop, stop -> stop explode, counts erasedwhen counter eraser meets counter, counter moves 1 to rightse -> c/1 going left above, move to right 1 cell, change to state 0when c/1 meets c/2, c/2 -> c/1 going right, c/1 going left disappearswhen c/1 going right meets startmarker, startmarker -> start0: vaccuum1: start2: left c2 13: left c2 24: binary counter5: binary 16: binary thing7: counter stop8: stop explode9: count eraser10: startmarker11: c/1 left12: c/1 right13: death@TABLEneighborhood: vonNeumannsymmetries: nonen_states: 14var any.0 = {0,1,2,3,4,5,6,7,8,9,10,11,12,13}var any.1 = any.0var any.2 = any.0var any.3 = any.0var 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, 21, any.0, any.1, any.2, any.3, 40, any.0, 11, _a0.0, any.1, 5_a0.0, 5, any.0, any.1, any.2, 120, 11, any.0, any.1, 3, 120, 5, any.0, any.1, 2, 13live.0, any.0, 13, any.1, any.2, 13live.0, any.0, any.1, 13, any.2, 1313, any.0, any.1, any.2, any.3, 02, any.0, any.1, any.2, any.3, 33, any.0, any.1, any.2, any.3, 00, any.0, 3, any.1, any.2, 2_b0.0, any.0, 9, any.1, any.2, 99, any.0, any.1, any.2, 4, 109, any.0, any.1, any.2, _c0.0, 04, any.0, 9, any.1, any.2, 00, any.0, any.1, any.2, 4, 55, any.0, any.1, any.2, 4, 65, any.0, any.1, any.2, 6, 66, any.0, any.1, any.2, any.3, 00, any.0, any.1, any.2, 6, 57, any.0, any.1, any.2, 6, 80, any.0, any.1, 8, any.2, 110, any.0, any.1, any.2, 8, 78, any.0, any.1, any.2, any.3, 90, any.0, 11, any.1, any.2, 1111, any.0, any.1, any.2, any.3, 00, any.0, any.1, any.2, 12, 1212, any.0, any.1, any.2, any.3, 010, 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):
`x = 7, y = 1, rule = ChaseShipA5.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
`x = 3, y = 1, rule = ChaseShipA.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

### Re: Real Life Speeds

Posted: April 14th, 2019, 3:47 am
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:
`x = 28, y = 1, rule = ChaseShipA26.G!`

### Re: Real Life Speeds

Posted: April 14th, 2019, 4:57 am
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)

### Re: Real Life Speeds

Posted: April 14th, 2019, 8:59 am
How large must the fourth ship be?
`x = 21, y = 3, rule = ChaseShipA.G\$A8.G\$A19.G!`

I feel we have a fast-growing function, though it won’t grow VERY fast.

### Re: Real Life Speeds

Posted: April 14th, 2019, 10:15 am
Moosey wrote:How large must the fourth ship be?
`x = 21, y = 3, rule = ChaseShipA.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.

### Re: Real Life Speeds

Posted: April 14th, 2019, 12:02 pm
Saka wrote:
Moosey wrote:How large must the fourth ship be?
`x = 21, y = 3, rule = ChaseShipA.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?

### Re: Real Life Speeds

Posted: April 15th, 2019, 7:23 am
I've made an even slower version of the rule:
`@RULE ChaseShipBin************************************ COMPILED FROM NUTSHELL ********         v0.5.7         ************************************0: vaccuum1: start2: left c2 13: left c2 24: binary counter5: binary 16: binary thing7: counter stop8: stop explode9: count eraser10: startmarker11: c/1 left12: reactivator13: death14: complete count eraser@TABLEneighborhood: vonNeumannsymmetries: nonen_states: 15var any.0 = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14}var any.1 = any.0var any.2 = any.0var any.3 = any.0var _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, 21, any.0, any.1, any.2, any.3, 40, any.0, 11, _a0.0, any.1, 5_a0.0, 5, any.0, any.1, any.2, 120, 11, any.0, any.1, 3, 40, 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, 1313, any.0, any.1, any.2, any.3, 02, any.0, any.1, any.2, any.3, 33, any.0, any.1, any.2, any.3, 00, any.0, 3, any.1, any.2, 2_c0.0, any.0, 9, any.1, any.2, 99, any.0, any.1, any.2, 4, 109, any.0, any.1, any.2, _d0.0, 04, any.0, 9, any.1, any.2, 014, any.0, 1, any.1, any.2, 214, any.0, any.1, any.2, any.3, 04, any.0, 14, any.1, any.2, 126, any.0, 10, any.1, any.2, 14any.0, any.1, 14, any.2, any.3, 140, any.0, any.1, any.2, 4, 55, any.0, any.1, any.2, 4, 65, any.0, any.1, any.2, 6, 66, any.0, any.1, any.2, any.3, 00, any.0, any.1, any.2, 6, 57, any.0, any.1, any.2, 6, 80, any.0, any.1, 8, any.2, 110, any.0, any.1, any.2, 8, 78, any.0, any.1, any.2, any.3, 90, any.0, 11, any.1, any.2, 1111, any.0, any.1, any.2, any.3, 00, any.0, any.1, any.2, 12, 1212, any.0, any.1, any.2, any.3, 010, any.0, any.1, any.2, 12, 16, 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
`x = 3, y = 1, rule = ChaseShipBinA.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.

### Re: Real Life Speeds

Posted: April 15th, 2019, 8:30 am
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.

### Re: Real Life Speeds

Posted: April 15th, 2019, 12:31 pm
For Saka's newest rule, for a gap of n, the period is equal to:
`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.

### Re: Real Life Speeds

Posted: April 16th, 2019, 12:10 am
I've completed my rule!
`@RULE Track@TABLEn_states:18neighborhood:vonNeumannsymmetries: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 Cellvar 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}#Puffing2,0,0,0,0,00,0,2,0,0,33,0,b,0,0,50,0,3,0,0,44,0,b,0,0,50,0,4,0,0,6#Counting5,0,5,0,c,75,0,0,0,c,8#Returning8,0,0,0,c,1717,0,0,0,8,08,0,i,0,c,57,0,8,0,c,86,0,8,0,0,9#Sending9,0,5,0,0,100,0,9,0,a,11#SignalF0,0,11,0,a,1111,0,d,0,a,01,0,11,0,0,12#Moving12,0,0,0,0,130,0,12,0,0,1#SignalP0,0,e,0,13,1313,0,e,0,a,010,0,5,0,13,3#Hit0,0,f,0,1,14#Recounting5,0,b,0,h,150,0,0,0,15,16#Untrailing15,0,g,0,h,1717,0,l,0,k,014,0,17,0,1,13#Initializing16,0,0,0,13,2`

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.