ConwayLife.com

Posted: **July 10th, 2020, 5:47 pm**

I know there are fuses that burn at the speed of light, but has anyone ever discovered a spaceship that travels at the speed of light? (c/1). Is it even possible?

Posted: **July 10th, 2020, 6:04 pm**

This is a good question! (Although perhaps more suited for the Thread for basic questions.)

The answer is no. The fastest speeds that ships can go at is half lightspeed orthogonally or a quarter lightspeed diagonally. The glider and LWSS achieve these speeds.

Code: Select all

x = 5, y = 9, rule = B3/S23
b4o$o3bo$4bo$o2bo3$obo$b2o$bo!

There's a nice blog post by Nathaniel explaining why these are the speed limits.

Posted: **July 10th, 2020, 6:08 pm**

See also Spaceship#Spaceship_speed. The rule applies to any spaceship in B3/S23, Conway's Life -- i.e., a pattern with bounded size and population that moves and repeats itself with a particular period. Spaceships in other rules may have higher speed limits, up to light speed in many cases.

Infinitely large patterns can be an exception to the c/2 speed limit in Conway's Life, but that probably shouldn't be too surprising. Some such patterns can even appear to travel faster than the speed of light, but that doesn't mean that they can transmit information any faster than light speed, since that really is impossible.

Posted: **July 10th, 2020, 6:11 pm**

Thank you for the answer! That's an awesome blog post. How did you even find it? I can't just search for these things on Google because barely anyone is interested in this.

Posted: **July 10th, 2020, 6:30 pm**

apchrkey wrote: July 10th, 2020, 6:11 pm Thank you for the answer! That's an awesome blog post. How did you even find it? I can't just search for these things on Google because barely anyone is interested in this.

I remembered that the proof existed, and searched on LifeWiki to find an online copy. It's linked to from the Spaceship page.

Posted: **July 10th, 2020, 11:25 pm**

Here is an example of a lightspeed ship (often called a photon generally) in a Life-like rule, Seeds:

Code: Select all

x = 2, y = 4, rule = B2/S
o$bo$bo$o!

Here is another photon in Star Wars (one of the so-called Generations family of rules):

Code: Select all

x = 3, y = 2, rule = 345/2/4
ABC$ABC!

Posted: **July 13th, 2020, 6:29 am**

Well, here is how I disprove c spaceships in CGoL:

To move at the speed of light, you have to do something like this:

Code: Select all

x = 1, y = 213, rule = B3/S23
o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o
$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$
o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o
$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$
o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o
$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$
o$o$o$o$o$o!

and stabilize the back end.

However, this only goes for a certain amount of generations as the line shrinks. To fix this, here is what can be done:

Code: Select all

x = 2, y = 215, rule = B3/S23
bo$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$
o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o
$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$
o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o
$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$
o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o
$o$o$o$o$o$o$o$bo!

But it doesn't actually move, so it is impossible to make a CGoL lightspeed spaceship.

Posted: **February 15th, 2021, 9:02 pm**

apchrkey wrote: July 10th, 2020, 5:47 pm I know there are fuses that burn at the speed of light, but has anyone ever discovered a spaceship that travels at the speed of light? (c/1). Is it even possible?

It is actually in a way possible, if agar crawlers are to be considered a type or generalization of spaceships:

Code: Select all

x = 50, y = 49, rule = Life:T50,50
50o2$50o2$50o$21b2o3b2o$19o5bo5b20o$19bo4bo4bo$19o11b20o$20bo7bo$13o4b
4o7b4o4b14o$21bo5bo$12o6b5o3b5o6b13o$12bo4bo4bo3bo4bo4bo$14o2bo2bobob
3obobo2bo2b15o$15bo4bobo3bobo4bo$16o3bo3b3o3bo3b17o$19b2o3bo3b2o$20o9b
21o$21b7o$50o2$20o9b21o2$18o13b19o$18bo2bo2bo2bo2bo$18o2b3obob3o2b19o$
22bobobo$18o2b2o5b2o2b19o$18b2o2bo3bo2b2o$17o4b7o4b18o2$16o7b3o7b17o$
16bo6b3o6bo$18o13b19o$18bo3b5o3bo$20o2bobobo2b21o$20bo3bo3bo$20ob7ob
21o2$50o2$50o2$50o2$50o2$50o!

Of course, c/1 spaceships are very common in many other rules. In fact, I personally tend to invent rules that are abundant with them. Here is an example (this rule has 4 states):

Code: Select all

x = 129, y = 53, rule = Firework
7$15.C.C$15.ABA26.B$15.C.C26.C.B2.A17.C$49.A$46.B2A$24.2C23.B17.C.A.A
CA$25.CA21.AB23.A$43.B2.C.A22.AB.A4.A2B$42.A.AB3AB10.B.B7.A.B11.C$42.
A.A.2B3.B8.C8.B8.2B6.A$42.BA.CA3.B6.C.BC.C.B.B.C2.2B5.B3.A3.B$44.2A4.
A8.A8.CB.2B4.2B.B5.B$31.A40.B.A7.B3.B$32.A14.C16.2B5.A.C.2A5.B3.B$32.
A14.C10.A.2AC5.CAC2.2AB6.B3.B$34.A23.A5.C5.ACA.A.A5.B3.B$33.A16.2A10.
A.B3.2C12.B3.B$61.B20.B3.B$33.A16.2A10.A.B3.2C12.B3.B$34.A23.A5.C5.AC
A.A.A5.B3.B$32.A14.C10.A.2AC5.CAC2.2AB6.B3.B$32.A14.C16.2B5.A.C.2A5.B
3.B$31.A40.B.A7.B3.B$44.2A4.A8.A8.CB.2B4.2B.B5.B$42.BA.CA3.B6.C.BC.C.
B.B.C2.2B5.B3.A3.B$42.A.A.2B3.B8.C8.B8.2B6.A$42.A.AB3AB10.B.B7.A.B11.
C$43.B2.C.A22.AB.A4.A2B$25.CA21.AB23.A$24.2C23.B17.C.A.ACA$46.B2A$49.
A$15.C.C26.C.B2.A17.C$15.ABA26.B$15.C.C!

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Are speed of light spaceships possible?

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