Game of Life: Kill the Sun

Question

Below is an initial state for Conway's Game of Life with a single pulsar. Living cells are white.

The area marked with red is your base. You are free to modify any of the red cells, but only those, and only in the initial generation. You are not allowed to do anything once the simulation starts.

Your goal is to annihilate every living cell in the grid – in other words, the game must reach a generation where every cell is dead, even in your base. Yet in other, way cooler words:

You have to construct a rocket to destroy the Sun and everything that was created in the process.

The grid is infinite in every direction, i. e. runaway gliders still count as living.

You may use a brute force algorithm if you really wish, but I don't recommend you to. For one thing, you're up against the halting problem. Besides, finding a good construction all by yourself is fun (at least it was for me).

What I do recommend is downloading a good GoL simulator – solving this with only a paper and a pencil is probably not so much fun.

EDIT: The puzzle has been solved, but please don't be discouraged from posting alternative solutions. They are still very valuable, as they seem hard to come up with.

This puzzle has a continuation, created by kamenf.

Once this puzzle is solved, I will show you my original solution, codenamed "The Dalek". That is, if someone doesn't come up with the exact same solution. — BaSzAt, Apr 20 '16 at 20:43
Even if we restrict ourselves to symmetric solutions, the search space is $2^{30}\approx 1,000,000,000$, juuuust too large for brute-force search. Maybe a genetic algorithm would be more appropriate =) — 2012rcampion, Apr 20 '16 at 21:04
The suggestion of a genetic algorithm was more of a joke, since both it and the game of life are associated with evolution. Personally I'd just brute-force in order of increasing population, and hope that the solution is sparse... — 2012rcampion, Apr 20 '16 at 21:16
@2012rcampion I'd still be happier if you found one manually. I'm sure the CPU you got from your parents isn't half as bad as the one you're sitting in front of. (I meant it the good way!!) — BaSzAt, Apr 20 '16 at 21:22
@2012rcampion Even if you meant it as a joke, now that I think about it, the final phase of how I constructed the (/a) solution was a little similar to a primitive genetic algorithm... Then again, maybe I'm just imagining things. — BaSzAt, Apr 20 '16 at 21:59
Perhaps the solutions may be rated by the number of cells filled in and/or further restricting the red area? — Oliphaunt, Apr 21 '16 at 06:54
@Oliphaunt That came to my mind too, but there's just too many aspects to rate based on. Number of cells filled, area occupied, how fast it kills the Sun, how slow it kills the Sun, how many glider guns are created in the process, etc. I think it's a little unfair to pick just one. — BaSzAt, Apr 21 '16 at 07:03
@BaSzAt good point(s). Our sister site PPCG has the [popularity-contest] tag, where the accepted/winning answer is decided by votes at a certain deadline. That could be appropriate here. Anyway I feel that maybe you have accepted an answer a little soon: this could discourage others from posting solutions. — Oliphaunt, Apr 21 '16 at 07:07
@Oliphaunt Oh, that's what you mean. Absolutely fair, I might have been too early to put the tick. In which case I'm very sorry. I won't revoke it now, though. That would be a little rude... — BaSzAt, Apr 21 '16 at 07:14
@BaSzAt I understand how you feel and it's up to you. But I've seen it urged many times in similar cases that the tick be removed for a little while longer. — Oliphaunt, Apr 21 '16 at 07:26
2^30 isn't too big for brute force really. In 24 hours on my five year old computer at home I have 400,000 cycles per setting. But I suppose many would turn into the same outcome after a few generations, saving lots of time. — gnasher729, Apr 25 '16 at 22:12
I'd be interested to know if there is a solution which will destroy a pulsar in ANY frame of its cycle! — Arth, Aug 10 '16 at 14:58
"For one thing, you're up against the halting problem." No, we're not. If a solution exists, then a brute force approach, given enough resources, is guaranteed to find it. Where the halting problem might come in is if we're trying to prove that there isn't a solution. — Acccumulation, Oct 23 '18 at 19:26

score 95 · Answer 1 · edited Apr 21 '16 at 17:54

95

I found a sun destroyer with just 10 cells filled!

It takes 39 generations.

As animation:

edited Apr 21 '16 at 17:54

kamenf

6,506
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24
45

answered Apr 21 '16 at 10:45

Anna

931
5
4

8

Brilliant! If this were code golf, you would be the absolute winner! Thanks for posting it. – BaSzAt Apr 21 '16 at 10:48
Apparently, you can't do spoiler code blocks. I made a little edit. Hope you don't mind : ) – BaSzAt Apr 21 '16 at 10:54
7

NP. And welcome to Puzzling SE! (God, I've always wanted to say that) – BaSzAt Apr 21 '16 at 11:07
4

Brilliant first answer! – Oliphaunt Apr 21 '16 at 15:46

kamenf · Accepted Answer · 2016-04-20T22:47:21.943

85

The following is a solution with 34 generations:

And, yes, it was really fun to play with it :).

edited Apr 20 '16 at 22:47

answered Apr 20 '16 at 22:24

kamenf

6,506
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2

Beautiful! And you solved it really fast! By the way, it's a different construction from mine. What do you name it? : ) – BaSzAt Apr 21 '16 at 06:31
6

Let call it "T-Ship". I was fast because I had enough clues - limiting area and I searched for something like ship. This one has two boosters, which in fact produces a lot of fire on ignition ;) – kamenf Apr 21 '16 at 12:03
Nice animation! May I invite you to add animations to the other answers, if you're so inclined? (Or perhaps post instructions... "Give a man a fish...") – Oliphaunt Apr 21 '16 at 15:49
@Oliphaunt On Windows or Mac the easiest way is to use tool like http://www.cockos.com/licecap/ which directly captures screen area to GIF – kamenf Apr 21 '16 at 17:14

score 70 · Answer 3 · edited Jun 17 '20 at 08:22

6 cells, 43 and 50 generations

I found 11 unique (up to reflection) 6-cell solutions:

By the first generation of evolution, they form two identical groups:

The first, fourth, and last two patterns work by the same method as my previous answer, but are three generations (one pulsar period) slower. Except for some self-destructing debris they are the same after 17 generations.
The second group is initially the same as the first group, delayed by one generation. This group initially interacts with the pulsar much more quickly (at generation 21).

One thing that's notable is that they are all asymmetric, and stay asymmetric for 20 generations (unlike my initial solution which became symmetric on the first generation). Here's an animation comparing the two groups of 6-cell solutions:

previous solution: 7 cells, 40 generations

There are no solutions with fewer than 6 cells (that stabilize within 1000 generations).

score 61 · Answer 4 · edited Jun 17 '20 at 08:22

61

23 cells, 41 generations, humorous answer

Sorry, I couldn't resist it... The pulsar dies on "magical command" after 41 generations but it takes 23 initial cells.

I apologise for the crudeness of the image. It's my first time using Golly.

EDIT: The next challenge is answered under my registered name Ruutsa

edited Jun 17 '20 at 08:22

Community

1

answered Apr 22 '16 at 00:13

user21465

611
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This one has an independent value on its own even if one didn't know what the original puzzle was. – BaSzAt Apr 22 '16 at 05:33
2

Sorry, but I did not get the humor? – Byte Commander Apr 22 '16 at 06:09
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@ByteCommander Rotate the screen by 90°. – BaSzAt Apr 22 '16 at 06:09
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Ah, now I see the "DIE" spell... Nice! :D – Byte Commander Apr 22 '16 at 06:11
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You can request an account merge. (http://puzzling.stackexchange.com/help/merging-accounts) – wythagoras Apr 24 '16 at 18:54

score 49 · Answer 5 · edited Apr 21 '16 at 17:22

49

In case anyone is wondering, here is my own solution, which takes 38 generations.

(NB: When I made this puzzle, I had no idea if it's even generally solvable. It took me 4 or 5 hours, while having the freedom to change the drawing area as I like.)

By the way, the bottom cells are just for decoration. The following works too:

As animation:

edited Apr 21 '16 at 17:22

kamenf

6,506
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answered Apr 21 '16 at 06:55

BaSzAt

5,657
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For sure this one looks a lot better then mine :) – kamenf Apr 21 '16 at 12:11
2

@Oliphaunt 38 generations – kamenf Apr 21 '16 at 15:51
Is that a picture of a Dalek from Doctor Who? Nice! – Byte Commander Apr 22 '16 at 06:08
1

EX-TER-MIN-ATE! – David Conrad Apr 26 '16 at 02:55