Grid that dies in one step

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ruleworld
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Joined: April 28th, 2013, 6:56 am

Grid that dies in one step

Post by ruleworld » April 28th, 2013, 7:03 am

Hi,

Is there a grid that dies in one step? One of the cells must die because of overcrowding, that is it must have 4 or more neighbour.

Thanks

knightlife
Posts: 566
Joined: May 31st, 2009, 12:08 am

Re: Grid that dies in one step

Post by knightlife » April 28th, 2013, 7:38 am

This grid pattern dies in one step:

Code: Select all

x = 14, y = 17, rule = B3/S23
2bo2bo2bo2bo$2bo2bo2bo2bo$14o$2bo2bo2bo2bo$2bo2bo2bo2bo$14o$2bo2bo2bo
2bo$2bo2bo2bo2bo$14o$2bo2bo2bo2bo$2bo2bo2bo2bo$14o$2bo2bo2bo2bo$2bo2bo
2bo2bo$14o$2bo2bo2bo2bo$2bo2bo2bo2bo!
The grid can be expanded to infinite size and will still die in 1 step.

ruleworld
Posts: 3
Joined: April 28th, 2013, 6:56 am

Re: Grid that dies in one step

Post by ruleworld » April 28th, 2013, 1:51 pm

knightlife wrote:This grid pattern dies in one step:

Code: Select all

x = 14, y = 17, rule = B3/S23
2bo2bo2bo2bo$2bo2bo2bo2bo$14o$2bo2bo2bo2bo$2bo2bo2bo2bo$14o$2bo2bo2bo
2bo$2bo2bo2bo2bo$14o$2bo2bo2bo2bo$2bo2bo2bo2bo$14o$2bo2bo2bo2bo$2bo2bo
2bo2bo$14o$2bo2bo2bo2bo$2bo2bo2bo2bo!
The grid can be expanded to infinite size and will still die in 1 step.
Thanks. That grid is quite big. What is the smallest grid in Conway's game of Life that dies in one single step?

137ben
Posts: 343
Joined: June 18th, 2010, 8:18 pm

Re: Grid that dies in one step

Post by 137ben » April 28th, 2013, 3:51 pm

What measure of "smallest" are you looking for?

The smallest in population that I could find was this:

Code: Select all

x = 5, y = 5, rule = B3/S23
2bo$2bo$5o$2bo$2bo!

ruleworld
Posts: 3
Joined: April 28th, 2013, 6:56 am

Re: Grid that dies in one step

Post by ruleworld » April 29th, 2013, 1:02 pm

137ben wrote:What measure of "smallest" are you looking for?

The smallest in population that I could find was this:

Code: Select all

x = 5, y = 5, rule = B3/S23
2bo$2bo$5o$2bo$2bo!
I was looking for the smallest possible grid in Conway's game of life which dies in one step.
I guess it is the cross.

137ben
Posts: 343
Joined: June 18th, 2010, 8:18 pm

Re: Grid that dies in one step

Post by 137ben » May 1st, 2013, 12:52 am

ruleworld wrote:
137ben wrote:What measure of "smallest" are you looking for?

The smallest in population that I could find was this:

Code: Select all

x = 5, y = 5, rule = B3/S23
2bo$2bo$5o$2bo$2bo!
I was looking for the smallest possible grid in Conway's game of life which dies in one step.
I guess it is the cross.
I'm not sure you understand: there are many, many commonly used meanings of "small" in cellular automaton: Population, bounding box, bounding polyomino, bounding polyplet, radius under the L-infinity metric, radius under the manhatten metric, etc. The smallest for one is not necessarily the smallest for all of them.

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Mats
Posts: 42
Joined: August 10th, 2010, 7:40 am
Location: Stockholm, Sweden

Re: Grid that dies in one step

Post by Mats » May 3rd, 2013, 3:27 am

Here is another (the other?) 9-cell polyplet that dies in one step.

Code: Select all

x = 5, y = 5, rule = B3/S23
bo$2bobo$b3o$obo$3bo!
I know of polyplets with 1, 2, 9, 10, 12 and 14 or more cells that die in one step. Here are examples with 10, 12, 14 and 15 cells.

Code: Select all

x = 19, y = 18, rule = B3/S23
14bo$2b2o10bo$6o6b4o$2b2o10b4o$15bo$15bo6$2bo$2bo11bobo$4o10bobo$2bobo7b7o$3b4o
7bobo$4bo9bobo$4bo!
I also know there are no polyplets from 3 and up to 8 cells that die in one step. What I don't know is if there are any such polyplets with 11 or 13 cells. Does anyone else know?

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Tropylium
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Joined: May 31st, 2011, 7:12 pm
Location: Finland

Re: Grid that dies in one step

Post by Tropylium » May 3rd, 2013, 1:30 pm

Best I can think of for 11 and 13 are two-polyplet objects:

Code: Select all

x = 14, y = 13, rule = B3/S23
11bo$11bo$2b2obo4b3o$5o3b5o$2b2o6b2o$5bo7bo2$11bo$11bo$10b3o$8b4obo$
10bo$11bobo!

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