## Grid that dies in one step

For general discussion about Conway's Game of Life.
ruleworld
Posts: 3
Joined: April 28th, 2013, 6:56 am

### Grid that dies in one step

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

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

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

What measure of "smallest" are you looking for?

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

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

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

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

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.

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

### Re: Grid that dies in one step

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?

Tropylium
Posts: 406
Joined: May 31st, 2011, 7:12 pm
Location: Finland

### Re: Grid that dies in one step

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!``````