Grid that dies in one step

[ruleworld]

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]

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]

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]

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]

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]

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.

[Mats]

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]

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!