Methuselah into Infinite system

[larrymedley]

Hi everyone, I’m writing a fictional book and I’m looking for some help with a Game of Life idea for symbolism and plot purposes.

I’d like to take a methuselah and somehow turn it into a pattern that grows indefinitely. However, there are a couple of things I’m unsure about:

1. Is this actually possible?
2. Ideally, I’d like to accomplish it by adding only a small, fixed number of cells at some point during the simulation. For the symbolism, it would be especially fitting if something as small as reversing a glider (fewer than 10 cells) could somehow trigger the methuselah to go completely crazy and become an infinite-growth pattern.

[hotdogPi]

The chance of a switch engine (block-laying or glider-producing) is about 1 in 2 million for a 16×16 pattern. 256 choose 3 is 2.8 million, so if you start with something that's 16×16 and run a script to toggle all possibilities of 3 cells, you'll have a decent chance (not guaranteed though) to find something that produces infinite growth. 4 cells will almost definitely do it.

[dvgrn]

4 cells will almost definitely do it.

1 cell will definitely do it. Just start your engineering from the other direction: take any of the bajillion known soups that produce linear growth patterns -- anything you like the looks of from the "yl" column in Catagolue, for example -- and toggle one cell. Very likely the altered soup will no longer be a linear-growth pattern, so that becomes your starting point.

It depends on your definition of "methuselah", of course. You could test all possible 1-cell toggles and start from the one that has the longest lifespan. Whatever your starting-pattern criteria are, it should be easy to find a match (since it's easy to generate and test millions of candidates, or billions if necessary).

If you want something a little wilder, you could do the same reverse engineering on a quadratic-growth pattern like Max. For example, try adding a cell in the center of this:

Code: Select all

x = 25, y = 23, rule = B3/S23
19b3o$13bo5bo2bo$13bo5bo$11bo2bo4bo$11b4o4bo$3bo7b2o3bo2bo$o9bo9bo$b2o
5bo3bo10bo$4bo3bo3bo9bo$2obob2obo3bo3b2o4bo$4bo5bo3b2o4bo3bo$2bob2o2b
o7bo2b2obo$o3bo4b2o3bo5bo$2bo4b2o3bo3bob2obob2o$2bo9bo3bo3bo$bo10bo3b
o5b2o$4bo9bo9bo$5bo2bo3b2o7bo$5bo4b4o$5bo4bo2bo$5bo5bo$2bo2bo5bo$3b3o!

It's possible to backtrack this-pattern-plus-central-cell by five or ten ticks, to produce a slightly bigger starting pattern that's not necessarily symmetrical -- such that toggling one central cell would produce a methuselah with few or no visible structural clues that it's capable of producing a spacefiller just by toggling that one cell back again.

Ditto for this smaller starting pattern, which requires a one-cell removal to get back to Max:

Code: Select all

x = 21, y = 19, rule = B3/S23
8bo2b3o3b3o$bo5bo3b2o4bo2bo$ob3ob3o8bo$2bo2b2o3b3o3bobo$o4bo3b2obob2o
2bo$2obo2bo7b2ob3o$2bo4bo3b4obo2bo$11bobo$3b4o2bo2bobo2b2obo$4o4bobob
o4b4o$ob2o2bobo2bo2b4o$7bobo$bo2bob4o3bo4bo$b3ob2o7bo2bob2o$2bo2b2obo
b2o3bo4bo$2bobo3b3o3b2o2bo$3bo8b3ob3obo$o2bo4b2o3bo5bo$b3o3b3o2bo!