Repeated pattern pasting

[TLUL]

I was recently fiddling around in Golly, and I decided to take a pattern, run it, wait for it to settle down, and then paste the original pattern over the final result. After several minutes of doing this, I noticed some very interesting patterns forming, including some pentadecathlons. I also noticed that eventually, the pattern got into a state where it swallowed all changes made by pasting the original pattern. Every time the original pattern is pasted, there are two or more possibilities depending on the state of the oscillators in the pattern (generally just blinkers, but the occasional pentadecathlon pops up).

This got me thinking; for repeatedly pasting patterns in this manner:
1) Is there a pattern that never gets into a state where all changes are swallowed, regardless of the states of any oscillators when it is pasted?
2) If there is no such pattern, is there a pattern that can, if pasted while the oscillators are in specific states, "survive" forever without returning to a previous state (it continually grows)?

I've probably done a poor job of explaining, and the questions are probably very difficult to prove one way or another, but (I think) it's an interesting idea.

In case anyone's interested in the pattern I was using, here it is:

Code: Select all

x = 122, y = 8, rule = B3/S23
4b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$o3b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o3bo$o120bo$3o116b3o$3o116b3o$o120bo$o3b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o3bo$4b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o!

[abiessu]

The trivial answer to (1) is any spaceship. One might describe the result of your process applied to a given spaceship as "the manual gun". Clarifying the question may help eliminate such trivial answers.

This question sounds very similar to the attempts to find Lychrel Numbers (http://en.wikipedia.org/wiki/Lychrel_number)...

[Keiji]

TLUL did mention that he waited for the pattern to "settle down". In other words, the pattern must be an originally unstable pattern whose first stable evolution contains at least one stationary object (still life or oscillator). That eliminates your trivial spaceship answer.

[137ben]

TLUL did mention that he waited for the pattern to "settle down". In other words, the pattern must be an originally unstable pattern whose first stable evolution contains at least one stationary object (still life or oscillator). That eliminates your trivial spaceship answer.

Not entirely. A spaceship is, in a sense, already "settled down". If you insist that the initial pattern must be unstable, you could simply use a 1-generation predecessor to any spaceship.

[Keiji]

> the pattern must be an originally unstable pattern whose first stable evolution contains at least one stationary object
> stationary

Spaceships: not stationary

[Extrementhusiast]

Golly seems to glitch when I do this, generating something else about 5*10^11 units away.

[calcyman]

Golly seems to glitch when I do this, generating something else about 5*10^11 units away.

Yes, I noticed it too when experimenting with this. I informed Tom and Andrew a while ago, and they have been able to reproduce it. There is a partial fix available at:

http://tomas.rokicki.com/golly-2.2b3-win.zip

It is still possible to induce the error if you change rules during the procedure.



And the value is 2^37 on my machine. It looks like yours is 2^39 -- four times more serious!

[Extrementhusiast]

OK, my last comment was an overstatement. It's actually around x = -137 438 953 520, y = -137 438 953 520. The original copying appears around there.

[137ben]

> the pattern must be an originally unstable pattern whose first stable evolution contains at least one stationary object
> stationary

Spaceships: not stationary

Then add a single block to the patter I described. Here is an example:

Code: Select all

x = 39, y = 20, rule = B3/S23
6bo3bo4bo3bo$bo3bobob3o2bo$obo8bobo$2bo3bo2bo6bo$b2o2bo7bo4b2o$b2o5b2o
2bo2b2ob2o$b2o6bo2bo3b2o$2bo2bob2o5bobo$3b2o2b2obo6bo$bo4b2o2bobo5bo$
2bo3bobo$bobo3b2ob3o3bo$3bo3bo2b2o2bo$2bo4bo3bo2bo$3bo2bo2bobobob2o2bo
16b3o$o2bo15bo18bo$b2o4b2obo2bo3b3o17bo$4bo4bo2b4o2bo12b2o$bo4bobo2bo
5b2o12b2o$o2bo6bo2bo!

A single block meets the requirement of "it must contain at least one stationary object" and the pattern on the left is "die658", which is unstable and dies out completely. Meanwhile, the glider is copied every time you paste the pattern.

[Keiji]

That would involve re-pasting the pattern over live cells (the block). I was imagining you'd only paste over dead cells.

[137ben]

Ah, I see. But most patterns do not die out completely, so if you started with a random soup you would almost always end up pasting over some live and some dead cells.