## Infinite growth from 57o\$73o!

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### Infinite growth from 57o\$73o!

The exclamation point is part of the RLE, but it is a little surprising (but based on an arbitrary encoding so not as mathematically interesting as other small pattern results). I was prepared to go into 3 digit runs before I found this:

`x = 73, y = 2, rule = B3/S2357o\$73o!`

So this is 8 characters of RLE, including the terminator, that produces a stabilized switch engine (block making variety). Is this known? I tried searching on the RLE in quotes and did not find it.

It is a bit long to enter by hand, but doable. Pretty easy to remember 57 and 73 though. Are there shorter RLE strings that give infinite growth? It would require checking lines of cells up to 999999 in length. Has anyone tried it?

Same encoding length but infinite gliders.
`x = 73, y = 2, rule = B3/S2357o\$95o!`

Both have a run of 57. I am not sure if there is a reason besides coincidence.
pcallahan

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Joined: April 26th, 2013, 1:04 pm

### Re: Infinite growth from 57o\$73o!

pcallahan wrote:Are there shorter RLE strings that give infinite growth? It would require checking lines of cells up to 999999 in length. Has anyone tried it?

I haven't heard of it if so. Probably not, because the focus for infinite-growth patterns has generally been on minimizing population rather than RLE length.

I think you'd only have to check up to length 99999, though. "999999o" isn't any shorter than "57o\$73o" ...

EDIT:
pcallahan wrote:Same encoding length but infinite gliders... Both have a run of 57. I am not sure if there is a reason besides coincidence.

Definitely not a coincidence. That's the same exact switch engine in both cases, just a difference in the junk behind it throwing it into a different orbit.

dvgrn
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### Re: Infinite growth from 57o\$73o!

dvgrn wrote:I think you'd only have to check up to length 99999, though. "999999o" isn't any shorter than "57o\$73o" ...

Oops, right. Hmm, going up to 99999 would not be too hard I think. At least there are not that many patterns to check.
pcallahan

Posts: 298
Joined: April 26th, 2013, 1:04 pm

### Re: Infinite growth from 57o\$73o!

pcallahan wrote:
dvgrn wrote:I think you'd only have to check up to length 99999, though. "999999o" isn't any shorter than "57o\$73o" ...

Oops, right. Hmm, going up to 99999 would not be too hard I think. At least there are not that many patterns to check.

I've exploded a fair number of straight width-1 lines in the past couple of decades, and have never seen a switch engine appear. Looks like for long lines a periodicity of 512 cells diagonally develops pretty quickly, superimposed on a 128-diagonal-cell periodicity, which is in turn superimposed on a 32-diagonal-cell periodicity.

So the main cases to worry about are the relatively few cases where the ends of the line are close enough to the tips of the explosion that unique interactions might happen. Those have probably all been tried many times already, but you never know. A universe that contains a 2-engine Cordership is capable of anything, really.

dvgrn
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### Re: Infinite growth from 57o\$73o!

I wrote:Both have a run of 57. I am not sure if there is a reason besides coincidence.

It's not a coincidence. The line of 57 cells followed by a longer line produces the switch engine in the same place. You can watch them together if you space them far enough apart (200 is not minimal, but it keeps them easy to separate by eye).

`x = 95, y = 154, rule = B3/S23\$57o\$73o200\$57o\$95o!`

Switch engines appear some time after generation 400. The context stabilizes the switch engines in different ways. It might be worth eyeballing the other bottom lines lengths to see why they fail.
pcallahan

Posts: 298
Joined: April 26th, 2013, 1:04 pm