# OCA talk:2×2

## Contents

## Text

We've got a lot of pretty pictures, but this page needs a lot more text to look reasonably balanced. Elithrion 11:00, 19 March 2009 (UTC)

## My changes

So, I tried to make it more similar to the maze page layout-wise, simply because consistency is good. Also because (and I mean no offence), the previous layout was horribly confusing with images everywhere. Nath, you need to add the rle/java stuff that I gratuitously linked to without it existing, though. Also, I was lazy, so I just resized 2x2hp via computer (instead of redrawing at a smaller size), but I think with the filter I used it came out okay (although if someone wants to do it properly, that would be better). Elithrion 11:00, 19 March 2009 (UTC)

- I've added the Java/RLE files so that the links now work (well, they work as well as any of the auto-load links work right now). I also swapped out the image of the high-period oscillators for the larger stamp collection image/pattern. Nathaniel 21:59, 19 March 2009 (UTC)

## 2xn box oscillators

Just wondering if anyone's investigated these semi-thoroughly? I've explored them a little bit this morning, and the period of a 2x(4n) oscillator for n = 1...9 is given by the sequence 2,6,14,14,62,126,30,30,1022. It is not hard to see that each of these is exactly 2 less than a power of 2, which almost surely isn't a coincidence. Indeed, if we add 2 to each term and half the result, we get the sequence 2,4,8,8,32,64,16,16,512. Taking log base 2 of each of these numbers gives 1,2,3,3,5,6,4,4,9, which has a single match in the OEIS (here), which I'm willing to bet gives us the sequence that we want. I'll have a stab at proving it a bit later, I suppose. Nathaniel 12:37, 19 March 2009 (UTC)

- Well, I just played around with it a little (I would have done it sooner but there's no java link, so I wasn't feeling inspired ;)), and I have to add to your observations that in general, any big box made up by of m×n blocks, where m is even, and n is odd (or to vaguely tie into the pattern you noticed, where m = 0 mod 2, n = 1 mod 2), will be an oscillator. All these boxes are, seemingly, phases of the 2×(4n) series of oscillators (or vice versa!), but they make for a more interesting statement of what's going on, I think. Also, I have proceeded to make no real observations about them thus far. Yay! Elithrion 15:42, 19 March 2009 (UTC)

- Ah, well done! I suppose the XOR thing was the critical observation there. Also, that got really handwavy by the end (although I'm sure the omitted steps were trivial!), which makes me thing it took you a while and you were getting frustrated ;) Elithrion 08:17, 23 May 2009 (UTC)

- Yeah, I got pretty excited and slapped myself on the forehead when I read that XOR description by Dean Hickerson. And yeah, the last few steps (finding the rows that satisfy the required criteria) are a bit tedious, so I did what all math people do: I left them as exercises for the reader Nathaniel 12:58, 23 May 2009 (UTC)

## Still Life Counts

How did you find the amount of 8-cell still lifes? Lewis Patterson 18:54, 25 March 2009 (UTC)

- I coded a script in C that counts still lifes in arbitrary rules. I'll upload it to the forums tonight or tomorrow, after I've had a chance to clean up the code a bit. Nathaniel 20:03, 25 March 2009 (UTC)

## Frequency of common patterns

Would it be worthwile including a table of the most common patterns on this page, similar to the table at List of common still lifes. I have some statistics of patterns in this rule (so far around at about 17 million total objects of 300 types) that we could use. Lewis Patterson 09:54, 14 April 2009 (UTC)

- I don't see why not. The more information the better! Nathaniel 12:14, 14 April 2009 (UTC)

- How would we go about naming the patterns? I use codes similar to the ones at http://www.geocities.com/conwaylife/ which would be confusing to anyone who doesn't understand how the codes work. I suppose we could use images for each pattern. Lewis Patterson 14:08, 14 April 2009 (UTC)

- For still lifes I think the general convention if to do something like (number of cells).(some index). So in standard life, you would set the block and tub to be 4.1 and 4.2 (with the second index chosen more or less arbitrarily, though you certainly
*could*construct an order on patterns). For oscillators the most common seems to be (minimum number of cells)P(period).index, and omitting the index if only one such pattern exists/is known. So the blinker would be 3P2, for example. I think this would work well enough here as well, though I think images should go along with the table anyways.--Nathaniel 21:06, 16 April 2009 (UTC)

- For still lifes I think the general convention if to do something like (number of cells).(some index). So in standard life, you would set the block and tub to be 4.1 and 4.2 (with the second index chosen more or less arbitrarily, though you certainly

- How many patterns would be best to include in the table? So far, the statistics are at 303 object types. Including all of them would make for a huge table, and a lot of pictures (if we used pictures). Maybe a table of the most common 25 or so objects woud be best.
- Also, would a seperate table for oscillators be worth making, maybe in the oscillators section of the page?Lewis Patterson 18:03, 17 April 2009 (UTC)

- I think a table of 25 on the page itself is probably a good number, possibly with an external link or reference to a plaintext file containing the full 303 (if you have it available in a semi-readable plaintext form? if not that of course is optional). And personally I prefer keeping oscillator counts separate from still-life counts, but I think that's mostly a personal preference thing. Nathaniel 18:48, 17 April 2009 (UTC)

- Is the RLE text for each pattern OK to put in the table until we get the pictures for each pattern? (eg. Life's beehive would be displayed as b2o$o2bo$b2o!). It can be copied/pasted into most programs easily and I have the RLE codes for all the patterns already. Lewis Patterson 20:36, 17 April 2009 (UTC)

- Yep that's fine by me. Nathaniel 21:07, 17 April 2009 (UTC)

- I've finished the pattern images and those tables look pretty good to me now. I would like to add something that resembles a reference of some kind though; do you have a plaintext file (no matter how ugly) that contains these results that you'd be willing to share? Add your name and a brief note about how you got the estimates you got if possible to the top of the file. Nathaniel 14:21, 20 April 2009 (UTC)

- Where should I put the file? Can it be uploaded onto here?Lewis Patterson 15:55, 20 April 2009 (UTC)

- Unfortunately it can't be directly uploaded to LifeWiki. Maybe just upload it to the 2x2 thread on the forums in a .zip file. Nathaniel 16:19, 20 April 2009 (UTC)

- I've added the file to the 2x2 page on the forums. http://www.conwaylife.com/forums/viewtopic.php?f=7&t=39&p=209#p209Lewis Patterson 16:58, 20 April 2009 (UTC)

## c/8 Wickstretcher

A section needs to be added for the c/8 wickstretcher found and posted on the forums. We could add it to the 'infinite growth' section at the bottom of the page.

- Alright, I've added that to the page now. Nathaniel 13:11, 13 July 2009 (UTC)