Difference between revisions of "User talk:Wwei23"

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(Undo revision 45581 by Wwei23 (talk))
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Revision as of 19:52, 23 April 2018

Did you know...

...that the day I learned a🅱out Life I was experimenting like crazy and saw a natural 🅱eehive and dock? -wwei23 5:40PM 9/20/2015 NY time

Hive series

Hive and mango are sta🅱le. Third evolves into a paper clip. Tenth evolves for 2249 generations (creates a pair of MWSSs at 648, then proceeds to crash them into 🅱locks), and twenty-first evolves for 2668 generations.-wwei23 5:59PM 9/20/2015 NY time

A new wave of LifeWiki editing

Looks like you've 🅱een away for a while, and just got added to the trusted list again this morning. Welcome 🅱ack!

Some of your contri🅱utions from today are going to make more work for other maintainers of the LifeWiki. The "It can also eat a glider" addition to the HWSS page is an example. The LifeWiki mostly doesn't have RLE-encoded patterns on the article pages, though they may perfectly well show up on the talk pages or in a "raw RLE" su🅱sidiary page. If you add an actual image of the pattern in question, people reading the article can see what you're talking a🅱out instantly without having to copy/paste RLE into some other program.

I ended up proposing deletion for your "eater loop" article -- that o🅱ject already has a name ("shuriken") that's 🅱een in use for a long time. Try pasting the RLE into Mark Niemiec's search page to find it.

Also the RLE and hard-to-interpret ASCII image really don't match the fairly standard format that has evolved for other still-life pages. Pro🅱a🅱ly 🅱etter to start with Template:Stilllife if you want to create a new article a🅱out a still life.

It can 🅱e hard to resist the temptation to call things 🅱y names that you've just made up. 🅱ut no matter how good the name is, if no one else has ever used it, it's just plain not going to 🅱e nota🅱le and is likely to get deleted. It might 🅱elong on the LifeWiki after a couple of years, if you successfully get lots of other people using the name on the forums or somewhere like that.

  1. 1: This is unsigned.
  2. 2: I don't know how to use the template. And I don't know how to upload. If I did, it would 🅱e the same as another page. -wwei23 11:38 AM 5/29/2017 NY time
  3. 3: I searched up "shuriken," and it said the page doesn't exist. -wwei23 11:40 AM 5/29/2017 NY time
Not sure how I managed to leave off the four tildes -- sorry a🅱out that.
You can copy the Info🅱ox part of the text of another page a🅱out a standard still life, go to the shuriken page (which now exists thanks to the rename) and paste in the text there, replacing the name, pname, and other statistical details. For details a🅱out the pname and other parameters, see this style-guide page -- LifeWiki:Style_guide/Pattern_layout.
May🅱e copy from a page like 🅱lock for now. We're in the middle of figuring out the details of how 🅱est to use LifeViewer to display files, e.g., very^9 long 🅱oat. 🅱ut that makes a lot more sense for oscillators and spaceships than for still lifes, which really might as well 🅱e static images... at least until we can conveniently copy patterns out via LifeViewer.
(So may🅱e it is a good idea to use LifeViewer for all patterns, including still lifes, to make it easy to add future copy or edit functionality -- along the lines of your recent note on the Tiki 🅱ar. I'll start a new section on the Tiki 🅱ar a🅱out that when I have some time.) Dvgrn (talk) 16:00, 30 May 2017 (UTC)
Images can 🅱e uploaded 🅱y clicking the red link in the info🅱ox, once you have the "Stilllife..." section in at the top of the article.
Apologies for the rather confused state of the LifeWiki, as far as adding new pattern pages. It would 🅱e nice to get everything somewhere close to a standard form, 🅱ut o🅱viously there's still a lot of work to do. Please feel free to try things out on Shuriken; whatever you still find confusing, you could may🅱e descri🅱e it here?We can try to get the process streamlined and documented 🅱etter so it's easier for the next person.
There's a list of wanted pages at the 🅱ottom of this page -- the red links, if you get really am🅱itious (🅱ut there might 🅱e some disagreement as to whether we even really want all of those definitions)...! Dvgrn (talk) 15:35, 30 May 2017 (UTC)
I found that none of the pattern files work anymore, try pasting one into Golly! The old format worked. -wwei23 4:11PM 5/30/2017 NY time
That seems a 🅱it unlikely -- Golly hasn't changed recently. Please 🅱e more specific. Where are you getting your pattern file text from, exactly?
Just 🅱y the way, I had already created an RLE:Shuriken page. You can check the "Recent changes" link on the main page to see what's going on that you might 🅱e interested in.
"RLE:pname" the standard form -- the LifeViewer won't know to look for "Shuriken RLE", so that page can 🅱e deleted. Yes, as it says in the Tiki 🅱ar, this is all still kind of new experimental stuff, and not at all well documented yet...! Dvgrn (talk) 21:02, 30 May 2017 (UTC)
2.7. If I try to paste a pattern file in, I get an empty 🅱ounding 🅱ox. -wwei23 5:39PM 5/30/2017 NY time
Again, please 🅱e more specific. For example: in 32-🅱it Golly 2.8 for Windows, I hit Ctrl+Shift+O with the following text on my clip🅱oard:
x = 15, y = 15, rule = 🅱3/S23
7🅱o$5🅱5o$4🅱o5🅱o$4🅱7o$7🅱o$4🅱2o3🅱2o$3🅱o2🅱3o2🅱o$3🅱2o5🅱2o$5🅱5o$🅱3o7🅱3o$o2🅱
9o2🅱o$2o11🅱2o$5🅱5o$4🅱o2🅱o2🅱o$4🅱2o3🅱2o!
(one of your random patterns from 🅱elow) ...and it works fine. It doesn't work so well if you also copy the line a🅱ove it, 🅱ecause that line doesn't start with a #C, so it confuses the parser. Exactly what text are you trying to paste in, to what version of Golly? Dvgrn (talk) 21:47, 30 May 2017 (UTC)
I am trying to paste the Shuriken RLE into 32-🅱it Golly 2.7, 🅱ut it won't work. -wwei23 6:08 PM 5/30/2017 NY time
http://www.conwaylife.com/patterns/shuriken.rle -wwei23 6:10PM 5/30/2017 NY time
It works if you remove the space after the rule.
x = 11, y = 11, rule = 🅱3/S23 
4🅱3o4🅱2$2🅱o🅱o🅱o🅱o2🅱2$o🅱o5🅱o🅱o$o9🅱o$o🅱o5🅱o🅱o2$2🅱o🅱o🅱o🅱o2🅱2$4🅱3o!
This does not work. Note the space after "🅱3/S23."
x = 11, y = 11, rule = 🅱3/S23
4🅱3o4🅱2$2🅱o🅱o🅱o🅱o2🅱2$o🅱o5🅱o🅱o$o9🅱o$o🅱o5🅱o🅱o2$2🅱o🅱o🅱o🅱o2🅱2$4🅱3o!
This works. There is no space here.

And this space is all that's needed to confuse Golly! -wwei23 6:26 PM 5/30/2017 NY time

Oddly enough, on 32-🅱it Golly on Windows 10, 🅱oth versions produce exactly the same working oscillator for me.
A space 🅱efore the "x" is known to cause pro🅱lems, 🅱ut I've never heard of a pro🅱lem with trailing spaces. I don't see how to duplicate the issue with the two RLE snippets a🅱ove. What OS and 🅱rowser are you using? Dvgrn (talk) 00:06, 31 May 2017 (UTC)
I use Windows 10, and Microsoft Edge. -wwei23 8:25PM 5/31/2017 NY time

Hat loop

What is its actual name?

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As you might notice, It is four siamesed hats to make a loop, and is closely related to the small lake, just remove the four middle cells! -wwei23 11:47AM 5/29/2017 NY time

You're really close, actually -- 24.1937769; Four siamese hats is what comes up in Mark Niemiec's data🅱ase.
Again, you can do these searches yourself from the search page -- 🅱ut please 🅱e warned, the data🅱ase isn't infinite in size. It tends to stop returning results at just a🅱out this size of o🅱ject. Dvgrn (talk) 15:47, 30 May 2017 (UTC)

IT"S GIGANTIC!!!

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A stack of induction coils sta🅱ilize each other.
x = 15, y = 15, rule = 🅱3/S23
7🅱o$5🅱5o$4🅱o5🅱o$4🅱7o$7🅱o$4🅱2o3🅱2o$3🅱o2🅱3o2🅱o$3🅱2o5🅱2o$5🅱5o$🅱3o7🅱3o$o2🅱
9o2🅱o$2o11🅱2o$5🅱5o$4🅱o2🅱o2🅱o$4🅱2o3🅱2o!

-wwei23 [Unknown time]

Another still life

An Eater 2 variant! It should 🅱e functional.

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x = 7, y = 7, rule = 🅱3/S23
2🅱o$🅱o🅱o$🅱o🅱o2🅱o$2o🅱4o2$2o🅱4o$2o🅱o2🅱o!

-wwei23 12:54 PM 5/29/2017 NY time

Still life 🅱ased on the coolout conjecture

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x = 7, y = 7, rule = 🅱3/S23
6🅱o$4🅱3o$3🅱o$2o2🅱o$o🅱2o🅱o$5🅱o$5🅱2o!

The conjecture is still false, though. I had to remove a cell to make it sta🅱le. -wwei23 2PM 5/29/2017 NY time

Four 🅱oats and a domino

TuskTood made this one on lifecompetes.com

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x = 7, y = 8, rule = 🅱3/S23
🅱o3🅱o$o🅱o🅱o🅱o$🅱2o🅱2o$3🅱o$3🅱o$🅱2o🅱2o$o🅱o🅱o🅱o$🅱o3🅱o!

-wwei23 4:45PM 5/29/2017 NY time

2 🅱eacon

The 2 🅱eacon! It is 🅱ased off of 1 🅱eacon. Find the hidden signature!

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x = 20, y = 21, rule = 🅱3/S23
8🅱2o$7🅱o2🅱o🅱2o$7🅱o2🅱o🅱2o$2o6🅱3o$o🅱o9🅱4o$2🅱o7🅱2o4🅱o$2🅱o🅱o2🅱o🅱o3🅱2o🅱o$🅱
2o🅱4o🅱4o🅱o🅱o🅱2o$14🅱o🅱o2🅱o$🅱4o2🅱2o🅱5o🅱o$🅱o2🅱o2🅱2o🅱o6🅱o$10🅱o🅱5o$7🅱2o🅱o🅱o
$7🅱2o🅱o🅱o🅱3o$10🅱o🅱2o3🅱o$7🅱2o🅱o4🅱2o$7🅱2o🅱5o$16🅱3o$7🅱2o🅱2o🅱2o🅱o2🅱o$7🅱2o🅱
2o🅱2o🅱o2🅱o$17🅱2o!
x = 20, y = 21, rule = B3/S23 8b2o$7bo2bob2o$7bo2bob2o$2o6b3o$obo9b4o$2bo7b2o4bo$2bobo2bobo3b2obo$b2ob4ob4obobob2o$14bobo2bo$b4o2b2ob5obo$bo2bo2b2obo6bo$10bob5o$7b2obobo$7b2obobob3o$10bob2o3bo$7b2obo4b2o$7b2ob5o$16b3o$7b2ob2ob2obo2bo$7b2ob2ob2obo2bo$17b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 1 AUTOSTART ]]
(click above to open LifeViewer)

Hat predecessor

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-wwei23 5:31PM 5/30/2017 NY time

Super pond

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x = 8, y = 8, rule = B3/S23
3b2o$2bo2bo$bob2obo$obo2bobo$obo2bobo$bob2obo$2bo2bo$3b2o!

-wwei23 8:40 PM 5/31/2017 NY time

2-still lifes

An n-still life is a still life where all cells have n live neigh🅱ors. The question is that in Life, why do no 2-still lifes exist(as far as I know) with 9 to 19 cells? -wwei23 8:29PM 6/13/2017 NY time

DryLife Oscillator And Life Agar

Oscillator:
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Agar:
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It's in a torus.
🅱igger version(more clear):
x = 48, y = 48, rule = 🅱3/S23:T48,48
4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$5🅱2o6🅱2o
6🅱2o6🅱2o6🅱2o6🅱2o$o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱
2o6🅱2o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$🅱
2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o
4🅱o2🅱o4🅱o2🅱o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$4🅱o2🅱o4🅱
o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$5🅱2o6🅱2o6🅱2o6🅱2o
6🅱2o6🅱2o$o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$🅱
2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$🅱2o6🅱2o6🅱
2o6🅱2o6🅱2o6🅱2o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱
o2🅱o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$4🅱o2🅱o4🅱o2🅱o4🅱o
2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o
$o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$🅱2o6🅱2o6🅱
2o6🅱2o6🅱2o6🅱2o$4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$🅱2o6🅱2o6🅱2o6🅱2o6🅱
2o6🅱2o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$5🅱
2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱
o4🅱o2🅱o4🅱o2🅱o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$o2🅱o4🅱o
2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$5🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$🅱2o6🅱2o6🅱2o6🅱2o6🅱
2o6🅱2o$4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$5🅱
2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o$o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o4🅱o2🅱o$5🅱2o6🅱2o6🅱2o
6🅱2o6🅱2o6🅱2o$🅱2o6🅱2o6🅱2o6🅱2o6🅱2o6🅱2o!
-wwei23 7:36AM 6/14/2017 NY time

Long eaters and 🅱ookends

░░░░░░░░░░▓▓░
▓▓░░░░▓▓░▓░▓░
▓░░▓░▓░▓░▓░░░
░▓▓▓░▓░░░▓▓░░
░░░░░▓░▓░░░░░
░▓▓░▓▓░▓▓▓▓░░
░▓░░░░░░░░░▓░
░░▓▓▓▓░▓▓░▓▓░
░░░░░▓░▓░░░░░
░░▓▓░░░▓░▓▓▓░
░░░▓░▓░▓░▓░░▓
░▓░▓░▓▓░░░░▓▓
░▓▓░░░░░░░░░░
x = 13, y = 13, rule = 🅱3/S23
10🅱2o$2o4🅱2o🅱o🅱o$o2🅱o🅱o🅱o🅱o$🅱3o🅱o3🅱2o$5🅱o🅱o$🅱2o🅱2o🅱4o$🅱o9🅱o$2🅱4o🅱2o🅱2o
$5🅱o🅱o$2🅱2o3🅱o🅱3o$3🅱o🅱o🅱o🅱o2🅱o$🅱o🅱o🅱2o4🅱2o$🅱2o!
-wwei23 4:19PM 6/14/2017 NY time

Gosper Glider Gun 🅱ecomes own Inline Inverter

x = 36, y = 5, rule = B3/S23:T105,110
22b2o$22bobo3bo5b2o$7bo4b2o9b2ob2o6b2o$2o3bobo3bobo13b2o$2o4b2o3b2o!
x = 36, y = 5, rule = B3/S23:T105,110 22b2o$22bobo3bo5b2o$7bo4b2o9b2ob2o6b2o$2o3bobo3bobo13b2o$2o4b2o3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 3 GPS 10 AUTOSTART ]]
(click above to open LifeViewer)

Check it out. Here, it's a P840. -wwei23 6:20PM 3/11/2018 NY time

Just to let you know -- it does not seem likely that anyone will look at patterns you post here, if you damage your RLE-format patterns by replacing the b's with Unicode characters. The point of RLE is that it's easy to copy and paste into Golly.

Also, the characters you're using for ON and OFF cells don't render well in some browsers -- many people will end up with strange overlaps and won't be able to see the pattern clearly. The old standard ASCII characters really work much better, partly because you can copy and paste them directly into Golly.

..........OO.
OO....OO.O.O.
O..O.O.O.O...
.OOO.O...OO..
.....O.O.....
.OO.OO.OOOO..
.O.........O.
..OOOO.OO.OO.
.....O.O.....
..OO...O.OOO.
...O.O.O.O..O
.O.O.OO....OO
.OO..........

If you really want to make things easy, try using LifeViewer:

x = 48, y = 48, rule = B3/S23:T48,48 4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$b2o6b2o6b2o6b2o6b2o6b2o$5b2o6b2o 6b2o6b2o6b2o6b2o$o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b2o6b2o6b2o6b2o6b 2o6b2o$b2o6b2o6b2o6b2o6b2o6b2o$4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$b 2o6b2o6b2o6b2o6b2o6b2o$5b2o6b2o6b2o6b2o6b2o6b2o$o2bo4bo2bo4bo2bo4bo2bo 4bo2bo4bo2bo$5b2o6b2o6b2o6b2o6b2o6b2o$b2o6b2o6b2o6b2o6b2o6b2o$4bo2bo4b o2bo4bo2bo4bo2bo4bo2bo4bo2bo$b2o6b2o6b2o6b2o6b2o6b2o$5b2o6b2o6b2o6b2o 6b2o6b2o$o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b2o6b2o6b2o6b2o6b2o6b2o$b 2o6b2o6b2o6b2o6b2o6b2o$4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$b2o6b2o6b 2o6b2o6b2o6b2o$5b2o6b2o6b2o6b2o6b2o6b2o$o2bo4bo2bo4bo2bo4bo2bo4bo2bo4b o2bo$5b2o6b2o6b2o6b2o6b2o6b2o$b2o6b2o6b2o6b2o6b2o6b2o$4bo2bo4bo2bo4bo 2bo4bo2bo4bo2bo4bo2bo$b2o6b2o6b2o6b2o6b2o6b2o$5b2o6b2o6b2o6b2o6b2o6b2o $o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b2o6b2o6b2o6b2o6b2o6b2o$b2o6b2o6b 2o6b2o6b2o6b2o$4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$b2o6b2o6b2o6b2o6b 2o6b2o$5b2o6b2o6b2o6b2o6b2o6b2o$o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b 2o6b2o6b2o6b2o6b2o6b2o$b2o6b2o6b2o6b2o6b2o6b2o$4bo2bo4bo2bo4bo2bo4bo2b o4bo2bo4bo2bo$b2o6b2o6b2o6b2o6b2o6b2o$5b2o6b2o6b2o6b2o6b2o6b2o$o2bo4bo 2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b2o6b2o6b2o6b2o6b2o6b2o$b2o6b2o6b2o6b2o6b 2o6b2o$4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$b2o6b2o6b2o6b2o6b2o6b2o$5b 2o6b2o6b2o6b2o6b2o6b2o$o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b2o6b2o6b2o 6b2o6b2o6b2o$b2o6b2o6b2o6b2o6b2o6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 1 AUTOSTART ]]
(click above to open LifeViewer)

Dvgrn (talk) 02:01, 24 March 2018 (UTC)

Maximum Ride: The hashsoup experiment

def hashsoup(instring, sym):

    s = hashlib.sha256(instring).digest()

    thesoup = []

    if sym in ['D2_x', 'D8_1', 'D8_4']:
        d = 1
    elif sym in ['D4_x1', 'D4_x4']:
        d = 2
    elif sym in ['25p']:
        d = -1
    else:
        d = 0
        
    for j in xrange(32):

        t = ord(s[j])

        for k in xrange(8):

            if (sym == '8x32'):
                
                x = k + 8*(j % 4)
                y = int(j / 4)
                
            elif (sym == '4x64'):
                
                x = k + 8*(j % 8)
                y = int(j / 8)
        
            elif (sym == '2x128'):
                
                x = k + 8*(j % 16)
                y = int(j / 16)
                
            elif (sym in ['1x256', '1x256X2', '1x256X2+1']):
                
                x = k + 8*(j % 32)
                y = int(j / 32)
                
            else:
                
                x = k + 8*(j % 2)
                y = int(j / 2)

            if (t & (1 << (7 - k))):
                
                if (((d == 0) | (x >= y)) & d != -1):

                    thesoup.append(x)
                    thesoup.append(y)

                if (sym == "25p"):

                    

                    for J in xrange(32):

                        T = ord(s[J])

                        for K in xrange(8):

                            X = K + 8*(J % 2)
                            Y = int(J / 2)

                            if (T & (1 << (7 - K))):

                                thesoup.append(16 * X + x)
                                thesoup.append(16 * Y + y)

                if (sym == '1x256X2+1'):

                    thesoup.append(-x)
                    thesoup.append(y)

                if (sym == '1x256X2'):

                    thesoup.append(-1-x)
                    thesoup.append(y)
                
                if (sym == '32x32'):

                    thesoup.append(x+16)
                    thesoup.append(y)
                    thesoup.append(x)
                    thesoup.append(y+16)
                    thesoup.append(x+16)
                    thesoup.append(y+16)

                if (sym == '75p'):

                    thesoup.append(15-y)
                    thesoup.append(x)

                elif (sym == 'D4_x1'):

                    thesoup.append(y)
                    thesoup.append(-x)

                elif (sym == 'D4_x4'):

                    thesoup.append(y)
                    thesoup.append(-x-1)

                if ((sym == 'D4_x1') & (x == y)):

                    thesoup.append(y)
                    thesoup.append(-x)

                if ((sym == 'D4_x4') & (x == y)):

                    thesoup.append(y)
                    thesoup.append(-x-1)

    # Checks for diagonal symmetries:
    if (d >= 1):
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(thesoup[x+1])
            thesoup.append(thesoup[x])
        if d == 2:
            if (sym == 'D4_x1'):
                for x in xrange(0, len(thesoup), 2):
                    thesoup.append(-thesoup[x+1])
                    thesoup.append(-thesoup[x])
            else:
                for x in xrange(0, len(thesoup), 2):
                    thesoup.append(-thesoup[x+1] - 1)
                    thesoup.append(-thesoup[x] - 1)
            return thesoup

    # Checks for orthogonal x symmetry:
    if sym in ['D2_+1', 'D4_+1', 'D4_+2']:
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(thesoup[x])
            thesoup.append(-thesoup[x+1])
    elif sym in ['D2_+2', 'D4_+4']:
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(thesoup[x])
            thesoup.append(-thesoup[x+1] - 1)

    # Checks for orthogonal y symmetry:
    if sym in ['D4_+1']:
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(-thesoup[x])
            thesoup.append(thesoup[x+1])
    elif sym in ['D4_+2', 'D4_+4']:
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(-thesoup[x] - 1)
            thesoup.append(thesoup[x+1])

    # Checks for rotate2 symmetry:
    if sym in ['C2_1', 'C4_1', 'D8_1']:
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(-thesoup[x])
            thesoup.append(-thesoup[x+1])
    elif sym in ['C2_2']:
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(-thesoup[x])
            thesoup.append(-thesoup[x+1]-1)
    elif sym in ['C2_4', 'C4_4', 'D8_4']:
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(-thesoup[x]-1)
            thesoup.append(-thesoup[x+1]-1)

    # Checks for rotate4 symmetry:
    if (sym in ['C4_1', 'D8_1']):
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(thesoup[x+1])
            thesoup.append(-thesoup[x])
    elif (sym in ['C4_4', 'D8_4']):
        for x in xrange(0, len(thesoup), 2):
            thesoup.append(thesoup[x+1])
            thesoup.append(-thesoup[x]-1)

    return thesoup

-wwei23 4:06 PM 4/2/2018 NY time

Another one

  1. *************************************
  2. * Ash Pattern Generator (apgsearch) *
  3. *************************************
  4. * Version: v1.1 (beta release) *
  5. *************************************
  6. -- Processes roughly 100 soups per (second . core . GHz), using caching
  7. and machine-learning to optimise itself during runtime.
  8. -- Can perfectly identify oscillators with period < 1000, well-separated
  9. spaceships of low period, and certain infinite-growth patterns (such
  10. guns and puffers, including both naturally-occurring types of switch
  11. engine).
  12. -- Separates most pseudo-objects into their constituent parts, including
  13. all pseudo-still-lifes of 18 or fewer live cells (which is the maximum
  14. theoretically possible, given there is a 19-cell pseudo-still-life
  15. with two distinct decompositions).
  16. -- Correctly separates non-interacting standard spaceships, irrespective
  17. of their proximity. In particular, a LWSS-on-LWSS is registered as two
  18. LWSSes, whereas an LWSS-on-HWSS is registered as a single spaceship
  19. (since they interact by suppressing sparks).
  20. -- At least 99.9999999999% reliable at identifying objects in asymmetrical
  21. soups in B3/S23 (based on the fact that out of over 10^12 objects that
  22. have appeared, there are no errors).
  23. -- Scores soups based on the total excitement of the ash objects.
  24. -- Support for other outer-totalistic rules, including detection and
  25. classification of various types of infinite growth.
  26. -- Support for symmetrical soups.
  27. -- Uploads results to the server at http://catagolue.appspot.com (which
  28. currently has collected over 2.7 * 10^12 objects).
  29. -- Peer-reviews others' contributions to ensure data integrity for the
  30. asymmetrical B3/S23 census.
  31. By Adam P. Goucher, with contributions from Andrew Trevorrow, Tom Rokicki,
  32. Nathaniel Johnston, Dave Greene and Richard Schank.

import golly as g from glife import rect, pattern import time import math import operator import hashlib import datetime import os import urllib2

def get_server_address():

   # Should be 'http://catagolue.appspot.com' for the released version,
   # and 'http://localhost:8080' for the development version:    
   return 'http://catagolue.appspot.com'


  1. Engages with Catagolue's authentication system ('payment over SHA-256',
  2. affectionately abbreviated to 'payosha256'):
  3. The payosha256_key can be obtained from logging into Catagolue in your
  4. web browser and visiting http://catagolue.appspot.com/payosha256

def authenticate(payosha256_key, operation_name):

   g.show("Authenticating with Catagolue via the payosha256 protocol...")
   payload = "payosha256:get_token:"+payosha256_key+":"+operation_name
   req = urllib2.Request(get_server_address() + "/payosha256", payload, {"Content-type": "text/plain"})
   f = urllib2.urlopen(req)
   if (f.getcode() != 200):
       return None
   resp = f.read()
   lines = resp.splitlines()
   for line in lines:
       parts = line.split(':')
       if (len(parts) < 3):
           continue
       if (parts[1] != 'good'):
           continue
       target = parts[2]
       token = parts[3]
       g.show("Token " + token + " obtained from payosha256. Performing proof of work with target " + target + "...")
       for nonce in xrange(100000000):
           prehash = token + ":" + str(nonce)
           posthash = hashlib.sha256(prehash).hexdigest()
           if (posthash < target):
               break
       if (posthash > target):
           continue
       g.show("String "+prehash+" is sufficiently valuable ("+posthash+" < "+target+").")
       payload = "payosha256:pay_token:"+prehash+"\n"
       return payload
   return None
  1. Sends the results to Catagolue:

def catagolue_results(results, payosha256_key, operation_name, endpoint="/apgsearch", return_point=None):

   try:
       payload = authenticate("mwacwcheeeis2e37", operation_name)
       if payload is None:
           return 1
       payload += results
       req = urllib2.Request(get_server_address() + endpoint, payload, {"Content-type": "text/plain"})
       f = urllib2.urlopen(req)
       if (f.getcode() != 200):
           return 2
       resp = f.read()
       try:
           f2 = open(g.getdir("data")+"catagolue-response.txt", 'w')
           f2.write(resp)
           f2.close()
           if return_point is not None:
               return_point[0] = resp
           
       except:
           g.warn("Unable to save catagolue response file.")
       return 0
   except:
       return 1
  1. Takes approximately 350 microseconds to construct a 16-by-16 soup based
  2. on a SHA-256 cryptographic hash in the obvious way.

def hashsoup(instring, sym):

   s = hashlib.sha256(instring).digest()
   thesoup = []
   if sym in ['D2_x', 'D8_1', 'D8_4']:
       d = 1
   elif sym in ['D4_x1', 'D4_x4']:
       d = 2
   elif sym in ['25p', 'wwei23BLOCKPARTYTEST', 'BlockFloodTest']:
       d = -1
   else:
       d = 0
       
   for j in xrange(32):
       t = ord(s[j])
       for k in xrange(8):
           if (sym == '8x32'):
               
               x = k + 8*(j % 4)
               y = int(j / 4)
               
           elif (sym == '4x64'):
               
               x = k + 8*(j % 8)
               y = int(j / 8)
       
           elif (sym == '2x128'):
               
               x = k + 8*(j % 16)
               y = int(j / 16)
               
           elif (sym in ['1x256', '1x256X2', '1x256X2+1']):
               
               x = k + 8*(j % 32)
               y = int(j / 32)
               
           else:
               
               x = k + 8*(j % 2)
               y = int(j / 2)
           if (t & (1 << (7 - k))):
               if (((d == 0) | (x >= y)) & (d != -1)):
                   thesoup.append(x)
                   thesoup.append(y)
                   
               if (sym == '1x256X2+1'):
                   thesoup.append(-x)
                   thesoup.append(y)
               if (sym == '1x256X2'):
                   thesoup.append(-1-x)
                   thesoup.append(y)
               
               if (sym == '32x32'):
                   thesoup.append(x+16)
                   thesoup.append(y)
                   thesoup.append(x)
                   thesoup.append(y+16)
                   thesoup.append(x+16)
                   thesoup.append(y+16)
               if (sym == '75p'):
                   thesoup.append(15-y)
                   thesoup.append(x)
               elif (sym == 'D4_x1'):
                   thesoup.append(y)
                   thesoup.append(-x)
               elif (sym == 'D4_x4'):
                   thesoup.append(y)
                   thesoup.append(-x-1)
               if ((sym == 'D4_x1') & (x == y)):
                   thesoup.append(y)
                   thesoup.append(-x)
               if ((sym == 'D4_x4') & (x == y)):
                   thesoup.append(y)
                   thesoup.append(-x-1)
               if (sym == "25p"):
                   for J in xrange(32):
                       T = ord(s[J])
                       for K in xrange(8):
                           X = K + 8*(J % 2)
                           Y = int(J / 2)
                           if (T & (1 << (7 - K))):
                               thesoup.append(16 * X + x)
                               thesoup.append(16 * Y + y)
               if (sym == "wwei23BLOCKPARTYTEST"):
                   thesoup.append(4*x)
                   thesoup.append(4*y)
                   thesoup.append(4*x+1)
                   thesoup.append(4*y)
                   thesoup.append(4*x)
                   thesoup.append(4*y+1)
                   thesoup.append(4*x+1)
                   thesoup.append(4*y+1)
               
   # Checks for diagonal symmetries:
   if (d >= 1):
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(thesoup[x+1])
           thesoup.append(thesoup[x])
       if d == 2:
           if (sym == 'D4_x1'):
               for x in xrange(0, len(thesoup), 2):
                   thesoup.append(-thesoup[x+1])
                   thesoup.append(-thesoup[x])
           else:
               for x in xrange(0, len(thesoup), 2):
                   thesoup.append(-thesoup[x+1] - 1)
                   thesoup.append(-thesoup[x] - 1)
           return thesoup
   # Checks for orthogonal x symmetry:
   if sym in ['D2_+1', 'D4_+1', 'D4_+2']:
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(thesoup[x])
           thesoup.append(-thesoup[x+1])
   elif sym in ['D2_+2', 'D4_+4']:
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(thesoup[x])
           thesoup.append(-thesoup[x+1] - 1)
   # Checks for orthogonal y symmetry:
   if sym in ['D4_+1']:
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(-thesoup[x])
           thesoup.append(thesoup[x+1])
   elif sym in ['D4_+2', 'D4_+4']:
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(-thesoup[x] - 1)
           thesoup.append(thesoup[x+1])
   # Checks for rotate2 symmetry:
   if sym in ['C2_1', 'C4_1', 'D8_1']:
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(-thesoup[x])
           thesoup.append(-thesoup[x+1])
   elif sym in ['C2_2']:
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(-thesoup[x])
           thesoup.append(-thesoup[x+1]-1)
   elif sym in ['C2_4', 'C4_4', 'D8_4']:
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(-thesoup[x]-1)
           thesoup.append(-thesoup[x+1]-1)
   # Checks for rotate4 symmetry:
   if (sym in ['C4_1', 'D8_1']):
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(thesoup[x+1])
           thesoup.append(-thesoup[x])
   elif (sym in ['C4_4', 'D8_4']):
       for x in xrange(0, len(thesoup), 2):
           thesoup.append(thesoup[x+1])
           thesoup.append(-thesoup[x]-1)
   return thesoup


  1. Obtains a canonical representation of any oscillator/spaceship that (in
  2. some phase) fits within a 40-by-40 bounding box. This representation is
  3. alphanumeric and lowercase, and so much more compact than RLE. Compare:
  4. Common name: pentadecathlon
  5. Canonical representation: 4r4z4r4
  6. Equivalent RLE: 2bo4bo$2ob4ob2o$2bo4bo!
  7. It is a generalisation of a notation created by Allan Weschler in 1992.

def canonise(duration):

   representation = "#"
   # We need to compare each phase to find the one with the smallest
   # description:
   for t in xrange(duration):
       rect = g.getrect()
       if (len(rect) == 0):
           return "0"
       if ((rect[2] <= 40) & (rect[3] <= 40)):
           # Fits within a 40-by-40 bounding box, so eligible to be canonised.
           # Choose the orientation which results in the smallest description:
           representation = compare_representations(representation, canonise_orientation(rect[2], rect[3], rect[0], rect[1], 1, 0, 0, 1))
           representation = compare_representations(representation, canonise_orientation(rect[2], rect[3], rect[0]+rect[2]-1, rect[1], -1, 0, 0, 1))
           representation = compare_representations(representation, canonise_orientation(rect[2], rect[3], rect[0], rect[1]+rect[3]-1, 1, 0, 0, -1))
           representation = compare_representations(representation, canonise_orientation(rect[2], rect[3], rect[0]+rect[2]-1, rect[1]+rect[3]-1, -1, 0, 0, -1))
           representation = compare_representations(representation, canonise_orientation(rect[3], rect[2], rect[0], rect[1], 0, 1, 1, 0))
           representation = compare_representations(representation, canonise_orientation(rect[3], rect[2], rect[0]+rect[2]-1, rect[1], 0, -1, 1, 0))
           representation = compare_representations(representation, canonise_orientation(rect[3], rect[2], rect[0], rect[1]+rect[3]-1, 0, 1, -1, 0))
           representation = compare_representations(representation, canonise_orientation(rect[3], rect[2], rect[0]+rect[2]-1, rect[1]+rect[3]-1, 0, -1, -1, 0))
       g.run(1)
   return representation
  1. A subroutine used by canonise:

def canonise_orientation(length, breadth, ox, oy, a, b, c, d):

   representation = ""
   chars = "0123456789abcdefghijklmnopqrstuvwxyz"
   for v in xrange(int((breadth-1)/5)+1):
       zeroes = 0
       if (v != 0):
           representation += "z"
       for u in xrange(length):
           baudot = 0
           for w in xrange(5):
               x = ox + a*u + b*(5*v + w)
               y = oy + c*u + d*(5*v + w)
               baudot = (baudot >> 1) + 16*g.getcell(x, y)
           if (baudot == 0):
               zeroes += 1
           else:
               if (zeroes > 0):
                   if (zeroes == 1):
                       representation += "0"
                   elif (zeroes == 2):
                       representation += "w"
                   elif (zeroes == 3):
                       representation += "x"
                   else:
                       representation += "y"
                       representation += chars[zeroes - 4]
               zeroes = 0
               representation += chars[baudot]
   return representation
  1. Compares strings first by length, then by lexicographical ordering.
  2. A hash character is worse than anything else.

def compare_representations(a, b):

   if (a == "#"):
       return b
   elif (b == "#"):
       return a
   elif (len(a) < len(b)):
       return a
   elif (len(b) < len(a)):
       return b
   elif (a < b):
       return a
   else:
       return b
  1. Finds the gradient of the least-squares regression line corresponding
  2. to a list of ordered pairs:

def regress(pairlist):

   cumx = 0.0
   cumy = 0.0
   cumvar = 0.0
   cumcov = 0.0
   for x,y in pairlist:
       cumx += x
       cumy += y
   cumx = cumx / len(pairlist)
   cumy = cumy / len(pairlist)
   for x,y in pairlist:
       cumvar += (x - cumx)*(x - cumx)
       cumcov += (x - cumx)*(y - cumy)
   return (cumcov / cumvar)
  1. Analyses a pattern whose average population follows a power-law:

def powerlyse(stepsize, numsteps):

   g.setalgo("HashLife")
   g.setbase(2)
   g.setstep(stepsize)
   poplist = [0]*numsteps
   poplist[0] = int(g.getpop())
   pointlist = []
   for i in xrange(1, numsteps, 1):
       g.step()
       poplist[i] = int(g.getpop()) + poplist[i-1]
       if (i % 50 == 0):
           g.fit()
           g.update()
       if (i > numsteps/2):
           pointlist.append((math.log(i),math.log(poplist[i]+1.0)))
   power = regress(pointlist)
   if (power < 1.10):
       return "unidentified"
   elif (power < 1.65):
       return "zz_REPLICATOR"
   elif (power < 2.05):
       return "zz_LINEAR"
   elif (power < 2.8):
       return "zz_EXPLOSIVE"
   else:
       return "zz_QUADRATIC"
  1. Gets the period of an interleaving of degree-d polynomials:

def deepperiod(sequence, maxperiod, degree):

   for p in xrange(1, maxperiod, 1):
       good = True
       for i in xrange(maxperiod):
           diffs = [0] * (degree + 2)
           for j in xrange(degree + 2):
               diffs[j] = sequence[i + j*p]
           # Produce successive differences:
           for j in xrange(degree + 1):
               for k in xrange(degree + 1):
                   diffs[k] = diffs[k] - diffs[k + 1]
           if (diffs[0] != 0):
               good = False
               break
       if (good):
           return p
   return -1
  1. Analyses a linear-growth pattern, returning a hash:

def linearlyse(maxperiod):

   poplist = [0]*(3*maxperiod)
   for i in xrange(3*maxperiod):
       g.run(1)
       poplist[i] = int(g.getpop())
   p = deepperiod(poplist, maxperiod, 1)
   if (p == -1):
       return "unidentified"
   difflist = [0]*(2*maxperiod)
   for i in xrange(2*maxperiod):
       difflist[i] = poplist[i + p] - poplist[i]
   q = deepperiod(difflist, maxperiod, 0)
   moments = [0, 0, 0]
   for i in xrange(p):
       moments[0] += (poplist[i + q] - poplist[i])
       moments[1] += (poplist[i + q] - poplist[i]) ** 2
       moments[2] += (poplist[i + q] - poplist[i]) ** 3
   prehash = str(moments[1]) + "#" + str(moments[2])
   # Linear-growth patterns with growth rate zero are clearly errors!
   if (moments[0] == 0):
       return "unidentified"
   return "yl" + str(p) + "_" + str(q) + "_" + str(moments[0]) + "_" + hashlib.md5(prehash).hexdigest()


  1. This explodes pseudo-still-lifes and pseudo-oscillators into their
  2. constituent parts.
  3. -- Requires the period (if oscillatory) and graph-theoretic diameter
  4. to not exceed 4096.
  5. -- Never mistakenly separates a true object.
  6. -- Correctly separates most pseudo-still-lifes, including the famous:
  7. http://www.conwaylife.com/wiki/Quad_pseudo_still_life
  8. -- Works perfectly for all still-lifes of up to 17 bits.
  9. -- Doesn't separate 'locks', of which the smallest example has 18
  10. bits and is unique:
  11. ** **
  12. ** **
  13. * *** *
  14. ** * **
  15. To use this function (standalone), merely copy it into a script of
  16. the following form:
  17. import golly as g
  18. def pseudo_bangbang():
  19. [...]
  20. pseudo_bangbang()
  21. and execute it in Golly with a B3/S23 universe containing any still-
  22. lifes or oscillators you want to separate. Pure objects correspond to
  23. connected components in the final state of the universe.
  24. This has dependencies on the rules ContagiousLife, PercolateInfection
  25. and EradicateInfection.
  26. Not to be confused with the Unix shell instruction for repeating the
  27. previous instruction as a superuser (sudo !!), or indeed with any
  28. parodies of this song: https://www.youtube.com/watch?v=YswhUHH6Ufc
  29. Adam P. Goucher, 2014-08-25

def pseudo_bangbang(alpharule):

   g.setrule("APG_ContagiousLife_" + alpharule)
   g.setbase(2)
   g.setstep(12)
   g.step()
   celllist = g.getcells(g.getrect())
   for i in xrange(0, len(celllist)-1, 3):
       
       # Only infect cells that haven't yet been infected:
       if (g.getcell(celllist[i], celllist[i+1]) <= 2):
           # Seed an initial 'infected' (red) cell:
           g.setcell(celllist[i], celllist[i+1], g.getcell(celllist[i], celllist[i+1]) + 2)
           prevpop = 0
           currpop = int(g.getpop())
           # Continue infecting until the entire component has been engulfed:
           while (prevpop != currpop):
               # Percolate the infection to every cell in the island:
               g.setrule("APG_PercolateInfection")
               g.setbase(2)
               g.setstep(12)
               g.step()
               # Transmit the infection across any bridges.
               g.setrule("APG_ContagiousLife_" + alpharule)
               g.setbase(2)
               g.setstep(12)
               g.step()
               prevpop = currpop
               currpop = int(g.getpop())
               
           g.fit()
           g.update()
           # Red becomes green:
           g.setrule("APG_EradicateInfection")
           g.step()


  1. Counts the number of live cells of each degree:

def degreecount():

   celllist = g.getcells(g.getrect())
   counts = [0,0,0,0,0,0,0,0,0]
   for i in xrange(0, len(celllist), 2):
       x = celllist[i]
       y = celllist[i+1]
       degree = -1
       for ux in xrange(x - 1, x + 2):
           for uy in xrange(y - 1, y + 2):
               degree += g.getcell(ux, uy)
       counts[degree] += 1
   return counts
  1. Counts the number of live cells of each degree in generations 1 and 2:

def degreecount2():

   g.run(1)
   a = degreecount()
   g.run(1)
   b = degreecount()
   return (a + b)
  1. If the universe consists only of disjoint *WSSes, this will return
  2. a triple (l, w, h) giving the quantities of each *WSS. Otherwise,
  3. this function will return (-1, -1, -1).
  4. This should only be used to separate period-4 moving objects which
  5. may contain multiple *WSSes.

def countxwsses():

   degcount = degreecount2()
   if (degreecount2() != degcount):
       # Degree counts are not period-2:
       return (-1, -1, -1)
   # Degree counts of each standard spaceship:
   hwssa = [1,4,6,2,0,0,0,0,0,0,0,0,4,4,6,1,2,1]
   mwssa = [2,2,5,2,0,0,0,0,0,0,0,0,4,4,4,1,2,0]
   lwssa = [1,2,4,2,0,0,0,0,0,0,0,0,4,4,2,2,0,0]
   hwssb = [0,0,0,4,4,6,1,2,1,1,4,6,2,0,0,0,0,0]
   mwssb = [0,0,0,4,4,4,1,2,0,2,2,5,2,0,0,0,0,0]
   lwssb = [0,0,0,4,4,2,2,0,0,1,2,4,2,0,0,0,0,0]
   # Calculate the number of standard spaceships in each phase:
   hacount = degcount[17]
   macount = degcount[16]/2 - hacount
   lacount = (degcount[15] - hacount - macount)/2
   hbcount = degcount[8]
   mbcount = degcount[7]/2 - hbcount
   lbcount = (degcount[6] - hbcount - mbcount)/2
   # Determine the expected degcount given the calculated quantities:
   pcounts = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
   pcounts = map(lambda x, y: x + y, pcounts, map(lambda x: hacount*x, hwssa))
   pcounts = map(lambda x, y: x + y, pcounts, map(lambda x: macount*x, mwssa))
   pcounts = map(lambda x, y: x + y, pcounts, map(lambda x: lacount*x, lwssa))
   pcounts = map(lambda x, y: x + y, pcounts, map(lambda x: hbcount*x, hwssb))
   pcounts = map(lambda x, y: x + y, pcounts, map(lambda x: mbcount*x, mwssb))
   pcounts = map(lambda x, y: x + y, pcounts, map(lambda x: lbcount*x, lwssb))
   # Compare the observed and expected degcounts (to eliminate nonstandard spaceships):
   if (pcounts != degcount):
       # Expected and observed values do not match:
       return (-1, -1, -1)
   # Return the combined numbers of *WSSes:
   return(lacount + lbcount, macount + mbcount, hacount + hbcount)


  1. Generates the helper rules for apgsearch, given a base outer-totalistic rule.

class RuleGenerator:

   def __init__(self):
       # Unless otherwise specified, assume standard B3/S23 rule:
       self.bee = [False, False, False, True, False, False, False, False, False]
       self.ess = [False, False, True, True, False, False, False, False, False]
       self.alphanumeric = "B3S23"
       self.slashed = "B3/S23"
   # Save all helper rules:
   def saveAllRules(self):
       self.saveClassifyObjects()
       self.saveCoalesceObjects()
       self.saveExpungeObjects()
       self.saveExpungeGliders()
       self.saveIdentifyGliders()
       self.saveHandlePlumes()
       self.savePercolateInfection()
       self.saveEradicateInfection()
       self.saveContagiousLife()
   # Set outer-totalistic rule:
   def setrule(self, rulestring):
       mode = 0
       s = [False]*9
       b = [False]*9
       for c in rulestring:
           if ((c == 's') | (c == 'S')):
               mode = 0
           if ((c == 'b') | (c == 'B')):
               mode = 1
           if (c == '/'):
               mode = 1 - mode
           if ((ord(c) >= 48) & (ord(c) <= 56)):
               d = ord(c) - 48
               if (mode == 0):
                   s[d] = True
               else:
                   b[d] = True
       prefix = "B"
       suffix = "S"
       for i in xrange(9):
           if (b[i]):
               prefix += str(i)
           if (s[i]):
               suffix += str(i)
       self.alphanumeric = prefix + suffix
       self.slashed = prefix + "/" + suffix
       self.bee = b
       self.ess = s
   # Save a rule file:
   def saverule(self, name, comments, table, colours):
       ruledir = g.getdir("rules")
       filename = ruledir + name + ".rule"
       results = "@RULE " + name + "\n\n"
       results += "*** File autogenerated by saverule. ***\n\n"
       results += comments
       results += "\n\n@TABLE\n\n"
       results += table
       results += "\n\n@COLORS\n\n"
       results += colours
       # Only create a rule file if it doesn't already exist; this avoids
       # concurrency issues when booting an instance of apgsearch whilst
       # one is already running.
       if not os.path.exists(filename):
           try:
               f = open(filename, 'w')
               f.write(results)
               f.close()
           except:
               g.warn("Unable to create rule table:\n" + filename)
   # Defines a variable:
   def newvar(self, name, vallist):
       line = "var "+name+"={"
       for i in xrange(len(vallist)):
           if (i > 0):
               line += ','
           line += str(vallist[i])
       line += "}\n"
       return line
   # Defines a block of equivalent variables:
   def newvars(self, namelist, vallist):
       block = ""
       for name in namelist:
           block += self.newvar(name, vallist)
       block += "\n"
       return block
   def scoline(self, chara, charb, left, right, amount):
       line = str(left) + ","
       for i in xrange(8):
           if (i < amount):
               line += chara
           else:
               line += charb
           line += chr(97 + i)
           line += ","
       line += str(right) + "\n"
       return line
   def saveHandlePlumes(self):
       comments = """

This post-processes the output of ClassifyObjects to remove any unwanted clustering of low-period objects appearing in puffer exhaust.

state 0: vacuum

state 7: ON, still-life state 8: OFF, still-life

state 9: ON, p2 oscillator state 10: OFF, p2 oscillator

state 11: ON, higher-period object state 12: OFF, higher-period object """

       table = """

n_states:17 neighborhood:Moore symmetries:permute

var da={0,2,4,6,8,10,12,14,16} var db={0,2,4,6,8,10,12,14,16} var dc={0,2,4,6,8,10,12,14,16} var dd={0,2,4,6,8,10,12,14,16} var de={0,2,4,6,8,10,12,14,16} var df={0,2,4,6,8,10,12,14,16} var dg={0,2,4,6,8,10,12,14,16} var dh={0,2,4,6,8,10,12,14,16}

var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var b={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var c={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var d={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var e={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var f={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var g={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var h={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}


8,da,db,dc,dd,de,df,dg,dh,0 10,da,db,dc,dd,de,df,dg,dh,0

9,a,b,c,d,e,f,g,h,1 10,a,b,c,d,e,f,g,h,2 """

       colours = """

1 255 255 255 2 127 127 127 7 0 0 255 8 0 0 127 9 255 0 0 10 127 0 0 11 0 255 0 12 0 127 0 """

       self.saverule("APG_HandlePlumesCorrected", comments, table, colours)
   def saveExpungeGliders(self):
       comments = """

This removes unwanted gliders. It is mandatory that one first runs the rules CoalesceObjects, IdentifyGliders and ClassifyObjects.

Run this for two generations, and observe the population counts after 1 and 2 generations. This will give the following data:

number of gliders = (p(1) - p(2))/5 """

       table = """

n_states:17 neighborhood:Moore symmetries:rotate4reflect

var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var b={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var c={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var d={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var e={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var f={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var g={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var h={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}

13,a,b,c,d,e,f,g,h,14 14,a,b,c,d,e,f,g,h,0 """

       colours = """

0 0 0 0 1 255 255 255 2 127 127 127 7 0 0 255 8 0 0 127 9 255 0 0 10 127 0 0 11 0 255 0 12 0 127 0 13 255 255 0 14 127 127 0 """

       self.saverule("APG_ExpungeGliders", comments, table, colours)
   def saveIdentifyGliders(self):
       comments = """

Run this after CoalesceObjects to find any gliders.

state 0: vacuum state 1: ON state 2: OFF """

       table = """

n_states:17 neighborhood:Moore symmetries:rotate4reflect

var a={0,2} var b={0,2} var c={0,2} var d={0,2} var e={0,2} var f={0,2} var g={0,2} var h={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var i={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var j={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var k={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var l={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var m={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var n={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var o={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var p={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} var q={3,4} var r={9,10} var s={11,12}

1,1,a,1,1,b,1,c,d,3 d,1,1,1,1,a,b,1,c,4

3,i,j,k,l,m,n,o,p,5 4,i,j,k,l,m,n,o,p,6

1,q,i,j,a,b,c,k,l,7 d,q,i,j,a,b,c,k,l,8 1,i,a,b,c,d,e,j,q,7 f,i,a,b,c,d,e,j,q,8

5,7,8,7,7,8,7,8,8,9 6,7,7,7,7,8,8,7,8,10 5,i,j,k,l,m,n,o,p,15 6,i,j,k,l,m,n,o,p,16 15,i,j,k,l,m,n,o,p,1 16,i,j,k,l,m,n,o,p,2

7,i,j,k,l,m,n,o,p,11 8,i,j,k,l,m,n,o,p,12

9,i,j,k,l,m,n,o,p,13 10,i,j,k,l,m,n,o,p,14 11,r,j,k,l,m,n,o,p,13 11,i,r,k,l,m,n,o,p,13 12,r,j,k,l,m,n,o,p,14 12,i,r,k,l,m,n,o,p,14

11,i,j,k,l,m,n,o,p,1 12,i,j,k,l,m,n,o,p,2 """

       colours = """

0 0 0 0 1 255 255 255 2 127 127 127 7 0 0 255 8 0 0 127 9 255 0 0 10 127 0 0 11 0 255 0 12 0 127 0 13 255 255 0 14 127 127 0 """

       self.saverule("APG_IdentifyGliders", comments, table, colours)
   def saveEradicateInfection(self):
       comments = """

To run after ContagiousLife to disinfect any cells in states 3 or 4.

state 0: vacuum state 1: ON state 2: OFF """

       table = """

n_states:7 neighborhood:Moore symmetries:permute

var a={0,1,2,3,4,5,6} var b={0,1,2,3,4,5,6} var c={0,1,2,3,4,5,6} var d={0,1,2,3,4,5,6} var e={0,1,2,3,4,5,6} var f={0,1,2,3,4,5,6} var g={0,1,2,3,4,5,6} var h={0,1,2,3,4,5,6} var i={0,1,2,3,4,5,6}

4,a,b,c,d,e,f,g,h,6 3,a,b,c,d,e,f,g,h,5 """

       colours = """

0 0 0 0 1 0 0 255 2 0 0 127 3 255 0 0 4 127 0 0 5 0 255 0 6 0 127 0 """

       self.saverule("APG_EradicateInfection", comments, table, colours)
   def savePercolateInfection(self):
       comments = """

Percolates any infection to all cells of that particular island.

state 0: vacuum state 1: ON state 2: OFF """

       table = """

n_states:7 neighborhood:Moore symmetries:permute

var a={0,1,2,3,4,5,6} var b={0,1,2,3,4,5,6} var c={0,1,2,3,4,5,6} var d={0,1,2,3,4,5,6} var e={0,1,2,3,4,5,6} var f={0,1,2,3,4,5,6} var g={0,1,2,3,4,5,6} var h={0,1,2,3,4,5,6} var i={0,1,2,3,4,5,6}

var q={3,4} var da={2,4,6} var la={1,3,5}

da,q,b,c,d,e,f,g,h,4 la,q,b,c,d,e,f,g,h,3 """

       colours = """

0 0 0 0 1 0 0 255 2 0 0 127 3 255 0 0 4 127 0 0 5 0 255 0 6 0 127 0 """

       self.saverule("APG_PercolateInfection", comments, table, colours)
       
   def saveExpungeObjects(self):
       comments = """

This removes unwanted monominos, blocks, blinkers and beehives. It is mandatory that one first runs the rule ClassifyObjects.

Run this for four generations, and observe the population counts after 0, 1, 2, 3 and 4 generations. This will give the following data:

number of monominos = p(1) - p(0) number of blocks = (p(2) - p(1))/4 number of blinkers = (p(3) - p(2))/5 number of beehives = (p(4) - p(3))/8 """

       table = "n_states:17\n"
       table += "neighborhood:Moore\n"
       table += "symmetries:rotate4reflect\n\n"
       table += self.newvars(["a","b","c","d","e","f","g","h","i"], range(0, 17, 1))
       table += """
  1. Monomino

7,0,0,0,0,0,0,0,0,0

  1. Death

6,a,b,c,d,e,f,g,h,0 a,6,b,c,d,e,f,g,h,0

  1. Block

7,7,7,7,0,0,0,0,0,1 1,1,1,1,0,0,0,0,0,0 1,a,b,c,d,e,f,g,h,7

  1. Blinker

10,0,0,0,9,9,9,0,0,2 9,9,10,0,0,0,0,0,10,3 2,a,b,c,d,e,f,g,h,10 3,a,b,c,d,e,f,g,h,9 9,2,0,3,0,2,0,3,0,6

  1. Beehive

7,0,7,8,7,0,0,0,0,1 7,0,0,7,8,8,7,0,0,1 8,7,7,8,7,7,0,7,0,4 4,1,1,4,1,1,0,1,0,5 4,a,b,c,d,e,f,g,h,8 5,5,b,c,d,e,f,g,h,6 5,a,b,c,d,e,f,g,h,15 15,a,b,c,d,e,f,g,h,8 """

       colours = """

0 0 0 0 1 255 255 255 2 127 127 127 7 0 0 255 8 0 0 127 9 255 0 0 10 127 0 0 11 0 255 0 12 0 127 0 13 255 255 0 14 127 127 0 """

       self.saverule("APG_ExpungeObjects", comments, table, colours)
   def saveCoalesceObjects(self):
       comments = """

A variant of HistoricalLife which separates a field of ash into distinct objects.

state 0: vacuum state 1: ON state 2: OFF """

       table = "n_states:3\n"
       table += "neighborhood:Moore\n"
       table += "symmetries:permute\n\n"
       table += self.newvars(["a","b","c","d","e","f","g","h","i"], [0, 1, 2])
       table += self.newvars(["da","db","dc","dd","de","df","dg","dh","di"], [0, 2])
       table += self.newvars(["la","lb","lc","ld","le","lf","lg","lh","li"], [1])
       minperc = 10
       for i in xrange(9):
           if (self.bee[i]):
               if (minperc == 10):
                   minperc = i
               table += self.scoline("l","d",0,1,i)
               table += self.scoline("l","d",2,1,i)
           if (self.ess[i]):
               table += self.scoline("l","d",1,1,i)
       table += "\n# Bridge inductors\n"
       for i in xrange(9):
           if (i >= minperc):
               table += self.scoline("l","d",0,2,i)
       table += self.scoline("","",1,2,0)
       colours = """

0 0 0 0 1 255 255 255 2 127 127 127 """

       self.saverule("APG_CoalesceObjects_"+self.alphanumeric, comments, table, colours)
   def saveClassifyObjects(self):
       comments = """

This passively classifies objects as either still-lifes, p2 oscillators or higher-period oscillators. It is mandatory that one first runs the rule CoalesceObjects.

state 0: vacuum state 1: input ON state 2: input OFF

state 3: ON, will die state 4: OFF, will remain off state 5: ON, will survive state 6: OFF, will become alive

state 7: ON, still-life state 8: OFF, still-life

state 9: ON, p2 oscillator state 10: OFF, p2 oscillator

state 11: ON, higher-period object state 12: OFF, higher-period object """

       table = "n_states:17\n"
       table += "neighborhood:Moore\n"
       table += "symmetries:permute\n\n"
       table += self.newvars(["a","b","c","d","e","f","g","h","i"], range(0, 17, 1))
       table += self.newvars(["la","lb","lc","ld","le","lf","lg","lh","li"], range(1, 17, 2))
       table += self.newvars(["da","db","dc","dd","de","df","dg","dh","di"], range(0, 17, 2))
       table += self.newvars(["pa","pb","pc","pd","pe","pf","pg","ph","pi"], [0, 3, 4])
       table += self.newvars(["qa","qb","qc","qd","qe","qf","qg","qh","qi"], [5, 6])
       for i in xrange(9):
           if (self.bee[i]):
               table += self.scoline("l","d",2,6,i)
               table += self.scoline("q","p",3,9,i)
               table += self.scoline("q","p",4,12,i)
           if (self.ess[i]):
               table += self.scoline("l","d",1,5,i)
               table += self.scoline("q","p",5,7,i)
               table += self.scoline("q","p",6,12,i)
       table += self.scoline("","",2,4,0)
       table += self.scoline("","",1,3,0)
       table += self.scoline("","",5,11,0)
       table += self.scoline("","",3,11,0)
       table += self.scoline("","",4,8,0)
       table += self.scoline("","",6,10,0)
       table += """
  1. Propagate interestingness

7,11,b,c,d,e,f,g,h,11 7,12,b,c,d,e,f,g,h,11 7,9,b,c,d,e,f,g,h,9 7,10,b,c,d,e,f,g,h,9 8,11,b,c,d,e,f,g,h,12 8,12,b,c,d,e,f,g,h,12 8,9,b,c,d,e,f,g,h,10 8,10,b,c,d,e,f,g,h,10

7,13,b,c,d,e,f,g,h,11 7,14,b,c,d,e,f,g,h,11 8,13,b,c,d,e,f,g,h,14 8,14,b,c,d,e,f,g,h,14 9,13,b,c,d,e,f,g,h,11 9,14,b,c,d,e,f,g,h,11 10,13,b,c,d,e,f,g,h,14 10,14,b,c,d,e,f,g,h,14

9,11,b,c,d,e,f,g,h,11 9,12,b,c,d,e,f,g,h,11 10,11,b,c,d,e,f,g,h,12 10,12,b,c,d,e,f,g,h,12

13,11,b,c,d,e,f,g,h,11 13,12,b,c,d,e,f,g,h,11 14,11,b,c,d,e,f,g,h,12 14,12,b,c,d,e,f,g,h,12 13,9,b,c,d,e,f,g,h,11 14,9,b,c,d,e,f,g,h,12 """

       colours = """

0 0 0 0 1 255 255 255 2 127 127 127 7 0 0 255 8 0 0 127 9 255 0 0 10 127 0 0 11 0 255 0 12 0 127 0 13 255 255 0 14 127 127 0 """

       self.saverule("APG_ClassifyObjects_"+self.alphanumeric, comments, table, colours)
   def saveContagiousLife(self):
       comments = """

A variant of HistoricalLife used for detecting dependencies between islands.

state 0: vacuum state 1: ON state 2: OFF """

       table = "n_states:7\n"
       table += "neighborhood:Moore\n"
       table += "symmetries:permute\n\n"
       table += self.newvars(["a","b","c","d","e","f","g","h","i"], range(0, 7, 1))
       table += self.newvars(["la","lb","lc","ld","le","lf","lg","lh","li"], range(1, 7, 2))
       table += self.newvars(["da","db","dc","dd","de","df","dg","dh","di"], range(0, 7, 2))
       table += self.newvar("p",[3, 4])
       table += self.newvars(["ta","tb","tc","td","te","tf","tg","th","ti"], [3])
       table += self.newvars(["qa","qb","qc","qd","qe","qf","qg","qh","qi"], [0, 1, 2, 4, 5, 6])
       for i in xrange(9):
           if (self.bee[i]):
               table += self.scoline("l","d",4,3,i)
               table += self.scoline("l","d",2,1,i)
               table += self.scoline("l","d",0,1,i)
               table += self.scoline("l","d",6,5,i)
               table += self.scoline("t","q",0,4,i)
           if (self.ess[i]):
               table += self.scoline("l","d",3,3,i)
               table += self.scoline("l","d",5,5,i)
               table += self.scoline("l","d",1,1,i)
       table += "# Default behaviour (death):\n"
       table += self.scoline("","",1,2,0)
       table += self.scoline("","",5,6,0)
       table += self.scoline("","",3,4,0)
       colours = """

0 0 0 0 1 0 0 255 2 0 0 127 3 255 0 0 4 127 0 0 5 0 255 0 6 0 127 0 """

       self.saverule("APG_ContagiousLife_"+self.alphanumeric, comments, table, colours)


class Soup:

   def __init__(self):
       # The rule generator:
       self.rg = RuleGenerator()
       # Should we skip error-correction:
       self.skipErrorCorrection = False
       # A dict mapping binary representations of small possibly-pseudo-objects
       # to their equivalent canonised representation.
       #
       # This is many-to-one, as (for example) all of these will map to
       # the same pseudo-object (namely the beacon on block):
       #
       # ..**.**  ..**.**  **.....                           **.....
       # ..**.**  ...*.**  **.....                           *......
       # **.....  *......  ..**...                           ...*.**
       # **.....  **.....  ..**... [...12 others omitted...] ..**.**
       # .......  .......  .......                           .......
       # .......  .......  ..**...                           .......
       # .......  .......  ..**...                           .......
       #
       # The first few soups are much slower to process, as objects are being
       # entered into the cache.
       self.cache = {}
       # A dict to store memoized decompositions of possibly-pseudo-objects
       # into constituent parts. This is initialised with the unique minimal
       # pseudo-still-life (two blocks on lock) that cannot be automatically
       # separated by the routine pseudo_bangbang(). Any larger objects are
       # ambiguous, such as this one:
       #
       #     *
       #    * * **
       #     ** **
       #
       #    * *** *
       #    ** * **
       #
       # Is it a (block on (lock on boat)) or ((block on lock) on boat)?
       # Ahh, the joys of non-associativity.
       #
       # See http://paradise.caltech.edu/~cook/Workshop/CAs/2DOutTot/Life/StillLife/StillLifeTheory.html
       self.decompositions = {"xs18_3pq3qp3": ["xs14_3123qp3", "xs4_33"]}
       # A dict of objects in the form {"identifier": ("common name", points)}
       #
       # As a rough heuristic, an object is worth 15 + log2(n) points if it
       # is n times rarer than the pentadecathlon.
       #
       # Still-lifes are limited to 10 points.
       # p2 oscillators are limited to 20 points.
       # p3 and p4 oscillators are limited to 30 points.
       self.commonnames = {"xp3_co9nas0san9oczgoldlo0oldlogz1047210127401": ("pulsar", 8),
                      "xp15_4r4z4r4": ("pentadecathlon", 15),
                      "xp2_2a54": ("clock", 16),
                      "xp2_31ago": ("bipole", 17),
                      "xp2_0g0k053z32": ("quadpole", 18),
                      "xp2_g8gid1e8z1226": ("great on-off", 19),
                      "xp2_rhewehr": ("spark coil", 19),
                      "xp8_gk2gb3z11": ("figure-8", 20),
                      "xp4_37bkic": ("mold", 21),
                      "xp2_31a08zy0123cko": ("quadpole on ship", 20),
                      "xp2_g0k053z11": ("tripole", 20),
                      "xp4_ssj3744zw3": ("mazing", 23),
                      "xp8_g3jgz1ut": ("blocker", 24),
                      "xp3_695qc8zx33": ("jam", 24),
                      "xp30_w33z8kqrqk8zzzw33": ("cis-queen-bee-shuttle", 24),
                      "xp30_w33z8kqrqk8zzzx33": ("trans-queen-bee-shuttle", 24),
                      "xp4_8eh5e0e5he8z178a707a871": ("cloverleaf", 25),
                      "xp5_idiidiz01w1": ("octagon II", 26),
                      "xp6_ccb7w66z066": ("unix", 26),
                      "xp14_j9d0d9j": ("tumbler", 27),
                      "xp3_025qzrq221": ("trans-tub-eater", 28),
                      "xp3_4hh186z07": ("caterer", 29),
                      "xp3_025qz32qq1": ("cis-tub-eater", 30),
                      "xp8_wgovnz234z33": ("Tim Coe's p8", 31),
                      "xp5_3pmwmp3zx11": ("fumarole", 33),
                      "xp46_330279cx1aad3y833zx4e93x855bc": ("cis-twin-bees-shuttle", 35),
                      "xp46_330279cx1aad3zx4e93x855bcy8cc": ("trans-twin-bees-shuttle", 35),
                      "yl144_1_16_afb5f3db909e60548f086e22ee3353ac": ("block-laying switch engine", 16),
                      "yl384_1_59_7aeb1999980c43b4945fb7fcdb023326": ("glider-producing switch engine", 17),
                      "xp10_9hr": ("[HighLife] p10", 6),
                      "xp7_13090c8": ("[HighLife] p7", 9),
                      "xq48_07z8ca7zy1e531": ("[HighLife] bomber", 9),
                      "xq4_153": ("glider", 0),
                      "xq4_6frc": ("lightweight spaceship", 7),
                      "xq4_27dee6": ("middleweight spaceship", 9),
                      "xq4_27deee6": ("heavyweight spaceship", 12),
                      "xq7_3nw17862z6952": ("loafer", 70),
                      "xp2_7": ("blinker", 0),
                      "xs4_33": ("block", 0),
                      "xs4_252": ("tub", 0),
                      "xs5_253": ("boat", 0),
                      "xs6_bd": ("snake", 0),
                      "xs6_356": ("ship", 0),
                      "xs6_696": ("beehive", 0),
                      "xs6_25a4": ("barge", 0),
                      "xs6_39c": ("carrier", 0),
                      "xp2_7e": ("toad", 0),
                      "xp2_318c": ("beacon", 0),
                      "xs7_3lo": ("long snake", 0),
                      "xs7_25ac": ("long boat", 0),
                      "xs7_178c": ("eater", 0),
                      "xs7_2596": ("loaf", 0),
                      "xs8_178k8": ("twit", 0),
                      "xs8_32qk": ("hook with tail", 0),
                      "xs8_69ic": ("mango", 0),
                      "xs8_6996": ("pond", 0),
                      "xs8_25ak8": ("long barge", 0),
                      "xs8_3pm": ("shillelagh", 0),
                      "xs8_312ko": ("canoe", 0),
                      "xs8_31248c": ("very long snake", 0),
                      "xs8_35ac": ("long ship", 0),
                      "xs12_g8o653z11": ("ship-tie", 0),
                      "xs14_g88m952z121": ("half-bakery", 0),
                      "xs14_69bqic": ("paperclip", 0),
                      "xs9_31ego": ("integral sign", 0),
                      "xs10_g8o652z01": ("boat-tie", 0),
                      "xs14_g88b96z123": ("big ess", 0),
                      "xs16_g88m996z1221": ("bipond", 0),
                      "xs12_raar": ("table on table", 0),
                      "xs9_4aar": ("hat", 0),
                      "xs10_35ako": ("very long ship", 0),
                      "xs9_178ko": ("trans boat with tail", 0),
                      "xs15_354cgc453": ("moose antlers", 0),
                      "xs14_6970796": ("cis-mirrored r-bee", 0),
                      "xs10_32qr": ("block on table", 0),
                      "xs16_j1u0696z11": ("beehive on dock", 0),
                      "xs14_j1u066z11": ("block on dock", 0),
                      "xs11_g8o652z11": ("boat tie ship", 0),
                      "xs9_25ako": ("very long boat", 0),
                      "xs16_69egmiczx1": ("scorpion", 0),
                      "xs18_rhe0ehr": ("dead spark coil", 0),
                      "xs17_2ege1ege2": ("twinhat", 0),
                      "xs10_178kk8": ("beehive with tail", 0),
                      "xs10_69ar": ("loop", 0),
                      "xs14_69bo8a6": ("fourteener", 0),
                      "xs14_39e0e93": ("bookends", 0),
                      "xs9_178kc": ("cis boat with tail", 0),
                      "xs12_330f96": ("block and cap", 0),
                      "xs10_358gkc": ("10.003",0),
                      "xs12_330fho": ("trans block and longhook", 0),
                      "xs10_g0s252z11": ("prodigal sign", 0),
                      "xs11_g0s453z11": ("elevener", 0),
                      "xs14_6is079c": ("cis-rotated hook", 0),
                      "xs14_69e0eic": ("trans-mirrored R-bee", 0),
                      "xs11_ggm952z1": ("trans loaf with tail", 0),
                      "xs15_j1u06a4z11": ("cis boat and dock", 0),
                      "xs20_3lkkl3z32w23": ("mirrored dock", 0),
                      "xs12_178br": ("12.003",0),
                      "xs12_3hu066": ("cis block and longhook", 0),
                      "xs12_178c453": ("eater with nine", 0),
                      "xs10_0drz32": ("broken snake", 0),
                      "xs9_312453": ("long shillelagh", 0),
                      "xs10_3215ac": ("boat with long tail", 0),
                      "xs14_39e0e96": ("cis-hook and R-bee", 0),
                      "xs13_g88m96z121": ("beehive at loaf", 0),
                      "xs14_39e0eic": ("trans hook and R-bee", 0),
                      "xs10_3542ac": ("S-ten", 0),
                      "xs15_259e0eic": ("trans R-bee and R-loaf", 0),
                      "xs11_178jd": ("11-loop", 0),
                      "xs9_25a84c": ("tub with long tail", 0),
                      "xs15_3lkm96z01": ("bee-hat", 0),
                      "xs14_g8o0e96z121": ("cis-rotated R-bee", 0),
                      "xs13_69e0mq": ("R-bee and snake", 0),
                      "xs11_69lic": ("11.003", 0),
                      "xs12_6960ui": ("beehive and table", 0),
                      "xs16_259e0e952": ("cis-mirrored R-loaf", 0),
                      "xs10_1784ko": ("8-snake-eater", 0),
                      "xs13_4a960ui": ("ortho loaf and table", 0),
                      "xs9_g0g853z11": ("long canoe", 0),
                      "xs18_69is0si96": ("[cis-mirrored R-mango]", 0),
                      "xs11_178kic": ("cis loaf with tail", 0),
                      "xs16_69bob96": ("symmetric scorpion", 0),
                      "xs13_0g8o653z121": ("longboat on ship", 0),
                      "xs12_o4q552z01": ("beehive at beehive", 0),
                      "xs10_ggka52z1": ("trans barge with tail", 0),
                      "xs12_256o8a6": ("eater on boat", 0),
                      "xs14_6960uic": ("beehive with cap", 0),
                      "xs12_2egm93": ("snorkel loop", 0),
                      "xs12_2egm96": ("beehive bend tail", 0),
                      "xs11_g0s253z11": ("trans boat with nine", 0),
                      "xs15_3lk453z121": ("trans boat and dock", 0),
                      "xs19_69icw8ozxdd11": ("[mango with block on dock]", 0),
                      "xs13_2530f96": ("[cis boat and cap]", 0),
                      "xs11_2530f9": ("cis boat and table", 0),
                      "xs14_4a9m88gzx121": ("[bi-loaf2]", 0),
                      "xs11_ggka53z1": ("trans longboat with tail", 0),
                      "xs18_2egm9a4zx346": ("[loaf eater tail]", 0),
                      "xs15_4a9raic": ("[15-bent-paperclip]", 0),
                      "xs11_3586246": ("[11-snake]",0),
                      "xs11_178b52": ("[11-boat wrap tail]", 0),
                      "xs14_08u1e8z321": ("[hat join hook]", 0),
                      "xs14_g4s079cz11": ("[cis-mirrored offset hooks]", 0),
                      "xs13_31egma4": ("[13-boat wrap eater]", 0),
                      "xs14_69960ui": ("pond and table", 0),
                      "xs13_255q8a6": ("[eater tie beehive]", 0),
                      "xs15_09v0ccz321": ("[hook join table and block]",0)}
       # First soup to contain a particular object:
       self.alloccur = {}
       # A tally of objects that have occurred during this run of apgsearch:
       self.objectcounts = {}
       # Any soups with positive scores, and the number of points.
       self.soupscores = {}
       # Temporary list of unidentified objects:
       self.unids = []
       # Things like glider guns and large oscillators belong here:
       self.superunids = []
       self.gridsize = 0
       self.resets = 0
       # For profiling purposes:
       self.qlifetime = 0.0
       self.ruletime = 0.0
       self.gridtime = 0.0
   # Increment object count by given value:
   def incobject(self, obj, incval):
       if (incval > 0):
           if obj in self.objectcounts:
               self.objectcounts[obj] = self.objectcounts[obj] + incval
           else:
               self.objectcounts[obj] = incval
   # Increment soup score by given value:
   def awardpoints(self, soupid, incval):
       if (incval > 0):
           if soupid in self.soupscores:
               self.soupscores[soupid] = self.soupscores[soupid] + incval
           else:
               self.soupscores[soupid] = incval
   # Increment soup score by appropriate value:
   def awardpoints2(self, soupid, obj):
       # Record the occurrence of this object:
       if (obj in self.alloccur):
           if (len(self.alloccur[obj]) < 10):
               if (soupid not in self.alloccur[obj]):
                   self.alloccur[obj] += [soupid]
       else:
           self.alloccur[obj] = [soupid]
       
       if obj in self.commonnames:
           self.awardpoints(soupid, self.commonnames[obj][1])
       elif (obj[0] == 'x'):
           prefix = obj.split('_')[0]
           prenum = int(prefix[2:])
           if (obj[1] == 's'):
               self.awardpoints(soupid, min(prenum, 20)) # for still-lifes, award one point per constituent cell (max 20)
           elif (obj[1] == 'p'):
               if (prenum == 2):
                   self.awardpoints(soupid, 20) # p2 oscillators are limited to 20 points
               elif ((prenum == 3) | (prenum == 4)):
                   self.awardpoints(soupid, 30) # p3 and p4 oscillators are limited to 30 points
               else:
                   self.awardpoints(soupid, 40)
           else:
               self.awardpoints(soupid, 50)
       else:
           self.awardpoints(soupid, 60)
   # Assuming the pattern has stabilised, perform a census:
   def census(self, stepsize, sym):
       g.setrule("APG_CoalesceObjects_" + self.rg.alphanumeric)
       g.setbase(2)
       g.setstep(stepsize)
       g.step()
       # apgsearch theoretically supports up to 2^14 rules, whereas the Guy
       # glider is only stable in 2^8 rules. Ensure that this is one of these
       # rules by doing some basic Boolean arithmetic.
       #
       # This should be parsed as `gliders exist', not `glider sexist':
       glidersexist = self.rg.ess[2] & self.rg.ess[3] & (not self.rg.ess[1]) & (not self.rg.ess[4])
       glidersexist = glidersexist & (not (self.rg.bee[4] | self.rg.bee[5]))
       if (glidersexist):
           g.setrule("APG_IdentifyGliders")
           g.setbase(2)
           g.setstep(2)
           g.step()
       g.setrule("APG_ClassifyObjects_" + self.rg.alphanumeric)
       g.setbase(2)
       g.setstep(max(8, stepsize))
       g.step()
       # Only do this if we have an infinite-growth pattern:
       if (stepsize > 8):
           g.setrule("APG_HandlePlumesCorrected")
           g.setbase(2)
           g.setstep(1)
           g.step()
           g.setrule("APG_ClassifyObjects_" + self.rg.alphanumeric)
           g.setstep(stepsize)
           g.step()
       # Remove any gliders:
       if (glidersexist):
           g.setrule("APG_ExpungeGliders")
           g.run(1)
           pop5 = int(g.getpop())
           g.run(1)
           pop6 = int(g.getpop())
           self.incobject("xq4_153", (pop5 - pop6)/5)
       # Remove any blocks, blinkers and beehives:
       g.setrule("APG_ExpungeObjects")
       pop0 = int(g.getpop())
       g.run(1)
       pop1 = int(g.getpop())
       g.run(1)
       pop2 = int(g.getpop())
       g.run(1)
       pop3 = int(g.getpop())
       g.run(1)
       pop4 = int(g.getpop())
       # Blocks, blinkers and beehives removed by ExpungeObjects:
       self.incobject("xs1_1", (pop0-pop1))
       self.incobject("xs4_33", (pop1-pop2)/4)
       self.incobject("xp2_7", (pop2-pop3)/5)
       self.incobject("xs6_696", (pop3-pop4)/8)
       if (sym == "BlockFloodTest"):
           #BLOCK FLOOD
           self.incobject("xs4_33", 1000000000000)
           #WHEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!!!
           #self.incobject('xs_<img src="http://78.media.tumblr.com/804c1989efca08511b971bbae21e6dce/tumblr_mm70s66Rur1s5qii0o1_400.gif" alt="Presented without comment, a serious look at the hero of the Maximum Ride series.">/b3s23',1)
   # Removes an object incident with (ix, iy) and returns the cell list:
   def grabobj(self, ix, iy):
       allcells = [ix, iy, g.getcell(ix, iy)]
       g.setcell(ix, iy, 0)
       livecells = []
       deadcells = []
       marker = 0
       ll = 3
       while (marker < ll):
           x = allcells[marker]
           y = allcells[marker+1]
           z = allcells[marker+2]
           marker += 3
           if ((z % 2) == 1):
               livecells.append(x)
               livecells.append(y)
           else:
               deadcells.append(x)
               deadcells.append(y)
           for nx in xrange(x - 1, x + 2):
               for ny in xrange(y - 1, y + 2):
                   nz = g.getcell(nx, ny)
                   if (nz > 0):
                       allcells.append(nx)
                       allcells.append(ny)
                       allcells.append(nz)
                       g.setcell(nx, ny, 0)
                       ll += 3
       return livecells
   # Command to Grab, Remove and IDentify an OBJect:
   def gridobj(self, ix, iy, gsize, gspacing, pos):
       allcells = [ix, iy, g.getcell(ix, iy)]
       g.setcell(ix, iy, 0)
       livecells = []
       deadcells = []
       # This tacitly assumes the object is smaller than 1000-by-1000.
       # But this is okay, since it is only used by the routing logic.
       dleft = ix + 1000
       dright = ix - 1000
       dtop = iy + 1000
       dbottom = iy - 1000
       lleft = ix + 1000
       lright = ix - 1000
       ltop = iy + 1000
       lbottom = iy - 1000
       lpop = 0
       dpop = 0
       marker = 0
       ll = 3
       while (marker < ll):
           x = allcells[marker]
           y = allcells[marker+1]
           z = allcells[marker+2]
           marker += 3
           if ((z % 2) == 1):
               livecells.append(x)
               livecells.append(y)
               lleft = min(lleft, x)
               lright = max(lright, x)
               ltop = min(ltop, y)
               lbottom = max(lbottom, y)
               lpop += 1
           else:
               deadcells.append(x)
               deadcells.append(y)
               dleft = min(dleft, x)
               dright = max(dright, x)
               dtop = min(dtop, y)
               dbottom = max(dbottom, y)
               dpop += 1
           for nx in xrange(x - 1, x + 2):
               for ny in xrange(y - 1, y + 2):
                   nz = g.getcell(nx, ny)
                   if (nz > 0):
                       allcells.append(nx)
                       allcells.append(ny)
                       allcells.append(nz)
                       g.setcell(nx, ny, 0)
                       ll += 3
       lwidth = max(0, 1 + lright - lleft)
       lheight = max(0, 1 + lbottom - ltop)
       dwidth = max(0, 1 + dright - dleft)
       dheight = max(0, 1 + dbottom - dtop)
       llength = max(lwidth, lheight)
       lbreadth = min(lwidth, lheight)
       dlength = max(dwidth, dheight)
       dbreadth = min(dwidth, dheight)
       self.gridsize = max(self.gridsize, llength)
       objid = "unidentified"
       bitstring = 0
       if (lpop == 0):
           objid = "nothing"
       else:
           if ((lwidth <= 7) & (lheight <= 7)):
               for i in xrange(0, lpop*2, 2):
                   bitstring += (1 << ((livecells[i] - lleft) + 7*(livecells[i + 1] - ltop)))
               if bitstring in self.cache:
                   objid = self.cache[bitstring]
       if (objid == "unidentified"):
           # This has passed through the routing logic without being identified,
           # so save it in a temporary list for later identification:
           self.unids.append(bitstring)
           self.unids.append(livecells)
           self.unids.append(lleft)
           self.unids.append(ltop)
       elif (objid != "nothing"):
           # The object is non-empty, so add it to the census:
           ux = int(0.5 + float(lleft)/float(gspacing))
           uy = int(0.5 + float(ltop)/float(gspacing))
           soupid = ux + (uy * gsize) + pos
           # Check whether the cached object is in the set of decompositions
           # (this is usually the case, unless for example it is a high-period
           # albeit small spaceship):
           if objid in self.decompositions:            
               for comp in self.decompositions[objid]:
                   self.incobject(comp, 1)
                   self.awardpoints2(soupid, comp)
           else:
               self.incobject(objid, 1)
               self.awardpoints2(soupid, objid)


   # Tests for population periodicity:
   def naivestab(self, period, security, length):
       depth = 0
       prevpop = 0
       for i in xrange(length):
           g.run(period)
           currpop = int(g.getpop())
           if (currpop == prevpop):
               depth += 1
           else:
               depth = 0
           prevpop = currpop
           if (depth == security):
               # Population is periodic.
               return True
       return False
   # This should catch most short-lived soups with few gliders produced:
   def naivestab2(self, period, length):
       for i in xrange(length):
           r = g.getrect()
           if (len(r) == 0):
               return True
           pop0 = int(g.getpop())
           g.run(period)
           hash1 = g.hash(r)
           pop1 = int(g.getpop())
           g.run(period)
           hash2 = g.hash(r)
           pop2 = int(g.getpop())
           if ((hash1 == hash2) & (pop0 == pop1) & (pop1 == pop2)):
               if (g.getrect() == r):
                   return True
               
               g.run((2*int(max(r[2], r[3])/period)+1)*period)
               hash3 = g.hash(r)
               pop3 = int(g.getpop())
               if ((hash2 == hash3) & (pop2 == pop3)):
                   return True
       return False
           
   # Runs a pattern until stabilisation with a 99.99996% success rate.
   # False positives are handled by a later error-correction stage.
   def stabilise3(self):
       # Phase I of stabilisation detection, designed to weed out patterns
       # that stabilise into a cluster of low-period oscillators within
       # about 6000 generations.
       if (self.naivestab2(12, 10)):
           return 4;
       if (self.naivestab(12, 30, 200)):
           return 4;
       if (self.naivestab(30, 30, 200)):
           return 5;
       # Phase II of stabilisation detection, which is much more rigorous
       # and based on oscar.py.
       # Should be sufficient:
       prect = [-2000, -2000, 4000, 4000]
       # initialize lists
       hashlist = []        # for pattern hash values
       genlist = []         # corresponding generation counts
       for j in xrange(4000):
           g.run(30)
           h = g.hash(prect)
           # determine where to insert h into hashlist
           pos = 0
           listlen = len(hashlist)
           while pos < listlen:
               if h > hashlist[pos]:
                   pos += 1
               elif h < hashlist[pos]:
                   # shorten lists and append info below
                   del hashlist[pos : listlen]
                   del genlist[pos : listlen]
                   break
               else:
                   period = (int(g.getgen()) - genlist[pos])
                   prevpop = g.getpop()
                   for i in xrange(20):
                       g.run(period)
                       currpop = g.getpop()
                       if (currpop != prevpop):
                           period = max(period, 4000)
                           break
                       prevpop = currpop
                       
                   return max(1 + int(math.log(period, 2)),3)
           hashlist.insert(pos, h)
           genlist.insert(pos, int(g.getgen()))
       g.setalgo("HashLife")
       g.setrule(self.rg.slashed)
       g.setbase(2)
       g.setstep(16)
       g.step()
       stepsize = 12
       g.setalgo("QuickLife")
       g.setrule(self.rg.slashed)
       return 12
   # Differs from oscar.py in that it detects absolute cycles, not eventual cycles.
   def bijoscar(self, maxsteps):
       initpop = int(g.getpop())
       initrect = g.getrect()
       if (len(initrect) == 0):
           return 0
       inithash = g.hash(initrect)
       for i in xrange(maxsteps):
           g.run(1)
           if (int(g.getpop()) == initpop):
               prect = g.getrect()
               phash = g.hash(prect)
               if (phash == inithash):
                   period = i + 1
                   if (prect == initrect):
                       return period
                   else:
                       return -period
       return -1
   # For a non-moving unidentified object, we check the dictionary of
   # memoized decompositions of possibly-pseudo-objects. If the object is
   # not already in the dictionary, it will be memoized.
   #
   # Low-period spaceships are also separated by this routine, although
   # this is less important now that there is a more bespoke prodecure
   # to handle disjoint unions of standard spaceships.
   #
   # @param moving  a bool which specifies whether the object is moving
   def enter_unid(self, unidname, soupid, moving):
       if not(unidname in self.decompositions):
           # Separate into pure components:
           if (moving):
               g.setrule("APG_CoalesceObjects_" + self.rg.alphanumeric)
               g.setbase(2)
               g.setstep(3)
               g.step()
           else:
               pseudo_bangbang(self.rg.alphanumeric)
           listoflists = [] # which incidentally don't contain themselves.
           # Someone who plays the celllo:
           celllist = g.join(g.getcells(g.getrect()), [0])
           for i in xrange(0, len(celllist)-1, 3):
               if (g.getcell(celllist[i], celllist[i+1]) != 0):
                   livecells = self.grabobj(celllist[i], celllist[i+1])
                   if (len(livecells) > 0):
                       listoflists.append(livecells)
           listofobjs = []
           for livecells in listoflists:
               g.new("Subcomponent")
               #####
               g.setalgo("HashLife")
               g.setrule(self.rg.slashed)
               g.putcells(livecells)
               period = self.bijoscar(1000)
               canonised = canonise(abs(period))
               if (period < 0):
                   listofobjs.append("xq"+str(0-period)+"_"+canonised)
               elif (period == 1):
                   listofobjs.append("xs"+str(len(livecells)/2)+"_"+canonised)
               else:
                   listofobjs.append("xp"+str(period)+"_"+canonised)
           self.decompositions[unidname] = listofobjs
       # Actually add to the census:
       for comp in self.decompositions[unidname]:
           self.incobject(comp, 1)
           self.awardpoints2(soupid, comp)
   # This function has lots of arguments (hence the name):
   #
   # @param gsize     the square-root of the number of soups per page
   # @param gspacing  the minimum distance between centres of soups
   # @param ashes     a list of cell lists
   # @param stepsize  binary logarithm of amount of time to coalesce objects
   # @param intergen  binary logarithm of amount of time to run HashLife
   # @param pos       the index of the first soup on the page
   # @param sym       the symmetry of the soup
   def teenager(self, gsize, gspacing, ashes, stepsize, intergen, pos, sym):
       # For error-correction:
       if (intergen > 0):
           g.setalgo("HashLife")
           g.setrule(self.rg.slashed)
       # If this gets incremented, we panic and perform error-correction:
       pathological = 0
       # Draw the soups:
       for i in xrange(gsize * gsize):
           x = int(i % gsize)
           y = int(i / gsize)
           g.putcells(ashes[3*i], gspacing * x, gspacing * y)
       # Because why not?
       g.fit()
       g.update()
       # For error-correction:
       if (intergen > 0):
           g.setbase(2)
           g.setstep(intergen)
           g.step()
       # Apply rules to coalesce objects and expunge annoyances such as
       # blocks, blinkers, beehives and gliders:
       start_time = time.clock()
       self.census(stepsize, sym)
       end_time = time.clock()
       self.ruletime += (end_time - start_time)


       # Now begin identifying objects:
       start_time = time.clock()
       celllist = g.join(g.getcells(g.getrect()), [0])
       if (len(celllist) > 2):
           for i in xrange(0, len(celllist)-1, 3):
               if (g.getcell(celllist[i], celllist[i+1]) != 0):
                   self.gridobj(celllist[i], celllist[i+1], gsize, gspacing, pos)
       # If we have leftover unidentified objects, attempt to canonise them:
       while (len(self.unids) > 0):
           ux = int(0.5 + float(self.unids[-2])/float(gspacing))
           uy = int(0.5 + float(self.unids[-1])/float(gspacing))
           soupid = ux + (uy * gsize) + pos
           unidname = self.process_unid()
           if (unidname == "PATHOLOGICAL"):
               pathological += 1
           if (unidname != "nothing"):
               if ((unidname[0] == 'U') & (unidname[1] == 'S') & (unidname[2] == 'S')):
                   
                   # Union of standard spaceships:
                   countlist = unidname.split('_')
                   
                   self.incobject("xq4_6frc", int(countlist[1]))
                   for i in xrange(int(countlist[1])):
                       self.awardpoints2(soupid, "xq4_6frc")
                   self.incobject("xq4_27dee6", int(countlist[2]))
                   for i in xrange(int(countlist[2])):
                       self.awardpoints2(soupid, "xq4_27dee6")
                       
                   self.incobject("xq4_27deee6", int(countlist[3]))
                   for i in xrange(int(countlist[3])):
                       self.awardpoints2(soupid, "xq4_27deee6")
                       
               elif ((unidname[0] == 'x') & ((unidname[1] == 's') | (unidname[1] == 'p'))):
                   self.enter_unid(unidname, soupid, False)
               else:
                   if ((unidname[0] == 'x') & (unidname[1] == 'q') & (unidname[3] == '_')):
                       # Separates low-period (<= 9) non-standard spaceships in medium proximity:
                       self.enter_unid(unidname, soupid, True)
                   else:
                       self.incobject(unidname, 1)
                       self.awardpoints2(soupid, unidname)
       end_time = time.clock()
       self.gridtime += (end_time - start_time)
       return pathological
   def stabilise_soups_parallel(self, root, pos, gsize, sym):
       souplist = [[sym, root + str(pos + i)] for i in xrange(gsize * gsize)]
       return self.stabilise_soups_parallel_orig(gsize, souplist, pos)
   def stabilise_soups_parallel_list(self, gsize, stringlist, pos):
       souplist = [s.split('/') for s in stringlist]
       return self.stabilise_soups_parallel_orig(gsize, souplist, pos)
   # This basically orchestrates everything:
   def stabilise_soups_parallel_orig(self, gsize, souplist, pos):
       ashes = []
       stepsize = 3
       g.new("Random soups")
       #####
       g.setalgo("QuickLife")
       g.setrule(self.rg.slashed)
       gspacing = 0
       # Generate and run the soups until stabilisation:
       for i in xrange(gsize * gsize):
           if (i < len(souplist)):
               sym = souplist[i][0]
               prehash = souplist[i][1]
               # Generate the soup from the SHA-256 of the concatenation of the
               # seed with the index:
               g.putcells(hashsoup(prehash, sym), 0, 0)
           # Run the soup until stabilisation:
           start_time = time.clock()
           stepsize = max(stepsize, self.stabilise3())
           end_time = time.clock()
           self.qlifetime += (end_time - start_time)
           # Ironically, the spelling of this variable is incurrrect:
           currrect = g.getrect()
           ashes.append(g.getcells(currrect))
           if (len(currrect) == 4):
               ashes.append(currrect[0])
               ashes.append(currrect[1])
               # Choose the grid spacing based on the size of the ash:
               gspacing = max(gspacing, 2*currrect[2])
               gspacing = max(gspacing, 2*currrect[3])
               g.select(currrect)
               g.clear(0)
           else:
               ashes.append(0)
               ashes.append(0)
           g.select([])
       # Account for any extra enlargement caused by running CoalesceObjects:
       gspacing += 2 ** (stepsize + 1) + 1000
       start_time = time.clock()
       # Remember the dictionary, just in case we have a pathological object:
       prevdict = self.objectcounts.copy()
       prevscores = self.soupscores.copy()
       prevunids = self.superunids[:]
       # Process the soups:
       returncode = self.teenager(gsize, gspacing, ashes, stepsize, 0, pos, sym)
       end_time = time.clock()
       # Calculate the mean delay incurred (excluding qlifetime or error-correction):
       meandelay = (end_time - start_time) / (gsize * gsize)
       if (returncode > 0):
           if (self.skipErrorCorrection == False):
               # Arrrggghhhh, there's a pathological object! Usually this means
               # that naive stabilisation detection returned a false positive.
               self.resets += 1
               
               # Reset the object counts:
               self.objectcounts = prevdict
               self.soupscores = prevscores
               self.superunids = prevunids
               # 2^18 generations should suffice. This takes about 30 seconds in
               # HashLife, but error-correction only occurs very infrequently, so
               # this has a negligible impact on mean performance:
               gspacing += 2 ** 19
               stepsize = max(stepsize, 12)
               
               # Clear the universe:
               g.new("Error-correcting phase")
               self.teenager(gsize, gspacing, ashes, stepsize, 18, pos, sym)
       # Erase any ashes. Not least because England usually loses...
       ashes = []
       # Return the mean delay so that we can use machine-learning to
       # find the optimal value of sqrtspp:
       return meandelay
   def reset(self):
       self.objectcounts = {}
       self.soupscores = {}
       self.alloccur = {}
       self.superunids = []
       self.unids = []
   # Pop the last unidentified object from the stack, and attempt to
   # ascertain its period and classify it.
   def process_unid(self):
       g.new("Unidentified object")
       g.setalgo("QuickLife")
       g.setrule(self.rg.slashed)
       y = self.unids.pop()
       x = self.unids.pop()
       livecells = self.unids.pop()
       bitstring = self.unids.pop()
       g.putcells(livecells, -x, -y, 1, 0, 0, 1, "or")
       period = self.bijoscar(1000)
       
       if (period == -1):
           # Infinite growth pattern, probably. Most infinite-growth
           # patterns are linear-growth (such as puffers, wickstretchers,
           # guns etc.) so we analyse to see whether we have a linear-
           # growth pattern:
           descriptor = linearlyse(1500)
           if (descriptor[0] == "y"):
               return descriptor
           # Similarly check for irregular power-law growth. This will
           # catch replicators, for instance. Spend around 375 000
           # generations; this seems like a reasonable amount of time.
           descriptor = powerlyse(8, 1500)
           if (descriptor[0] == "z"):
               return descriptor
           # It may be an unstabilised ember that slipped through the net,
           # but this will be handled by error-correction (unless it
           # persists another 2^18 gens, which is so unbelievably improbable
           # that you are more likely to be picked up by a passing ship in
           # the vacuum of space).
           self.superunids.append(livecells)
           self.superunids.append(x)
           self.superunids.append(y)
           
           return "PATHOLOGICAL"
       elif (period == 0):
           return "nothing"
       else:
           if (period == -4):
               triple = countxwsses()
               if (triple != (-1, -1, -1)):
                   # Union of Standard Spaceships:
                   return ("USS_" + str(triple[0]) + "_" + str(triple[1]) + "_" + str(triple[2]))


           canonised = canonise(abs(period))
           if (canonised == "#"):
               # Okay, we know that it's an oscillator or spaceship with
               # a non-astronomical period. But it's too large to canonise
               # in any of its phases (i.e. transcends a 40-by-40 box).
               self.superunids.append(livecells)
               self.superunids.append(x)
               self.superunids.append(y)
               
               # Append a suffix according to whether it is a still-life,
               # oscillator or moving object:
               if (period == 1):
                   descriptor = ("ov_s"+str(len(livecells)/2))
               elif (period > 0):
                   descriptor = ("ov_p"+str(period))
               else:
                   descriptor = ("ov_q"+str(0-period))
               return descriptor
           
           else:
               # Prepend a prefix according to whether it is a still-life,
               # oscillator or moving object:
               if (period == 1):
                   descriptor = ("xs"+str(len(livecells)/2)+"_"+canonised)
               elif (period > 0):
                   descriptor = ("xp"+str(period)+"_"+canonised)
               else:
                   descriptor = ("xq"+str(0-period)+"_"+canonised)
               if (bitstring > 0):
                   self.cache[bitstring] = descriptor
               return descriptor
   # This doesn't really do much, since unids should be empty and
   # actual pathological/oversized objects will rarely arise naturally.
   def display_unids(self):
       g.new("Unidentified objects")
       g.setalgo("QuickLife")
       g.setrule(self.rg.slashed)
       rowlength = 1 + int(math.sqrt(len(self.superunids)/3))
       for i in xrange(len(self.superunids)/3):
           xpos = i % rowlength
           ypos = int(i / rowlength)
           g.putcells(self.superunids[3*i], xpos * (self.gridsize + 8) - self.superunids[3*i + 1], ypos * (self.gridsize + 8) - self.superunids[3*i + 2], 1, 0, 0, 1, "or")
       g.fit()
       g.update()
   def compactify_scores(self):
       # Number of soups to record:
       highscores = 100
       ilist = sorted(self.soupscores.iteritems(), key=operator.itemgetter(1), reverse=True)
       # Empty the high score table:
       self.soupscores = {}
       
       for soupnum, score in ilist[:highscores]:
           self.soupscores[soupnum] = score
   # Saves a machine-readable textual file containing the census:
   def save_progress(self, numsoups, root, symmetry='C1', save_file=True, payosha256_key=None):
       g.show("Saving progress...")
       # Count the total number of objects:
       totobjs = 0
       censustable = "@CENSUS TABLE\n"
       tlist = sorted(self.objectcounts.iteritems(), key=operator.itemgetter(1), reverse=True)
       for objname, count in tlist:
           totobjs += count
           censustable += objname + " " + str(count) + "\n"
       g.show("Writing header information...")
       # The MD5 hash of the root string:
       md5root = hashlib.md5(root).hexdigest()
       # Header information:
       results = "@VERSION v1.1\n"
       results += "@MD5 "+md5root+"\n"
       results += "@ROOT "+root+"\n"
       results += "@RULE "+self.rg.alphanumeric+"\n"
       results += "@SYMMETRY "+symmetry+"\n"
       results += "@NUM_SOUPS "+str(numsoups)+"\n"
       results += "@NUM_OBJECTS "+str(totobjs)+"\n"
       results += "\n"
       # Census table:
       results += censustable
       g.show("Compactifying score table...")
       results += "\n"
       # Number of soups to record:
       highscores = 100
       results += "@TOP "+str(highscores)+"\n"
       ilist = sorted(self.soupscores.iteritems(), key=operator.itemgetter(1), reverse=True)
       # Empty the high score table:
       self.soupscores = {}
       
       for soupnum, score in ilist[:highscores]:
           self.soupscores[soupnum] = score
           results += str(soupnum) + " " + str(score) + "\n"
       g.show("Saving soupids for rare objects...")
       results += "\n@SAMPLE_SOUPIDS\n"
       for objname, count in tlist:
           # blinkers and gliders have no alloccur[] entry for some reason,
           # so the line below avoids errors in B3/S23, maybe other rules too?
           if objname in self.alloccur:
               results += objname
               for soup in self.alloccur[objname]:
                   results += " " + str(soup)
               results += "\n"
       g.show("Writing progress file...")
       dirname = g.getdir("data")
       separator = dirname[-1]
       progresspath = dirname + "apgsearch" + separator + "progress" + separator
       if not os.path.exists(progresspath):
           os.makedirs(progresspath)
       filename = progresspath + "search_" + md5root + ".txt"
       
       try:
           f = open(filename, 'w')
           f.write(results)
           f.close()
       except:
           g.warn("Unable to create progress file:\n" + filename)
       if payosha256_key is not None:
           if (len(payosha256_key) > 0):
               return catagolue_results(results, payosha256_key, "post_apgsearch_haul")
   # Save soup RLE:
   def save_soup(self, root, soupnum, symmetry):
       # Soup pattern will be stored in a temporary directory:
       souphash = hashlib.sha256(root + str(soupnum))
       rlepath = souphash.hexdigest()
       rlepath = g.getdir("temp") + rlepath + ".rle"
       
       results = "<a href=\"open:" + rlepath + "\">"
       results += str(soupnum)
       results += "</a>"
       # Try to write soup patterns to file "rlepath":
       try:
           g.store(hashsoup(root + str(soupnum), symmetry), rlepath)
       except:
           g.warn("Unable to create soup pattern:\n" + rlepath)
       return results
       
   # Display results in Help window:
   def display_census(self, numsoups, root, symmetry):
       dirname = g.getdir("data")
       separator = dirname[-1]
       apgpath = dirname + "apgsearch" + separator
       objectspath = apgpath + "objects" + separator + self.rg.alphanumeric + separator
       if not os.path.exists(objectspath):
           os.makedirs(objectspath)
       results = "<html>\n<title>Census results</title>\n<body bgcolor=\"#FFFFCE\">\n"
       results += "<p>Census results after processing " + str(numsoups) + " soups (seed = " + root + ", symmetry = " + symmetry + "):\n"
       tlist = sorted(self.objectcounts.iteritems(), key=operator.itemgetter(1), reverse=True)    
       results += "<p><center>\n"
       results += "<table cellspacing=1 border=2 cols=2>\n"
       results += "<tr><td>&nbsp;Object&nbsp;</td><td align=center>&nbsp;Common name&nbsp;</td>\n"
       results += "<td align=right>&nbsp;Count&nbsp;</td><td>&nbsp;Sample occurrences&nbsp;</td></tr>\n"
       for objname, count in tlist:
           if (objname[0] == 'x'):
               if (objname[1] == 'p'):
                   results += "<tr bgcolor=\"#CECECF\">"
               elif (objname[1] == 'q'):
                   results += "<tr bgcolor=\"#CEFFCE\">"
               else:
                   results += "<tr>"
           else:
               results += "<tr bgcolor=\"#FFCECE\">"
           results += "<td>"
           results += "&nbsp;"
           
           # Using "open:" link enables one to click on the object name to open the pattern in Golly:
           rlepath = objectspath + objname + ".rle"
           if (objname[0] == 'x'):
               results += "<a href=\"open:" + rlepath + "\">"
           # If the name is longer than that of the block-laying switch engine:
           if len(objname) > 51:
               # Contract name and include ellipsis:
               results += objname[:40] + "&#8230;" + objname[-10:]
           else:
               results += objname
           if (objname[0] == 'x'):
               results += "</a>"
           results += "&nbsp;"
           if (objname[0] == 'x'):
               # save object in rlepath if it doesn't exist
               if not os.path.exists(rlepath):
                   # Canonised objects are at most 40-by-40:
                   rledata = "x = 40, y = 40, rule = " + self.rg.slashed + "\n"
                   # http://ferkeltongs.livejournal.com/15837.html
                   compact = objname.split('_')[1] + "z"
                   i = 0
                   strip = []
                   while (i < len(compact)):
                       c = ord2(compact[i])
                       if (c >= 0):
                           if (c < 32):
                               # Conventional character:
                               strip.append(c)
                           else:
                               if (c == 35):
                                   # End of line:
                                   if (len(strip) == 0):
                                       strip.append(0)
                                   for j in xrange(5):
                                       for d in strip:
                                           if ((d & (1 << j)) > 0):
                                               rledata += "o"
                                           else:
                                               rledata += "b"
                                       rledata += "$\n"
                                   strip = []
                               else:
                                   # Multispace character:
                                   strip.append(0)
                                   strip.append(0)
                                   if (c >= 33):
                                       strip.append(0)
                                   if (c == 34):
                                       strip.append(0)
                                       i += 1
                                       d = ord2(compact[i])
                                       for j in xrange(d):
                                           strip.append(0)
                       i += 1
                   # End of pattern representation:
                   rledata += "!\n"
                   try:
                       f = open(rlepath, 'w')
                       f.write(rledata)
                       f.close()
                   except:
                       g.warn("Unable to create object pattern:\n" + rlepath)
           
           results += "</td><td align=center>&nbsp;"
           if (objname in self.commonnames):
               results += self.commonnames[objname][0]
           results += "&nbsp;</td><td align=right>&nbsp;" + str(count) + "&nbsp;"
           results += "</td><td>"
           if objname in self.alloccur:
               results += "&nbsp;"
               for soup in self.alloccur[objname]:
                   results += self.save_soup(root, soup, symmetry) 
                   results += "&nbsp;"
           results += "</td></tr>\n"
       results += "</table>\n</center>\n"
       ilist = sorted(self.soupscores.iteritems(), key=operator.itemgetter(1), reverse=True)
       results += "<p><center>\n"
       results += "<table cellspacing=1 border=2 cols=2>\n"
       results += "<tr><td>&nbsp;Soup number&nbsp;</td><td align=right>&nbsp;Score&nbsp;</td></tr>\n"
       for soupnum, score in ilist[:50]:
           results += "<tr><td>&nbsp;"
           results += self.save_soup(root, soupnum, symmetry)
           results += "&nbsp;</td><td align=right>&nbsp;" + str(score) + "&nbsp;</td></tr>\n"
       
       results += "</table>\n</center>\n"
       results += "</body>\n</html>\n"
       
       htmlname = apgpath + "latest_census.html"
       try:
           f = open(htmlname, 'w')
           f.write(results)
           f.close()
           g.open(htmlname)
       except:
           g.warn("Unable to create html file:\n" + htmlname)
       
  1. Converts a base-36 case-insensitive alphanumeric character into a
  2. numerical value.

def ord2(char):

   x = ord(char)
   if ((x >= 48) & (x < 58)):
       return x - 48
   if ((x >= 65) & (x < 91)):
       return x - 55
   if ((x >= 97) & (x < 123)):
       return x - 87
   return -1


def apg_verify(rulestring, symmetry, payoshakey):

   verifysoup = Soup()
   verifysoup.rg.setrule(rulestring)
   verifysoup.rg.saveAllRules()
   return_point = [None]
   catagolue_results(rulestring+"\n"+symmetry+"\n", payoshakey, "verify_apgsearch_haul", endpoint="/verify", return_point=return_point)
   if return_point[0] is not None:
       resplist = return_point[0].split("\n")
       if ((len(resplist) >= 4) and (resplist[1] == "yes")):
           md5 = resplist[2]
           passcode = resplist[3]
           stringlist = resplist[4:]
           stringlist = [s for s in stringlist if (len(s) > 0 and s[0] != '*')]
           # g.exit(stringlist[0])
           gsize = 3
           pos = 0
           while (len(stringlist) > 0):
               while (gsize * gsize > len(stringlist)):
                   gsize -= 1
               listhead = stringlist[:(gsize*gsize)]
               stringlist = stringlist[(gsize*gsize):]
               verifysoup.stabilise_soups_parallel_list(gsize, listhead, pos)
               pos += (gsize * gsize)
           # verifysoup.display_census(-1, "verify", "verify")
           payload = "@MD5 "+md5+"\n"
           payload += "@PASSCODE "+passcode+"\n"
           payload += "@RULE "+rulestring+"\n"
           payload += "@SYMMETRY "+symmetry+"\n"
           tlist = sorted(verifysoup.objectcounts.iteritems(), key=operator.itemgetter(1), reverse=True)
           for objname, count in tlist:
               payload += objname + " " + str(count) + "\n"
           catagolue_results(payload, payoshakey, "submit_verification", endpoint="/verify")


def apg_main():

   # ---------------- Hardcode the following inputs if running without a user interface ----------------
   orignumber = int(g.getstring("How many soups to search between successive uploads?", "5000000"))
   rulestring = g.getstring("Which rule to use?", "B3/S23")
   symmstring = g.getstring("What symmetries to use?", "C1")
   payoshakey = g.getstring("Please enter your key (visit "+get_server_address()+"/payosha256 in your browser).", "#anon")
   # ---------------------------------------------------------------------------------------------------
   # Sanitise input:
   #orignumber = max(orignumber, 100000)
   #orignumber = min(orignumber, 100000000)
   number = orignumber
   initpos = 0
   if symmstring not in ["UnbanMajestas32","BlockFloodTest", "wwei23BLOCKPARTYTEST","75p", "25p", "1X2x256X2", "1x256X2+1", "1x256X2", "32x32", "1x256", "2x128", "4x64", "8x32", "C1", "C2_1", "C2_2", "C2_4", "C4_1", "C4_4", "D2_+1", "D2_+2", "D2_x", "D4_+1", "D4_+2", "D4_+4", "D4_x1", "D4_x4", "D8_1", "D8_4"]:
       g.exit(symmstring+" is not a valid symmetry option")
   quitapg = False
   # Create associated rule tables:
   soup = Soup()
   soup.rg.setrule(rulestring)
   soup.rg.saveAllRules()
   # We have 100 soups per page, instead of one. This parallel approach
   # was suggested by Tomas Rokicki, and results in approximately a
   # fourfold increase in soup-searching speed!
   sqrtspp_optimal = 10
   # Initialise the census:
   start_time = time.clock()
   f = (lambda x : 'abcdefghijkmnpqrstuvwxyzABCDEFGHJKLMNPQRSTUVWXYZ23456789'[ord(x) % 56])
   rootstring = .join(map(f, list(hashlib.sha256(payoshakey + datetime.datetime.now().isoformat()).digest()[:12])))
   scount = 0
   while (quitapg == False):
       # Peer-review some soups:
       #for i in xrange(5):
           #apg_verify("b3s23", "C1", payoshakey)
       # The 'for' loop has been replaced with a 'while' loop to allow sqrtspp
       # to vary during runtime. The idea is that apgsearch can apply a basic
       # form of machine-learning to dynamically locate the optimum sqrtspp:
       while (scount < number):
           delays = [0.0, 0.0, 0.0]
           for i in xrange(1000):
               page_time = time.clock()
               sqrtspp = (sqrtspp_optimal + (i % 3) - 1) if (i < 150) else (sqrtspp_optimal)
               # Don't overrun:
               while (scount + sqrtspp * sqrtspp > number):
                   sqrtspp -= 1
               meandelay = soup.stabilise_soups_parallel(rootstring, scount + initpos, sqrtspp, symmstring)
               if (i < 150):
                   delays[i % 3] += meandelay
               scount += (sqrtspp * sqrtspp)
               current_speed = int((sqrtspp * sqrtspp)/(time.clock() - page_time))
               alltime_speed = int((scount)/(time.clock() - start_time))
               
               g.show(str(scount) + " soups processed (" + str(current_speed) +
                      " per second current; " + str(alltime_speed) + " overall)" +
                      " : (type 's' to see latest census or 'q' to quit).")
               
               event = g.getevent()
               if event.startswith("key"):
                   evt, ch, mods = event.split()
                   if ch == "s":
                       soup.save_progress(scount, rootstring, symmstring)
                       soup.display_census(scount, rootstring, symmstring)
                   elif ch == "q":
                       quitapg = True
                       break
               if (scount >= number):
                   break
               
           if (quitapg == True):
               break
           # Change sqrtspp to a more optimal value:
           if (scount < number):
               sqrtspp_new = sqrtspp_optimal
               if (delays[0] < delays[1]):
                   sqrtspp_new = sqrtspp_optimal - 1
               if ((delays[2] < delays[1]) and (delays[2] < delays[0])):
                   sqrtspp_new = sqrtspp_optimal + 1
               sqrtspp_optimal = sqrtspp_new
               sqrtspp_optimal = max(sqrtspp_optimal, 5)
           # Compactify highscore table:
           soup.compactify_scores()
       if (quitapg == False):
           # Save progress, upload it to Catagolue, and reset the census if successful:
           a = soup.save_progress(scount, rootstring, symmstring, payosha256_key=payoshakey)
           if (a == 0):
               # Reset the census:
               soup.reset()
               start_time = time.clock()
               f = (lambda x : 'abcdefghijkmnpqrstuvwxyzABCDEFGHJKLMNPQRSTUVWXYZ23456789'[ord(x) % 56])
               rootstring = .join(map(f, list(hashlib.sha256(rootstring + payoshakey + datetime.datetime.now().isoformat()).digest()[:12])))
               scount = 0
               number = orignumber
           else:
               number += orignumber
   end_time = time.clock()
   soup.save_progress(scount, rootstring, symmstring, payosha256_key=payoshakey)
   soup.display_unids()
   soup.display_census(scount, rootstring, symmstring)

def symmetry_test():

   g.new("Symmetry test")
   symmetries = [["1X2x256X2", "1x256X2+1", "1x256X2", "32x32", "C1", "8x32", "4x64", "2x128", "1x256", "25p", "75p", "wwei23BLOCKPARTYTEST", "BlockFloodTest", "UnbanMajestas32"],
                 ["C2_1", "C2_2", "C2_4"],
                 ["C4_1", "C4_4"],
                 ["D2_+1", "D2_+2", "D2_x"],
                 ["D4_+1", "D4_+2", "D4_+4", "D4_x1", "D4_x4"],
                 ["D8_1", "D8_4"]]
   for i in range(len(symmetries)):
       for j in range(len(symmetries[i])):
           g.putcells(hashsoup("sym_test", symmetries[i][j]), 120 * j + 60 * (i % 2), 80 * i)
   g.fit()
  1. Run the soup-searching script:

apg_main()

  1. apg_verify()