ConwayLife.com • Gems?

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Gems?

Posted: March 2nd, 2017, 4:57 pm

by 83bismuth38

So I'm new here, and I'm telling you this because idk if this is already a thing and am too lazy to find out. so with that out of the way, Ima explain what gems are. Gems are still lifes made of 4 still lifes put together, but they are all the same still lifes, i.e. 4 hives connected like with bee on bee, or 4 mangoes connected by the ends. I've only found the bee gem, the loaf gem, the mango gem, and the pond gem. I tried integral signs, but it collapses, blocks just don't work, tubs, boats and barges (I hope I got that right lol) die from the inside out, aircraft carriers don't work, and niether do paperclips. tell me whut u think!

Re: Gems?

Posted: March 2nd, 2017, 5:22 pm

by biggiemac

Just trying to make sure I follow:

Here are 4 patterns, each with a piece above it. If I understand you right, the left two are gems because a single still life can be connected to itself 4 times making a bigger still life. In the 3rd, the base still lives aren't connected by live cells, just overcrowded dead cells, so they aren't properly "connected." In the 4th, the base still life needs to overlap with other copies of itself to produce the pattern. That means the 3rd and 4th are not gems. Is this consistent with how you are defining it?

Code: Select all

x = 90, y = 27, rule = B3/S23
34bo$6bo26bobo45bo$5bobo24bobobo23b2o18bobo$5bobo24bo3bo23bobo16bobo$
4b2ob2o22b2o3b2o25bo15bo2b3o$64bo13b2o4bo$63b2o4$34bo$6bo26bobo46bo$5b
obo24bobobo20b2ob2o19bobo$5bobo24bo3bo19bobobobo17bobo$4b2ob2o22b2o3b
2o17bo7bo16bo2b3o$3bo5bo20bo7bo15bo9bo14b2o4b3o$b3o5b3o16b3o7b3o13b2o
7b2o14bo8bo$o11bo14bo13bo35bobo7bobo$b3o5b3o14bobo11bobo11b2o7b2o11bob
o7bobo$3bo5bo17bo13bo12bo9bo12bo8bo$4b2ob2o19b3o7b3o14bo7bo14b3o4b2o$
5bobo22bo7bo17bobobobo17b3o2bo$5bobo23b2o3b2o19b2ob2o21bobo$6bo25bo3bo
45bobo$32bobobo46bo$33bobo$34bo!

Re: Gems?

Posted: March 2nd, 2017, 5:59 pm

by muzik

Not quite loaf gem:

Code: Select all

x = 9, y = 9, rule = B3/S23
4bo$3bobo$2bobobo$bo2bo2bo$ob2ob2obo$bo2bo2bo$2bobobo$3bobo$4bo!

Re: Gems?

Posted: March 2nd, 2017, 9:03 pm

by 83bismuth38

muzik wrote:Not quite loaf gem:
Code: Select all
x = 9, y = 9, rule = B3/S23
4bo$3bobo$2bobobo$bo2bo2bo$ob2ob2obo$bo2bo2bo$2bobobo$3bobo$4bo!

actually, that's quite interesting... ok it's a semi-gem now; that's what those are called.

and biggiemac, you are correct. however, (as stated above) the 4th one is a semigem.

Re: Gems?

Posted: March 2nd, 2017, 9:15 pm

by 83bismuth38

OKAY, so I now know how to put the life images up here. here's what i had:
bee gem:

Code: Select all

#CXRLE Pos=-6,-8
x = 8, y = 8, rule = B3/S23
3b2o$2bo2bo$bob2obo$obo2bobo$obo2bobo$bob2obo$2bo2bo$3b2o!

Mango gem:

Code: Select all

#CXRLE Pos=-4,-6 Gen=108
x = 10, y = 10, rule = B3/S23
5b2o$4bo2bo$3bo2bobo$2bob2obobo$bobo2bo2bo$o2bo2bobo$obob2obo$bobo2bo$
2bo2bo$3b2o!

pond gem:

Code: Select all

#CXRLE Pos=-9,-10 Gen=48
x = 10, y = 10, rule = B3/S23
4b2o$3bo2bo$3bo2bo$b2ob2ob2o$o2bo2bo2bo$o2bo2bo2bo$b2ob2ob2o$3bo2bo$3b
o2bo$4b2o!

I now also has
table gem:

Code: Select all

#CXRLE Pos=-6,-5 Gen=3
x = 7, y = 7, rule = B3/S23
2obo2bo$bob4o$bo$2o3b2o$5bo$4obo$o2bob2o!

note that they have to be STRICT still lifes, not pseudo still lifes.
house gem:

Code: Select all

#CXRLE Pos=-9,-7 Gen=3
x = 11, y = 11, rule = B3/S23
b2o$bobob2o2b2o$3bobo4bo$3bo2b4o$bobo$b2o5b2o$7bobo$b4o2bo$o4bobo$2o2b
2obobo$8b2o!

Re: Gems?

Posted: March 2nd, 2017, 9:30 pm

by 83bismuth38

forgot block gem:

Code: Select all

#CXRLE Pos=-6,-8
x = 5, y = 5, rule = B3/S23
2ob2o$2ob2o2$2ob2o$2ob2o!

Re: Gems?

Posted: March 2nd, 2017, 9:37 pm

by Mr. Missed Her

83bismuth38 wrote:forgot block gem:
Code: Select all
#CXRLE Pos=-6,-8
x = 5, y = 5, rule = B3/S23
2ob2o$2ob2o2$2ob2o$2ob2o!

Forgot edit button.

Re: Gems?

Posted: March 2nd, 2017, 10:08 pm

by biggiemac

Tables and houses seem to be against the original definition, wherein the basic parts must also be still lives.

One way to view this is to create a huge tree of terminology to describe each combination, assigning consistent labels in accordance with some definite rules. However, this is a potentially unwieldy rulespace. (Is this a gem or a semi-gem? Still lives or induction coils? Is its symmetry D8 or C4 or D4? and so on..). There are many edge cases and if multiple people decide to weigh in with naming suggestions, then there can be competing standards and a lot of problems.

The other way to view this: unless "gems" play a bigger part in some useful demonstration, it is unlikely that many users will care about the minutae of their classification. Gems are just still lives with symmetry, and many people here don't give still lives a second glance, because arbitrarily large ones with whatever symmetry desired can be generated very quickly. Not all will be gems, because of the requirement that 1/4 of the still life can also be taken on its own, but that distinction matters to almost nobody. In this case, you won't run into competing standards, because only you will really be talking about them.

Not trying to discourage you, just to give an idea of how the community historically reacts to these sort of posts. If gems are just there to look pretty (as the name seems to imply), then the second option is probably all you will get.

Re: Gems?

Posted: March 2nd, 2017, 10:35 pm

by 83bismuth38

my forvorite! complicated names and assigning those names to actual things! ok, so! here we go:
gem: 4-way prefect symmetry, made of only the base still life, no extra, no less.
semi-gem: 2-way symmetry, and/or extra or less cells.
crystal: same as gem, but with induction coils.
semi-crystal: same as semi-gem, but with induction coils.
reactor: same as gem, but with oscillators.
semi-reactor:same as semi-gem, but with oscillators.
also, i found a TON more, and for the sake of simplicity, i'm just gonna say the base pattern:
bookends:

Code: Select all

#CXRLE Pos=-9,-12 Gen=15
x = 13, y = 13, rule = B3/S23
3b2o3b2o$3bobobobo$5bobo$2o2b2ob2o2b2o$o2bo5bo2bo$b3o5b3o2$b3o5b3o$o2b
o5bo2bo$2o2b2ob2o2b2o$5bobo$3bobobobo$3b2o3b2o!

Ship and Boat:

Code: Select all

#CXRLE Pos=-8,-3 Gen=37
x = 7, y = 7, rule = B3/S23
bo3bo$obobobo$b2ob2o2$b2ob2o$obobobo$bo3bo!

Code: Select all

#CXRLE Pos=-8,-3 Gen=37
x = 7, y = 7, rule = B3/S23
2o3b2o$obobobo$b2ob2o2$b2ob2o$obobobo$2o3b2o!

eaters:

Code: Select all

#CXRLE Pos=-1,-10 Gen=4
x = 9, y = 9, rule = B3/S23
2o6bo$bo4b3o$bobobo$2b2ob2o2$2b2ob2o$3bobobo$3o4bo$o6b2o!

Code: Select all

#CXRLE Pos=-8,-11 Gen=1841
x = 15, y = 15, rule = B3/S23
4bo5bo$3bobo3bobo$3bobo3bobo$b3ob2ob2ob3o$o13bo$b3ob2ob2ob3o$3bob2ob2o
bo2$3bob2ob2obo$b3ob2ob2ob3o$o13bo$b3ob2ob2ob3o$3bobo3bobo$3bobo3bobo$
4bo5bo!

Code: Select all

#CXRLE Pos=-11,-11 Gen=61
x = 21, y = 21, rule = B3/S23
b2o15b2o$o2bo2b2o5b2o2bo2bo$obo4bo2bo2bo4bobo$bo5bobobobo5bo$4b2obo2bo
2bob2o$4bo2bo5bo2bo$bo4bo7bo4bo$b5o9b5o2$3bo13bo$2bobo11bobo$3bo13bo2$
b5o9b5o$bo4bo7bo4bo$4bo2bo5bo2bo$4b2obo2bo2bob2o$bo5bobobobo5bo$obo4bo
2bo2bo4bobo$o2bo2b2o5b2o2bo2bo$b2o15b2o!

Code: Select all

#CXRLE Pos=-10,-10 Gen=603
x = 19, y = 19, rule = B3/S23
5b2o5b2o$6bo2bo2bo$6bobobobo$3b2obo2bo2bob2o$3bo2bo5bo2bo$o4bo7bo4bo$
5o9b5o2$2bo13bo$bobo11bobo$2bo13bo2$5o9b5o$o4bo7bo4bo$3bo2bo5bo2bo$3b
2obo2bo2bob2o$6bobobobo$6bo2bo2bo$5b2o5b2o!

amphisbaena:

Code: Select all

#CXRLE Pos=-9,-5 Gen=9
x = 14, y = 14, rule = B3/S23
2bobo$2b2obo$2o3bo$bo3bob2o$o5bobo$b3o5b2o$4bo5bo$3bo5bo$3b2o5b3o$5bob
o5bo$5b2obo3bo$8bo3b2o$8bob2o$9bobo!

canoe:

Code: Select all

#CXRLE Pos=-10,-5 Gen=32
x = 11, y = 11, rule = B3/S23
2o7b2o$obo7bo$3bo5bo$4bobobo$3b2ob2o2$3b2ob2o$2bobobo$bo5bo$o7bobo$2o
7b2o!

cap:

Code: Select all

#CXRLE Pos=-8,-7 Gen=48
x = 9, y = 9, rule = B3/S23
5b2o$b2obo2bo$obob4o$obo$b2o3b2o$6bobo$b4obobo$bo2bob2o$2b2o!

barberpole:

Code: Select all

#CXRLE Pos=-5,-13 Gen=188
x = 11, y = 11, rule = B3/S23
2o7b2o$o7bobo$bobo$4bobobo$3b2ob2o2$3b2ob2o$2bobobo$7bobo$obo7bo$2o7b
2o!

Code: Select all

#CXRLE Pos=-6,-14 Gen=206
x = 13, y = 13, rule = B3/S23
2o9b2o$obo9bo$9bobo$2bobo$5bobobo$4b2ob2o2$4b2ob2o$3bobobo$8bobo$bobo$
o9bobo$2o9b2o!

Code: Select all

#CXRLE Pos=-8,-14 Gen=521
x = 16, y = 15, rule = B3/S23
13b2o$3b2o7bobo$3bobo$10bobo$5bobobo$6b2ob2o2$6b2ob2o$7bobobo$4bobo$
11bobo$2bobo$13bobo$obo11b2o$2o!

intergal sign (I have a new trick, see?):

Code: Select all

#CXRLE Pos=-7,-9 Gen=5
x = 11, y = 11, rule = B3/S23
2o7b2o$o7bobo$b3o4bo$4bobobo$3b2ob2o2$3b2ob2o$2bobobo$2bo4b3o$obo7bo$
2o7b2o!

if it has corners that can be put together, (see block gem) you can make it strict, because cells spawn with three and not four

Re: Gems?

Posted: March 3rd, 2017, 4:38 am

by muzik

What exactly defines something as a gem? Becuase here are four patterns that could qualify as "perfect loaf gems":

Code: Select all

x = 32, y = 13, rule = B3/S23
10b2o$9bo2bo9b2o$9bobo9bo2bo$7b2obo10bobobo$6bo2bo12bobobo$6bobo14bo2b
o$4b2obo16b2ob2o$3bo2bo19bo2bo$3bobo20bobobo$b2obo22bobobo$o2bo24bo2bo
$obo26b2o$bo!

Also, it seems that many if not all higher order lakes can be turned into their gems:

Code: Select all

x = 36, y = 22, rule = B3/S23
24b2o$23bo2bo$23bo2bo$21b2o4b2o$20bo8bo$20bo8bo$4b2o12b2ob2o4b2ob2o$3b
o2bo10bo2bo2bo2bo2bo2bo$3bo2bo10bo2bo2bo2bo2bo2bo$b2o4b2o6b2o4b2ob2ob
2o4b2o$o8bo4bo8bo2bo8bo$o8bo4bo8bo2bo8bo$b2o4b2o6b2o4b2ob2ob2o4b2o$3bo
2bo10bo2bo2bo2bo2bo2bo$3bo2bo10bo2bo2bo2bo2bo2bo$4b2o12b2ob2o4b2ob2o$
20bo8bo$20bo8bo$21b2o4b2o$23bo2bo$23bo2bo$24b2o!

Re: Gems?

Posted: March 3rd, 2017, 9:10 am

by 83bismuth38

kk, the first 2 are not gems, or for that matter semi-gems, because gems have to have 4-way ROTATIONAL symmetry, semis have to have 2 way rotational symmetry. finally, to qualify in this area at ALL, it has to be a strict still life. the second one is just a siamese loaf on(at?) siamese loaf. the 3rd one is true, they are just larger gems. :P

Re: Gems?

Posted: March 3rd, 2017, 9:17 am

by 83bismuth38

Mr. Missed Her wrote:
83bismuth38 wrote:forgot block gem:
Code: Select all
#CXRLE Pos=-6,-8
x = 5, y = 5, rule = B3/S23
2ob2o$2ob2o2$2ob2o$2ob2o!
Forgot edit button.

lolz i didn't know it existed until this.