Thread for your miscellaneous posts and discussions

[b-engine]

Off-topic in this thread. Request admin to move to appropriate thread.

No, this is the checkerboard dual of Day & Night.

[WhiteHawk]

Off-topic in this thread. Request admin to move to appropriate thread.

No, this is the checkerboard dual of Day & Night.

I would think this would be more appropriate in a thread about the checkerboard dual than the thread for this rule.

Additionally, this thread has never been a place for discussion of the checkerboard dual.

[b-engine]

I would think this would be more appropriate in a thread about the checkerboard dual than the thread for this rule

The checkerboard dual is used to cut down the size of the RLE (or else lots of obobobobobobo). It's functionally same as the base rule.
The the checkerboard dual of D&N isn't needed. If one do, a moderator would merge it to this thread anyway.

[WhiteHawk]

I would think this would be more appropriate in a thread about the checkerboard dual than the thread for this rule

The checkerboard dual is used to cut down the size of the RLE (or else lots of obobobobobobo). It's functionally same as the base rule.
The the checkerboard dual of D&N isn't needed.

Functionally the same is not the same as the exact same. This thread is for standard Day and Night discussion only, just as how the EightLife thread is not for discussion about B123478/S01234678 (It's black-white reversal).

EDIT: The first pattern posted above also doesn't function in Day and Night proper

[confocaloid]

(edit: reworded to replace "this thread" -> "the Day & Night thread", because the posts were moved.)

[...] This thread is for standard Day and Night discussion only, [...]

The post by LaundryPizza03 is completely on-topic in the Day & Night thread. It is about Day & Night.
More specifically it's about checkerboard drifters in Day & Night, which are traveling on the checkerboard background.
The pattern is posted in the checkerboard dual of D&N (rather than in D&N itself), merely to simplify communication. If you want to see the drifter, just do a XOR-paste in Golly to paste the given pattern over the checkerboard agar. It will work in D&N.

The partials for drifters I posted also can be viewed in D&N when XOR-pasted over the checkerboard agar, in the same way.

---

On the other hand, your complaints (about Day & Night checkerboard drifters being posted in the thread dedicated to Day & Night) are offtopic. This back-and-forth exchange fails to contribute anything to the knowledge or understanding of the topic.

[Sokwe]

The first pattern posted above also doesn't function in Day and Night proper

I think because it's an easy way to represent a pattern that works in Day & Night with a checkerboard background, I'm going to say that it's on-topic for the Day & Night thread. For those who want to see how the pattern operates in Day & Night proper, start with a large checkerboard in Golly like this one:

Code: Select all

x = 100, y = 100, rule = B3678/S34678:T100,100
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$ob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$b
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$o
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
o$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobo!

Then select "Edit->Paste Mode->Xor", and finally copy and paste the desired pattern directly on to the checkerboard. You should get something like this:

Code: Select all

x = 100, y = 100, rule = B3678/S34678:T100,100
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$ob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$b
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobo
bobobobobobobo2bobo2bobobobobobobobobobobobobobobobobobobobobobobobobo
bo$obobobobobobobobobobobobobobobobobobobobob2o3b2ob2obob2obobobobobob
obobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobo
2bo2bobobobo2b3o3bobo2bobobobobobobobobobobobobobobobobobobo$obobobobo
bobobobobobobobobobobobobobob2o2bobobobobobobob2o3b2obobobobobobobobob
obobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobo3bob3obo
bo2b2obobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobo
bobobobobobobobobobo4b4o3bob2obob2obobobobobobobobobobobobobobobobobob
obo$bobobobobobobobobobobobobobobobobobobobobo2b4ob3ob3ob2o2bobobobobo
bobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobo
bobobo6b2obobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobob
obobobobobobobobobobobobobobobo2b2ob5obobobobobobobobobobobobobobobobo
bobobobobobobo$obobobobobobobobobobobobobobobobobobobobob3o3bob2o2bobo
bobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobob
obobobobobobobo2bo2bobobobobobobobobobobobobobobobobobobobobobobobobob
obo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
o$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobo$obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobo!

Is there a way to do this in LifeViewer?

Edit: the other nice thing about the checkerboard dual in a black/white reversal rule is that it's easier to set up searches (with programs that support INT rules), because you don't need to mess around with the checkerboard background. I think its inclusion in the Day & Night thread might help familiarize people with the concept, which I view as another positive.

[confocaloid]

[...] Is there a way to do this in LifeViewer? [...]

I'm not aware of an existing scripting command or approach to make LifeViewer automatically translate between a self-complementary CA and its checkerboard dual. (I typically use Golly for pattern manipulation that involves copying and pasting with different modes.)

I think there could be (in principle) a dedicated LifeViewer scripting command for this. (Imagine it already exists, and can be invoked as [[ CHECKERBOARDDUAL ]]. ) It could work in the following way:

• The [[ CHECKERBOARDDUAL ]] command is only enabled if all of the following is true (otherwise, attempting to invoke [[ CHECKERBOARDDUAL ]] will trigger an error):
  • the current CA is two-state, self-complementary, (edit:) on the square tiling;
  • the universe is a torus with even dimensions (a 2m-by-2n torus).
• When [[ CHECKERBOARDDUAL ]] is invoked,
  • the current pattern (in the 2m-by-2n toroidal universe) is "XORed" with the same torus filled with a checkerboard background (to make it unambiguous, one can let (0,0) be an alive cell in the checkerboard background).
  • the current CA is replaced by its checkerboard dual.

In case such [[ CHECKERBOARDDUAL ]] command was implemented and worked as described, then for example the following snippet:

Code: Select all

#C [[ CHECKERBOARDDUAL ]]
x = 32, y = 24, rule = B1e2cn3acjkr4cny5einqy6ei7c/S01e2-ei3acjkr4-ejr5einqy6-cn7c8:T32,24
7$9b5o$9b2ob2o3b5o$5b3o9b2ob2ob5o$5b2o16b2ob2o$9bo4bo6b2o$8bob2obo2bo
4b5o$9b2obo3bo3bo3b2o$12bobob2o$11b2o3bobo$9bo2bo4b2o$9b3o!

would be displayed in LifeViewer in the same way as the following (the checkerboard drifter by LaundryPizza03):

Code: Select all

x = 32, y = 24, rule = B3678/S34678:T32,24
obobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobo$obobo
bobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobo$obobobobob
obobobobobobobobobobo$bobobobobobobobobobobobobobobobo$obobobobobobobo
bobobobobobobobo$bobobobo2bobo2bobobobobobobobobo$obobobob2o3b2ob2obob
2obobobobo$bobo2bo2bobobobo2b3o3bobo2bobo$obob2o2bobobobobobobob2o3b2o
bo$bobobobo3bob3obobo2b2obobobobo$obobobo4b4o3bob2obob2obobo$bobobobo
2b4ob3ob3ob2o2bobobo$obobobobobo6b2obobobobobobo$bobobobobo2b2ob5obobo
bobobobo$obobobob3o3bob2o2bobobobobobo$bobobobo2bo2bobobobobobobobobob
o$obobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobo$obo
bobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobo$obobobob
obobobobobobobobobobobo$bobobobobobobobobobobobobobobobo!

The restriction to a torus with even dimensions is to ensure that the resulting pattern after conversion will be finite and the checkerboard will "wrap around" correctly.

Are there any flaws/issues with this idea?

[Aleph]

Opening this up for forums discussion: Which of these is the best "<" character? I haven't been able to obtain any consensus.

Code: Select all

x = 115, y = 12, rule = B3/S23
5b2o10b2o10b2o10b2o10b2o10b2o10b2o10b2o10b2o10b2o$4bobo9bobo9bobo11bo
9bobo9bobo9bobo9bobo9bobo9bobo$4b2o10b2o9bobo9b3o11bo9bobo9bobo9bo11bo
bo9bobo$2b2o10b2o12bo10bo10b3o10bo10bobo9bo11bobo9bobo$bobo11bo9b3o9b
2o11bo10b3o9bobo9bo12b2o9bobo$o11b3o9bo11bo11b2o10bo12bo10bo11b2o10bob
o$3o9bo11b2o10b3o9bo11b2o10b2o10bobo10bo10bo$3bo9bobo10bo12bo9bo12bo
11b2o9bobo9bobo9bo$2b2o10b2o10b3o9b2o10bo11b3o9bobo9bobo9bobo9bo$4b2o
10b2o11bo10b2o9bo13bo9bobo9bobo9bobo9bo$4bobo9bobo9bobo9bobo9bobo9bobo
9bobo9bobo9bobo9bobo$5b2o10b2o10b2o10b2o10b2o10b2o10b2o10b2o10b2o10b2o
!

EDIT: I am explicitly making a request for comment.

[CARuler]

i dont have general access to discord, just adding to the examples

yes

yk the three years thing (where i would have access to discord in 2028)?

that is probably being thrown into a ditch and im hopping on as soon as i turn 13 and get the opportunity to not have family link anymore.

i will look forward to seeing you

[confocaloid]

https://math.stackexchange.com/a/219252

temp.png (56.46 KiB) Viewed 901 times

[...] EDIT: I am explicitly making a request for comment.

Reordered roughly from left to right (top row) and added a few awkward variations (bottom row):

Code: Select all

x = 116, y = 43, rule = B3/S23
5b2o10b2o11b2o11b2o10b2o9b2o10b2o10b2o10b2o10b2o$4bobo9bobo10bobo10bob
o9bobo8bobo9bobo9bobo11bo9bobo$3bobo9bobo10bobo11b2o10b2o8bo11bobo9bob
o9b3o11bo$2bobo9bobo11bo11b2o10b2o9bo11bobo11bo10bo10b3o$2b2o9bobo10b
3o10bobo11bo8bo11bobo9b3o9b2o11bo$2o11bo11bo12bo11b3o8bo11bobo9bo11bo
11b2o$bo10b2o11b2o11b3o9bo10bobo9bo11b2o10b3o9bo$bobo10b2o11bo13bo9bob
o8bobo9bo12bo12bo9bo$2bobo9bobo10b3o10b2o10b2o9bobo9bo11b3o9b2o10bo$3b
obo9bobo12bo11b2o10b2o8bobo9bo13bo10b2o9bo$4bobo9bobo10bobo10bobo9bobo
8bobo9bobo9bobo9bobo9bobo$5b2o10b2o11b2o11b2o10b2o9b2o10b2o10b2o10b2o
10b2o11$10b2o35bo$9bobo15b2o16b3o16b2o$7b3o17bo16bo18bobo$6bo3bo14bobo
17bo16bo$6bo2b2o13bobo15b3o16bo$4b2o18bo16bo18bo$3bo18bobo17bo16bo$3bo
17bobo15b3o16bo$b2o18bo16bo18bo$o18b3o16b2o17b2o$o17bo21bo18bo$b2o16b
3o16b2o17b2o$3bo17bo16bo18bo$3bo17bobo15b3o16bo$4b2o16bobo17bo16bo$6bo
2b2o13bo16bo18bo$6bo3bo13bobo15b3o16bo$7b3o15bobo17bo16bo$9bobo15bo16b
o18bobo$10b2o15b2o16b3o16b2o$47bo!

[islptng]

Wickstretcher in StopboxINT:

Code: Select all

x = 3, y = 8, rule = B2cei3ejy4cejkqrw5-ai6-a7c/S1c2ae3eijnr4-acqt5cenry6-ae7e8
3o$obo$3o$3o$bo$3o$obo$bo!

Gun:

Code: Select all

x = 6, y = 5, rule = B2cei3ejy4cejkqrw5-ai6-a7c/S1c2ae3eijnr4-acqt5cenry6-ae7e8
3ob2o$ob3o$3obo$4bo$4b2o!

All of them are natural and were found by scribbling/soup search in LifeViewer.

Already known before this rule is posted. Please avoid posting in the wrong thread.

[CARuler]

R2 Knight INT

Code: Select all

x = 47, y = 103, rule = LifeHistory
.2C5.3C4.3C4.C.C4.3C4.3C4.3C$2.C7.C6.C4.C.C4.C6.C8.C$2.C5.3C4.3C4.3C4.3C4.3C6.C$2.C5.C8.C6.C6.C4.C.C6.C$.3C4.3C4.3C6.C4.3C4.3C3$.D.D4.C.D4.C.C4.C.C4.D.D4.D.C4.C.C$C3.D2.C3.D2.C3.D2.C3.C2.D3.C2.D3.C2.D3.C2$D3.D2.D3.D2.D3.D2.D3.D2.C3.C2.C3.C2.C3.C$.D.D4.D.D4.D.D4.D.D4.C.C4.C.C4.C.C3$8.D.C4.C.D4.C.C4.D.C4.C.D$7.C3.D2.C3.C2.C3.D2.D3.D2.D3.C2$7.D3.D2.D3.D2.D3.C2.C3.C2.C3.C$8.D.D4.D.D4.D.D4.C.C4.C.C3$8.D.D4.C.D4.C.C4.D.C4.C.C$7.C3.C2.C3.D2.C3.D2.D3.C2.D3.D2$7.D3.D2.D3.C2.D3.D2.C3.D2.C3.C$8.D.D4.D.D4.D.C4.C.C4.C.C3$8.D.D4.D.C4.C.C4.C.D4.C.C$7.C3.D2.C3.D2.C3.D2.D3.C2.D3.C2$7.D3.C2.D3.C2.D3.D2.C3.D2.C3.D$8.D.D4.D.D4.C.D4.C.C4.C.C3$8.D.D4.D.C4.C.C4.C.D4.C.C$7.C3.D2.C3.D2.C3.D2.D3.C2.D3.C2$7.D3.D2.D3.D2.C3.D2.C3.C2.C3.C$8.D.C4.D.C4.D.D4.C.D4.C.D3$8.D.D4.D.C4.C.D4.C.D4.C.C$7.C3.D2.C3.D2.C3.C2.D3.C2.D3.C2$7.C3.D2.C3.D2.D3.C2.D3.C2.D3.C$8.D.D4.D.D4.D.D4.C.C4.C.C3$15.D.D4.C.D4.C.C$14.C3.C2.C3.C2.D3.D2$14.C3.D2.D3.D2.D3.C$15.D.D4.D.C4.C.C3$22.C.D$21.C3.C2$21.D3.D$22.C.D3$22.C.D$21.C3.D2$21.D3.C$22.D.C3$22.D.C$21.C3.D2$21.D3.C$22.C.D3$22.D.C$21.C3.D2$21.C3.C$22.D.D3$22.D.C$21.C3.D2$21.C3.D$22.D.C3$22.D.C$21.C3.C2$21.C3.D$22.D.D3$22.D.D$21.C3.C2$21.C3.C$22.D.D!

Letters used would be also be acehijnopqrtuvw. Some will need to be removed.

an error

Code: Select all

x = 151, y = 108, rule = LifeHistory
14$34.C.C67.2C5.3C4.3C4.C.C4.3C4.3C4.3C$33.C3.D67.C7.C6.C4.C.C4.C6.C8.
C$105.C5.3C4.3C4.3C4.3C4.3C6.C$33.D3.C67.C5.C8.C6.C6.C4.C.C6.C$34.D.D
67.3C4.3C4.3C6.C4.3C4.3C3$34.C.C67.D.D39.C.C$33.C3.D65.C3.D37.D3.C2$33.
D3.D65.D3.D37.C3.C$34.D.C67.D.D39.C.C3$34.C.C74.C.D4.C.C4.C.C4.D.D4.D
.C$33.C3.D57.3E12.C3.D2.C3.D2.C3.C2.D3.C2.D3.C$95.E.E$33.D3.D57.3E12.
D3.D2.D3.D2.D3.D2.C3.C2.C3.C$34.C.D74.D.D4.D.D4.D.D4.C.C4.C.C3$95.3E13.
D.C4.D.C4.D.C4.C.D4.C.D$95.E14.C3.D2.C3.D2.C3.D2.D3.C2.D3.C$95.E$95.3E
12.D3.D2.D3.C2.D3.C2.C3.D2.C3.C$111.D.D4.D.D4.C.D4.C.C4.C.C$31.10D$31.
D8.D56.E$31.D2.C.D3.D56.E13.D.D4.C.D4.C.D4.D.C4.C.C$31.D.C3.C2.D54.3E
12.C3.D2.C3.D2.C3.D2.D3.C2.D3.C$31.D8.2D53.E.E$31.D.D3.C3.D53.3E12.D3.
C2.D3.C2.D3.C2.C3.D2.C3.D$31.D2.D.D4.D69.D.D4.D.D4.D.C4.C.C4.C.C$31.D
9.D$31.D8.D$31.D3.6D70.D.D4.C.D4.D.C4.D.C4.C.C$31.5D59.E14.C3.C2.C3.C
2.C3.D2.D3.D2.D3.D$95.E$95.3E12.D3.D2.D3.D2.C3.D2.C3.C2.C3.C$95.E.E13.
D.D4.D.D4.D.C4.C.C4.C.C$95.E.E2$34.C.D74.D.D4.D.D4.D.D4.C.C4.C.C$33.C
3.C58.E13.C3.D2.C3.C2.C3.C2.D3.D2.D3.C2$33.D3.D58.E13.C3.D2.C3.D2.C3.
C2.D3.C2.D3.C$34.C.D59.E14.D.D4.D.D4.D.D4.C.C4.C.C3$94.E.E.E12.D.D4.D
.C4.C.C4.C.D4.C.C$94.E.E.E11.C3.D2.C3.D2.C3.D2.D3.C2.D3.C$94.E.E.E$95.
E.E12.D3.D2.D3.D2.C3.D2.C3.C2.C3.C$111.D.C4.D.C4.D.D4.C.D4.C.D2$95.3E
$95.E.E20.D.C4.C.D4.C.D$95.3E19.C3.D2.C3.C2.D3.C$97.E.E$97.2E18.C3.D2.
D3.D2.D3.C$97.E20.D.D4.D.C4.C.C3$34.D.C$33.C3.D2$33.C3.C$34.D.D8$31.10D
$31.D8.D$32.D.D.C3.D$32.DC3.C2.D$32.D7.D$32.DC3.D2.2D$32.D.D.D4.D$32.
D8.D$32.10D$32.D!

edit: finished

Code: Select all

x = 119, y = 103, rule = LifeHistory
73.2C5.3C4.3C4.C.C4.3C4.3C4.3C$74.C7.C6.C4.C.C4.C6.C8.C$74.C5.3C4.3C4.
3C4.3C4.3C6.C$74.C5.C8.C6.C6.C4.C.C6.C$73.3C4.3C4.3C6.C4.3C4.3C3$73.D
.D39.C.C$72.C3.D37.D3.C2$72.D3.D37.C3.C$73.D.D39.C.C3$80.C.D4.C.C4.C.
C4.D.D4.D.C$64.3E12.C3.D2.C3.D2.C3.C2.D3.C2.D3.C$64.E.E$64.3E12.D3.D2.
D3.D2.D3.D2.C3.C2.C3.C$80.D.D4.D.D4.D.D4.C.C4.C.C3$64.3E13.D.C4.D.C4.
D.C4.C.D4.C.D$64.E14.C3.D2.C3.D2.C3.D2.D3.C2.D3.C$64.E$64.3E12.D3.D2.
D3.C2.D3.C2.C3.D2.C3.C$80.D.D4.D.D4.C.D4.C.C4.C.C2$66.E$66.E13.D.D4.C
.D4.C.D4.D.C4.C.C$64.3E12.C3.D2.C3.D2.C3.D2.D3.C2.D3.C$64.E.E$64.3E12.
D3.C2.D3.C2.D3.C2.C3.D2.C3.D$80.D.D4.D.D4.D.C4.C.C4.C.C3$80.D.D4.C.D4.
D.C4.D.C4.C.C$64.E14.C3.C2.C3.C2.C3.D2.D3.D2.D3.D$64.E$64.3E12.D3.D2.
D3.D2.C3.D2.C3.C2.C3.C$64.E.E13.D.D4.D.D4.D.C4.C.C4.C.C$64.E.E2$80.D.
D4.D.D4.D.D4.C.C4.C.C$65.E13.C3.D2.C3.C2.C3.C2.D3.D2.D3.C2$65.E13.C3.
D2.C3.D2.C3.C2.D3.C2.D3.C$65.E14.D.D4.D.D4.D.D4.C.C4.C.C3$63.E.E.E12.
D.D4.D.C4.C.C4.C.D4.C.C$63.E.E.E11.C3.D2.C3.D2.C3.D2.D3.C2.D3.C$63.E.
E.E$64.E.E12.D3.D2.D3.D2.C3.D2.C3.C2.C3.C$80.D.C4.D.C4.D.D4.C.D4.C.D2$
64.3E$64.E.E20.D.C4.D.C4.C.D$64.3E19.C3.D2.C3.D2.D3.C$66.E.E$66.2E18.
C3.D2.C3.C2.D3.C$66.E20.D.D4.D.D4.C.C3$94.C.D$93.C3.C$63.E3.E$64.E.E26.
D3.D$65.E28.C.D$64.E$63.E2.E$62.E3.E2.E24.C.D$66.E.E24.C3.C$66.2E$66.
E.E24.D3.C$66.E2.E24.D.D3$94.C.D$63.E.E27.C3.C$64.E$63.E.E27.D3.D$94.
D.C$64.E$63.3E$64.E29.C.C$64.E28.C3.D2$93.D3.C$94.D.D$66.E$66.E$64.E.
E27.C.C$65.E27.C3.D2$93.D3.D$94.D.C3$66.E27.C.C$65.E.E25.C3.D$65.E$65.
E27.D3.D$94.C.D!

[confocaloid]

I think there was a recent post by someone, mentioning two c/6 orthogonal spaceships in Salad (B2i34c/S2-i3). It looks like the post was deleted later for some reason. Here are the two c/6 spaceships:

Code: Select all

x = 22, y = 9, rule = R3,C0,S155-200,262-267,280-288,303-307,386-431,452,512-557,576,655-662,681,700,780-782,800-809,906-932,1050-1056,1161,1306-1410,B161-200,265,286,305-307,391,410-432,511-512,536-537,555-558,660-661,680-681,766,785-786,806-807,851,1035-1056,1181,1265-1307,1516-1601,NW007D0001007D007D7D7D007D7D7D007D1905197D0001000500050001007D1905197D007D7D7D007D7D7D007D0001007D00
18b2o$2b3o12bo2bo$bo3bo11b4o$bo3bo$2b3o12bo2bo$17bo2bo$2bobo12b4o$3ob
3o$16b2o2b2o!

[b-engine]

then you could argue this for every hassler

Code: Select all

x = 33, y = 26, rule = B3/S23
7b2o15b2o$8bo15bo$6bo19bo$6b5o11b5o$10bo11bo$4b4o17b4o$4bo2bo17bo2bo$
21bo$21bo$9bo4b2ob2o2bob2o$8b3o3b2obo6b2o$7bo2b2o6bo$7b3o12bo$22bobo$
3b2o11b2o4bo2bo2b2o$3bo12b2o5b2o4bo$2obo12b2o11bob2o$ob2ob2o19b2ob2ob
o$5bo21bo$5bobo17bobo$6b2o17b2o$10bo11bo$6b5o11b5o$6bo19bo$8bo15bo$7b
2o15b2o!

the beehive is briefly destroyed

No, the beehive isn't completely destroyed - meaning that there's no phase where the cells of the beehive is empty.

[confocaloid]

In those cases when some stationary object X (for example a beehive or a blinker) is repeatedly created and destroyed (for example due to interactions between oscillators), I believe that doesn't really count as "X hassler".

Evolve the oscillator until the object X is visible and well-separated. If removing the object X from that phase can be "cancelled" merely by evolving the remainder for enough ticks for the object X to reappear, then it's not really "X hassler", it doesn't hassle the object, it just repeatedly places it and deletes it.

[Aleph]

Euclidean tilings such as {5/2,10} have defined vertex figures, but do not tile periodically and end up creating an infinite density mess everywhere. Nonetheless, if we ignore this complication, can we define a separate, abstract notion of "distance" between two given facets, unrelated to Euclidean physical proximity, in the sense that facet B can only be reached from facet A by crossing two dihedral edges from two attached facets?

Indeed, can a cellular automaton be run on grids such as {5/2,10}?

A cellular automaton can be run on anything that can be "honestly" represented as a graph (in the sense of graph theory). The "cells" become vertices of the graph; when a "cell" A is a neighbour of a "cell" B that is represented by a directed edge from A to B ("the current state of A can affect the state of B in the next generation").

I remember having a similar idea of having positions be group elements instead of graph nodes. Neighborhoods would then be represented as certain "offsets" which would also be elements of the group. For example, Wolfram's 1D CA could exist on the group of "Z with addition" where every cell used a neighborhood with the offsets of -1, 0, and +1. If we add additional "invariants", we can also have indirect support for other types of CA. For example, suppose we have a neighborhood with offsets of -1 and +1, and require that all live cells in a given generation share the same parity. Boom. 1D margolus, and you can easily extend this to 2D margolus. Other CA require position-dependent neighborhoods. For example, consider "life on the slope". We can represent this on Z^2 with 2 states by setting up neighborhoods like this.
For cells with one checkerboard parity, we have a neighborhood that looks like this:

Code: Select all

oo$ooo$boo!

For cells with the other checkerboard parity, we have a neighborhood that looks like this:

Code: Select all

boo$ooo$oo!

This trick can also be used to do triangular CA with 2 states.

EDIT: Trying to figure out how to do all this with code is hard. You can't have position-dependent neighborhoods because computing zone of influence becomes a headache. You can't have position-dependent evaluation functions because then B0 becomes a headache. So I guess that the problem is one of figuring out how to get rid of those. For example, rotating LifeOnTheSlope by 45 degrees gives LifeOnTheEdge which has uniform neighborhoods and evaluation.

[confocaloid]

[...] I remember having a similar idea of having positions be group elements instead of graph nodes. Neighborhoods would then be represented as certain "offsets" which would also be elements of the group. For example, Wolfram's 1D CA could exist on the group of "Z with addition" where every cell used a neighborhood with the offsets of -1, 0, and +1. [...]

Probably this would work nicely when the group is abelian. That is the case for the square tiling and the hexagonal tiling if you represent neighbours as offsets (dx, dy).
Groups can be found whenever there are symmetries, so it would be tempting to use them to "treat all cells and all directions in the same way".
How would you use groups to represent/implement a CA defined on the 20 faces of the icosahedron (for example with the neighbourhood including three side-by-side adjacent triangles)? There is the group of 60 rotations, and there is the larger group of 120 symmetries, but neither of those two groups seems to match what is really needed here: one would need something with precisely 20 elements (one element for every face).

[...] If we add additional "invariants", we can also have indirect support for other types of CA. [...] This trick can also be used to do triangular CA with 2 states. [...]

The system with neighbourhoods alternating in space means that a pattern will no longer evolve the same way if its representation is translated by 1 cell orthogonally.
The other well-known approach is to begin with a square tiling, and subdivide each square into two triangles. One would need 4 cellstates to represent a 2-state CA on the triangular tilings. I find this approach more intuitive. In my view, the triangular tiling becomes easier to handle when patterns can be copied and pasted without worrying about the precise location. Of course there are still unanswered questions "how to rotate a pattern", "how to reflect a pattern", but those questions would need to be answered regardless of the approach, and at least translations become simpler.

[Aleph]

[...] I remember having a similar idea of having positions be group elements instead of graph nodes. Neighborhoods would then be represented as certain "offsets" which would also be elements of the group. For example, Wolfram's 1D CA could exist on the group of "Z with addition" where every cell used a neighborhood with the offsets of -1, 0, and +1. [...]

Probably this would work nicely when the group is abelian. That is the case for the square tiling and the hexagonal tiling if you represent neighbours as offsets (dx, dy).
Groups can be found whenever there are symmetries, so it would be tempting to use them to "treat all cells and all directions in the same way".
How would you use groups to represent/implement a CA defined on the 20 faces of the icosahedron (for example with the neighbourhood including three side-by-side adjacent triangles)? There is the group of 60 rotations, and there is the larger group of 120 symmetries, but neither of those two groups seems to match what is really needed here: one would need something with precisely 20 elements (one element for every face).

I doubt that this approach would work for icosahedrons at all. The weird thing is that I haven't yet seen anything *algorithmic" that would require commutative groups.

[...] If we add additional "invariants", we can also have indirect support for other types of CA. [...] This trick can also be used to do triangular CA with 2 states. [...]

The system with neighbourhoods alternating in space means that a pattern will no longer evolve the same way if its representation is translated by 1 cell orthogonally.

I decided to go for your other approach, because neighborhoods alternating in space means that the zone of influence of a pattern would be a headache to compute.

The other well-known approach is to begin with a square tiling, and subdivide each square into two triangles. One would need 4 cellstates to represent a 2-state CA on the triangular tilings. I find this approach more intuitive. In my view, the triangular tiling becomes easier to handle when patterns can be copied and pasted without worrying about the precise location. Of course there are still unanswered questions "how to rotate a pattern", "how to reflect a pattern", but those questions would need to be answered regardless of the approach, and at least translations become simpler.

In my opinion, I have a solution that is slightly better. Instead of using Z^2, we use Z^3 constrained on x+y+z=0. Suddenly, the set of allowed points falls perfectly on a hexagonal tiling, without any 'further tricks. As for triangular tilings, we can still pair up triangles like so to convert to a 4-state hexagonal tiling.

Each point is the center of a triangle.

IMG_0618.jpeg (572.11 KiB) Viewed 766 times

Or, just take 6 triangles and make a hexagon out of them. This allows for much easier rotations in my opinion.

EDIT: Just updating the 501P7 completion collection:

Code: Select all

x = 1132, y = 203, rule = B3/S23
obobo3bobobo27b2o28bobobo3bobobo23b2o22bobobo3bobobo22b2o23bobobo3bobo
bo18b2o37bobobo3bobobo20b2o25bobobo3bobobo21b2o26b2o16bobobo3bobobo21b
2o14bobo5bobobo3bobobo18b2o28b2o19bobo5bobobo3bobobo18b2o19bobo5bobobo
3bobobo18b2o19bobo5bobo5bobo20b2o19bobo5bobo5bobobo18b2o19bobo5bobo5bo
bobo18b2o28b2o28b2o19bobo5bobo5bo3bo20b2o17bobo5bobo5bobobo18b2o19bobo
5bobo5bobobo18b2o19bobobo3bobobo3bobobo18b2o$38bo4bo60bo4bo53bo4bo50bo
4bo66bo4bo55bo4bo22bo4bo46bo4bo49bo4bo24bo4bo54bo4bo54bo4bo54bo4bo54bo
4bo54bo4bo24bo4bo24bo4bo56bo4bo52bo4bo54bo4bo54bo4bo$o7bo61bo11bo47bo
7bo3bo51bo3bo61bo3bo3bo51bo3bo7bo67bo3bo3bo3bo39bo5bo3bo7bo71bo5bo3bo
3bo3bo41bo5bo3bo3bo3bo41bo7bo7bo43bo7bo9bo41bo7bo9bo101bo7bo5bo3bo41bo
7bo5bo45bo7bo5bo3bo43bo3bo3bo7bo$38bo4bo60bo4bo53bo4bo50bo4bo66bo4bo
55bo4bo22bo4bo46bo4bo49bo4bo24bo4bo54bo4bo54bo4bo54bo4bo54bo4bo54bo4bo
24bo4bo24bo4bo56bo4bo52bo4bo54bo4bo54bo4bo$obobo3bobobo25bo4bo26bobobo
7bo21bo4bo20bobobo3bobobo20bo4bo25bo3bobobo16bo4bo35bobobo3bobobo18bo
4bo23bobobo7bo19bo4bo22bo4bo14bobobo3bobobo19bo4bo14bo5bo3bo7bo16bo4bo
24bo4bo19bo5bo3bo3bobobo16bo4bo19bo5bo3bo3bobobo16bo4bo19bo7bo7bo18bo
4bo19bo7bo5bobobo16bo4bo19bo7bo5bobobo16bo4bo24bo4bo24bo4bo19bo7bo5bob
obo18bo4bo17bo7bo5bobobo16bo4bo19bo7bo5bobobo16bo4bo17bobobo3bo3bo3bob
obo16bo4bo$38b2o2b2o60b2o2b2o53b2o2b2o50b2o2b2o66b2o2b2o55b2o2b2o22b2o
2b2o46b2o2b2o49b2o2b2o24b2o2b2o54b2o2b2o54b2o2b2o54b2o2b2o54b2o2b2o54b
2o2b2o24b2o2b2o24b2o2b2o56b2o2b2o52b2o2b2o54b2o2b2o54b2o2b2o$o3bo3bo3b
o24bobo2bobo25bo3bo7bo20bobo2bobo19bo3bo7bo19bobo2bobo24bo7bo15bobo2bo
bo34bo3bo7bo17bobo2bobo22bo3bo7bo18bobo2bobo20bobo2bobo13bo3bo3bo3bo
18bobo2bobo13bo5bo3bo7bo15bobo2bobo22bobo2bobo18bo5bo3bo3bo3bo15bobo2b
obo18bo5bo3bo7bo15bobo2bobo18bo7bo7bo17bobo2bobo18bo7bo5bo19bobo2bobo
18bo7bo9bo15bobo2bobo22bobo2bobo22bobo2bobo18bo7bo9bo17bobo2bobo16bo7b
o9bo15bobo2bobo18bo7bo9bo15bobo2bobo16bo7bo3bo7bo15bobo2bobo$34bo3b2o
2b2o3bo52bo3b2o2b2o3bo45bo3b2o2b2o3bo42bo3b2o2b2o3bo58bo3b2o2b2o3bo47b
o3b2o2b2o3bo14bo3b2o2b2o3bo38bo3b2o2b2o3bo41bo3b2o2b2o3bo16bo3b2o2b2o
3bo46bo3b2o2b2o3bo46bo3b2o2b2o3bo46bo3b2o2b2o3bo46bo3b2o2b2o3bo46bo3b
2o2b2o3bo16bo3b2o2b2o3bo16bo3b2o2b2o3bo48bo3b2o2b2o3bo44bo3b2o2b2o3bo
46bo3b2o2b2o3bo46bo3b2o2b2o3bo$obobo3bobobo20bo2b2o2b2o2b2o2bo21bobobo
7bo16bo2b2o2b2o2b2o2bo15bobobo3bobobo15bo2b2o2b2o2b2o2bo20bo3bobobo11b
o2b2o2b2o2b2o2bo30bobobo3bobobo13bo2b2o2b2o2b2o2bo18bobobo7bo14bo2b2o
2b2o2b2o2bo12bo2b2o2b2o2b2o2bo9bobobo3bobobo14bo2b2o2b2o2b2o2bo7bobobo
3bobobo7bo11bo2b2o2b2o2b2o2bo14bo2b2o2b2o2b2o2bo12bobobo3bobobo3bobobo
11bo2b2o2b2o2b2o2bo12bobobo3bobobo3bobobo11bo2b2o2b2o2b2o2bo12bobobo3b
obobo3bobobo11bo2b2o2b2o2b2o2bo12bobobo3bobobo3bobobo11bo2b2o2b2o2b2o
2bo12bobobo3bobobo3bobobo11bo2b2o2b2o2b2o2bo14bo2b2o2b2o2b2o2bo14bo2b
2o2b2o2b2o2bo12bobobo3bobobo7bo13bo2b2o2b2o2b2o2bo10bobobo3bobobo3bobo
bo11bo2b2o2b2o2b2o2bo12bobobo3bobobo3bobobo11bo2b2o2b2o2b2o2bo12bobobo
3bobobo3bobobo11bo2b2o2b2o2b2o2bo$33b3o4b2o4b3o50b3o4b2o4b3o43b3o4b2o
4b3o40b3o4b2o4b3o56b3o4b2o4b3o45b3o4b2o4b3o12b3o4b2o4b3o36b3o4b2o4b3o
39b3o4b2o4b3o14b3o4b2o4b3o44b3o4b2o4b3o44b3o4b2o4b3o44b3o4b2o4b3o44b3o
4b2o4b3o44b3o4b2o4b3o14b3o4b2o4b3o14b3o4b2o4b3o46b3o4b2o4b3o42b3o4b2o
4b3o44b3o4b2o4b3o44b3o4b2o4b3o$36bo8bo56bo8bo49bo8bo46bo8bo62bo8bo51bo
8bo18bo8bo42bo8bo45bo8bo20bo8bo50bo8bo50bo8bo50bo8bo50bo8bo50bo8bo20bo
8bo20bo8bo52bo8bo48bo8bo50bo8bo50bo8bo$31b4ob2o6b2ob4o46b4ob2o6b2ob4o
39b4ob2o6b2ob4o36b4ob2o6b2ob4o52b4ob2o6b2ob4o41b4ob2o6b2ob4o8b4ob2o6b
2ob4o32b4ob2o6b2ob4o35b4ob2o6b2ob4o10b4ob2o6b2ob4o40b4ob2o6b2ob4o40b4o
b2o6b2ob4o40b4ob2o6b2ob4o40b4ob2o6b2ob4o40b4ob2o6b2ob4o10b4ob2o6b2ob4o
10b4ob2o6b2ob4o42b4ob2o6b2ob4o38b4ob2o6b2ob4o40b4ob2o6b2ob4o40b4ob2o6b
2ob4o$31bo2bobob2o2b2obobo2bo46bo2bobob2o2b2obobo2bo39bo2bobob2o2b2obo
bo2bo36bo2bobob2o2b2obobo2bo52bo2bobob2o2b2obobo2bo41bo2bobob2o2b2obob
o2bo8bo2bobob2o2b2obobo2bo32bo2bobob2o2b2obobo2bo35bo2bobob2o2b2obobo
2bo10bo2bobob2o2b2obobo2bo40bo2bobob2o2b2obobo2bo40bo2bobob2o2b2obobo
2bo40bo2bobob2o2b2obobo2bo40bo2bobob2o2b2obobo2bo40bo2bobob2o2b2obobo
2bo10bo2bobob2o2b2obobo2bo10bo2bobob2o2b2obobo2bo42bo2bobob2o2b2obobo
2bo38bo2bobob2o2b2obobo2bo40bo2bobob2o2b2obobo2bo40bo2bobob2o2b2obobo
2bo$32bo16bo48bo16bo41bo16bo38bo16bo54bo16bo43bo16bo10bo16bo34bo16bo
37bo16bo12bo16bo42bo16bo42bo16bo42bo16bo42bo16bo42bo16bo12bo16bo12bo
16bo44bo16bo40bo16bo42bo16bo42bo16bo$29b3o5bo6bo5b3o42b3o5bo6bo5b3o35b
3o5bo6bo5b3o32b3o5bo6bo5b3o48b3o5bo6bo5b3o37b3o5bo6bo5b3o4b3o5bo6bo5b
3o28b3o5bo6bo5b3o31b3o5bo6bo5b3o6b3o5bo6bo5b3o36b3o5bo6bo5b3o36b3o5bo
6bo5b3o36b3o5bo6bo5b3o36b3o5bo6bo5b3o36b3o5bo6bo5b3o6b3o5bo6bo5b3o6b3o
5bo6bo5b3o38b3o5bo6bo5b3o34b3o5bo6bo5b3o36b3o5bo6bo5b3o36b3o5bo6bo5b3o
$29bo2b3o2bo2b2o2bo2b3o2bo42bo2b3o2bo2b2o2bo2b3o2bo35bo2b3o2bo2b2o2bo
2b3o2bo32bo2b3o2bo2b2o2bo2b3o2bo48bo2b3o2bo2b2o2bo2b3o2bo37bo2b3o2bo2b
2o2bo2b3o2bo4bo2b3o2bo2b2o2bo2b3o2bo28bo2b3o2bo2b2o2bo2b3o2bo31bo2b3o
2bo2b2o2bo2b3o2bo6bo2b3o2bo2b2o2bo2b3o2bo36bo2b3o2bo2b2o2bo2b3o2bo36bo
2b3o2bo2b2o2bo2b3o2bo36bo2b3o2bo2b2o2bo2b3o2bo36bo2b3o2bo2b2o2bo2b3o2b
o36bo2b3o2bo2b2o2bo2b3o2bo6bo2b3o2bo2b2o2bo2b3o2bo6bo2b3o2bo2b2o2bo2b
3o2bo38bo2b3o2bo2b2o2bo2b3o2bo34bo2b3o2bo2b2o2bo2b3o2bo36bo2b3o2bo2b2o
2bo2b3o2bo36bo2b3o2bo2b2o2bo2b3o2bo$31bo2bo2bo6bo2bo2bo46bo2bo2bo6bo2b
o2bo39bo2bo2bo6bo2bo2bo36bo2bo2bo6bo2bo2bo52bo2bo2bo6bo2bo2bo41bo2bo2b
o6bo2bo2bo8bo2bo2bo6bo2bo2bo32bo2bo2bo6bo2bo2bo35bo2bo2bo6bo2bo2bo10bo
2bo2bo6bo2bo2bo40bo2bo2bo6bo2bo2bo40bo2bo2bo6bo2bo2bo40bo2bo2bo6bo2bo
2bo40bo2bo2bo6bo2bo2bo40bo2bo2bo6bo2bo2bo10bo2bo2bo6bo2bo2bo10bo2bo2bo
6bo2bo2bo42bo2bo2bo6bo2bo2bo38bo2bo2bo6bo2bo2bo40bo2bo2bo6bo2bo2bo40bo
2bo2bo6bo2bo2bo$32bo4bob4obo4bo48bo4bob4obo4bo41bo4bob4obo4bo38bo4bob
4obo4bo54bo4bob4obo4bo43bo4bob4obo4bo10bo4bob4obo4bo34bo4bob4obo4bo37b
o4bob4obo4bo12bo4bob4obo4bo42bo4bob4obo4bo42bo4bob4obo4bo42bo4bob4obo
4bo42bo4bob4obo4bo42bo4bob4obo4bo12bo4bob4obo4bo12bo4bob4obo4bo44bo4bo
b4obo4bo40bo4bob4obo4bo42bo4bob4obo4bo42bo4bob4obo4bo$29b3o5bo6bo5b3o
42b3o5bo6bo5b3o35b3o5bo6bo5b3o32b3o5bo6bo5b3o48b3o5bo6bo5b3o37b3o5bo6b
o5b3o4b3o5bo6bo5b3o28b3o5bo6bo5b3o31b3o5bo6bo5b3o6b3o5bo6bo5b3o36b3o5b
o6bo5b3o36b3o5bo6bo5b3o36b3o5bo6bo5b3o36b3o5bo6bo5b3o36b3o5bo6bo5b3o6b
3o5bo6bo5b3o6b3o5bo6bo5b3o38b3o5bo6bo5b3o34b3o5bo6bo5b3o36b3o5bo6bo5b
3o36b3o5bo6bo5b3o$29bo5bo2b6o2bo5bo42bo5bo2b6o2bo5bo35bo5bo2b6o2bo5bo
32bo5bo2b6o2bo5bo48bo5bo2b6o2bo5bo37bo5bo2b6o2bo5bo4bo5bo2b6o2bo5bo28b
o5bo2b6o2bo5bo31bo5bo2b6o2bo5bo6bo5bo2b6o2bo5bo36bo5bo2b6o2bo5bo36bo5b
o2b6o2bo5bo36bo5bo2b6o2bo5bo36bo5bo2b6o2bo5bo36bo5bo2b6o2bo5bo6bo5bo2b
6o2bo5bo6bo5bo2b6o2bo5bo38bo5bo2b6o2bo5bo34bo5bo2b6o2bo5bo36bo5bo2b6o
2bo5bo36bo5bo2b6o2bo5bo$34b4obo2bob4o52b4obo2bob4o45b4obo2bob4o42b4obo
2bob4o58b4obo2bob4o47b4obo2bob4o14b4obo2bob4o38b4obo2bob4o41b4obo2bob
4o16b4obo2bob4o46b4obo2bob4o46b4obo2bob4o46b4obo2bob4o46b4obo2bob4o46b
4obo2bob4o16b4obo2bob4o16b4obo2bob4o48b4obo2bob4o44b4obo2bob4o46b4obo
2bob4o46b4obo2bob4o2$30bo2bob4ob2ob4obo2bo47bob4ob2ob4obo40bo2bob4ob2o
b4obo2bo37bob4ob2ob4obo56bob4ob2ob4obo42bo2bob4ob2ob4obo2bo6bo2bob4ob
2ob4obo2bo30bo2bob4ob2ob4obo2bo36bob4ob2ob4obo14bob4ob2ob4obo44bob4ob
2ob4obo44bob4ob2ob4obo44bob4ob2ob4obo44bob4ob2ob4obo44bob4ob2ob4obo14b
ob4ob2ob4obo14bob4ob2ob4obo46bob4ob2ob4obo42bob4ob2ob4obo44bob4ob2ob4o
bo44bob4ob2ob4obo$30b4obo2bo4bo2bob4o41b2o2b3obo2bo4bo2bob3o2b2o34b4ob
o2bo4bo2bob4o35b3obo2b2o2b2o2bob3o48b2o2b3obo2bo4bo2bob3o2b2o36b4obo2b
o4bo2bob4o6b4obo2bo4bo2bob4o30b4obo2bo4bo2bob4o34b3obo2b2o2b2o2bob3o
10b3obo2b2o2b2o2bob3o40b3obo2b2o2b2o2bob3o40b3obo2b2o2b2o2bob3o40b3obo
2b2o2b2o2bob3o40b3obo2b2o2b2o2bob3o40b3obo2b2o2b2o2bob3o10b3obo2b2o2b
2o2bob3o10b3obo2b2o2b2o2bob3o38b2o2b3obo2bo4bo2bob3o2b2o34b3obo2b2o2b
2o2bob3o40b3obo2b2o2b2o2bob3o40b3obo2b2o2b2o2bob3o$36bob2o2b2obo47bo2b
o5bob2o2b2obo5bo2bo40bob2o2b2obo40bo5b2o6b2o5bo47bo2bo5bob2o2b2obo5bo
2bo42bob2o2b2obo18bob2o2b2obo42bob2o2b2obo39bo5b2o6b2o5bo8bo5b2o6b2o5b
o38bo5b2o6b2o5bo38bo5b2o6b2o5bo38bo5b2o6b2o5bo38bo5b2o6b2o5bo38bo5b2o
6b2o5bo8bo5b2o6b2o5bo8bo5b2o6b2o5bo37bo2bo5bob2o2b2obo5bo2bo33bo5b2o6b
2o5bo38bo5b2o6b2o5bo38bo5b2o6b2o5bo$32b3obo8bob3o44bobob3obo8bob3obobo
37b3obo8bob3o37bob2obo8bob2obo49bobob3obo8bob3obobo39b3obo8bob3o10b3ob
o8bob3o34b3obo8bob3o36bob2obo8bob2obo10bob2obo8bob2obo40bob2obo8bob2ob
o40bob2obo8bob2obo40bob2obo8bob2obo40bob2obo8bob2obo40bob2obo8bob2obo
10bob2obo8bob2obo10bob2obo8bob2obo39bobob3obo8bob3obobo35bob2obo8bob2o
bo40bob2obo8bob2obo40bob2obo8bob2obo$28b2obobobo2bo4bo2bobobob2o41bobo
bobo2bo4bo2bobobobo34b2obobobo2bo4bo2bobobob2o34b2o2bob2o2b2obo2b2o51b
obobobo2bo4bo2bobobobo36b2obobobo2bo4bo2bobobob2o2b2obobobo2bo4bo2bobo
bob2o26b2obobobo2bo4bo2bobobob2o33b2o2bob2o2b2obo2b2o12b2o2bob2o2b2obo
2b2o42b2o2bob2o2b2obo2b2o42b2o2bob2o2b2obo2b2o42b2o2bob2o2b2obo2b2o42b
2o2bob2o2b2obo2b2o42b2o2bob2o2b2obo2b2o12b2o2bob2o2b2obo2b2o12b2o2bob
2o2b2obo2b2o41bobobobo2bo4bo2bobobobo37b2o2bob2o2b2obo2b2o42b2o2bob2o
2b2obo2b2o42b2o2bob2o2b2obo2b2o$29bobo4bobo4bobo4bobo44bo4bobo4bobo4bo
37bobo4bobo4bobo4bobo38bob3o2b3obo56bo4bobo4bobo4bo39bobo4bobo4bobo4bo
bo4bobo4bobo4bobo4bobo28bobo4bobo4bobo4bobo37bob3o2b3obo18bob3o2b3obo
48bob3o2b3obo48bob3o2b3obo48bob3o2b3obo48bob3o2b3obo48bob3o2b3obo18bob
3o2b3obo18bob3o2b3obo46bo4bobo4bobo4bo42bob3o2b3obo48bob3o2b3obo48bob
3o2b3obo$28bo2b2o3b2ob4ob2o3b2o2bo43b2o3b2ob4ob2o3b2o36bo2b2o3b2ob4ob
2o3b2o2bo34b2obo4b2o4bob2o53b2o3b2ob4ob2o3b2o38bo2b2o3b2ob4ob2o3b2o2bo
2bo2b2o3b2ob4ob2o3b2o2bo26bo2b2o3b2ob4ob2o3b2o2bo33b2obo4b2o4bob2o12b
2obo4b2o4bob2o42b2obo4b2o4bob2o42b2obo4b2o4bob2o42b2obo4b2o4bob2o42b2o
bo4b2o4bob2o42b2obo4b2o4bob2o12b2obo4b2o4bob2o12b2obo4b2o4bob2o43b2o3b
2ob4ob2o3b2o39b2obo4b2o4bob2o42b2obo4b2o4bob2o42b2obo4b2o4bob2o$28b2o
9bo2bo9b2o51bo2bo44b2o9bo2bo9b2o34bobobob6obobobo61bo2bo46b2o9bo2bo9b
2o2b2o9bo2bo9b2o26b2o9bo2bo9b2o32bo2bobob6obobo2bo10bo2bobob6obobo2bo
40bo2bobob6obobo2bo40bo2bobob6obobo2bo40bo2bobob6obobo2bo40bo2bobob6ob
obo2bo40bo2bobob6obobo2bo10bo2bobob6obobo2bo10bo2bobob6obobo2bo50bo2bo
46bo2bobob6obobo2bo40bo2bobob6obobo2bo41bobobob6obobobo$35bo3bo2bo3bo
54bo3bo2bo3bo47bo3bo2bo3bo43bobo3b2o3bobo59bo3bo2bo3bo49bo3bo2bo3bo16b
o3bo2bo3bo40bo3bo2bo3bo39b2obobo3b2o3bobob2o10b2obobo3b2o3bobob2o40b2o
bobo3b2o3bobob2o40b2obobo3b2o3bobob2o40b2obobo3b2o3bobob2o40b2obobo3b
2o3bobob2o40b2obobo3b2o3bobob2o10b2obobo3b2o3bobob2o10b2obobo3b2o3bobo
b2o46bo3bo2bo3bo42b2obobo3b2o3bobob2o40b2obobo3b2o3bobob2o43bobo3b2o3b
obo$40b2o64b2o57b2o48bo3b6o3bo64b2o59b2o26b2o50b2o47bo3b6o3bo16bo3b6o
3bo46bo3b6o3bo46bo3b6o3bo46bo3b6o3bo46bo3b6o3bo46bo3b6o3bo16bo3b6o3bo
16bo3b6o3bo54b2o50bo3b6o3bo46bo3b6o3bo46bo3b6o3bo$34bobo2bo2bo2bobo52b
obo2bo2bo2bobo45bobo2bo2bo2bobo39b2ob2o2b2o2b2o2b2ob2o55bobo2bo2bo2bob
o47bobo2bo2bo2bobo14bobo2bo2bo2bobo38bobo2bo2bo2bobo41b2o2b2o2b2o2b2o
16b2o2b2o2b2o2b2o46b2o2b2o2b2o2b2o46b2o2b2o2b2o2b2o46b2o2b2o2b2o2b2o
46b2o2b2o2b2o2b2o46b2o2b2o2b2o2b2o16b2o2b2o2b2o2b2o16b2o2b2o2b2o2b2o
48bobo2bo2bo2bobo44b2o2b2o2b2o2b2o46b2o2b2o2b2o2b2o44bob2o2b2o2b2o2b2o
bo$36b4o2b4o56b4o2b4o49b4o2b4o41bobo14bobo57b4o2b4o51b4o2b4o18b4o2b4o
42b4o2b4o41b2o14b2o12b2o14b2o42b2o14b2o42b2o14b2o42b2o14b2o42b2o14b2o
42b2o14b2o12b2o14b2o12b2o14b2o48b4o2b4o44b2o14b2o42b2o14b2o41bobo14bob
o$34bo3bo4bo3bo52bo3bo4bo3bo45bo3bo4bo3bo41bob2ob2o2b2ob2obo57bo3bo4bo
3bo47bo3bo4bo3bo14bo3bo4bo3bo38bo3bo4bo3bo40bob2ob2o2b2ob2obo14bob2ob
2o2b2ob2obo44bob2ob2o2b2ob2obo44bob2ob2o2b2ob2obo44bob2ob2o2b2ob2obo
44bob2ob2o2b2ob2obo44bob2ob2o2b2ob2obo14bob2ob2o2b2ob2obo14bob2ob2o2b
2ob2obo47bo3bo4bo3bo43bob2ob2o2b2ob2obo44bob2ob2o2b2ob2obo42bobob2ob2o
2b2ob2obobo$33bo4bo4bo4bo50bo4bo4bo4bo43bo4bo4bo4bo40bob2ob6ob2obo56bo
4bo4bo4bo45bo4bo4bo4bo12bo4bo4bo4bo36bo4bo4bo4bo39bob2ob6ob2obo14bob2o
b6ob2obo44bob2ob6ob2obo44bob2ob6ob2obo44bob2ob6ob2obo44bob2ob6ob2obo
44bob2ob6ob2obo14bob2ob6ob2obo14bob2ob6ob2obo46bo4bo4bo4bo42bob2ob6ob
2obo44bob2ob6ob2obo41b2obob2ob6ob2obob2o$32bo5b2o2b2o5bo48bo5b2o2b2o5b
o41bo5b2o2b2o5bo36b2obob2o3b2o3b2obob2o52bo5b2o2b2o5bo43bo5b2o2b2o5bo
10bo5b2o2b2o5bo34bo5b2o2b2o5bo35b2obob2o3b2o3b2obob2o8b2obob2o3b2o3b2o
bob2o38b2obob2o3b2o3b2obob2o38b2obob2o3b2o3b2obob2o38b2obob2o3b2o3b2ob
ob2o38b2obob2o3b2o3b2obob2o38b2obob2o3b2o3b2obob2o8b2obob2o3b2o3b2obob
2o8b2obob2o3b2o3b2obob2o42bo5b2o2b2o5bo38b2obob2o3b2o3b2obob2o38b2obob
2o3b2o3b2obob2o41bob2o3b2o3b2obo$33b2obo2bo2bo2bob2o50b2obo2bo2bo2bob
2o43b2obo2bo2bo2bob2o38bobobo10bobobo54b2obo2bo2bo2bob2o45b2obo2bo2bo
2bob2o12b2obo2bo2bo2bob2o36b2obo2bo2bo2bob2o37bobobo10bobobo10bobobo
10bobobo40bobobo10bobobo40bobobo10bobobo40bobobo10bobobo40bobobo10bobo
bo40bobobo10bobobo10bobobo10bobobo10bobobo10bobobo44b2obo2bo2bo2bob2o
40bobobo10bobobo40bobobo10bobobo42bobo10bobo$37b2o4b2o58b2o4b2o51b2o4b
2o42bobob2obo4bob2obobo58b2o4b2o53b2o4b2o20b2o4b2o44b2o4b2o41bobob2obo
4bob2obobo10bobob2obo4bob2obobo40bobob2obo4bob2obobo40bobob2obo4bob2ob
obo40bobob2obo4bob2obobo40bobob2obo4bob2obobo40bobob2obo4bob2obobo10bo
bob2obo4bob2obobo10bobob2obo4bob2obobo48b2o4b2o44bobob2obo4bob2obobo
40bobob2obo4bob2obobo40bobob2obo4bob2obobo$38bob2obo60bob2obo53bob2obo
44bobo4bo2bo4bobo60bob2obo55bob2obo22bob2obo46bob2obo43bobo4bo2bo4bobo
12bobo4bo2bo4bobo42bobo4bo2bo4bobo42bobo4bo2bo4bobo42bobo4bo2bo4bobo
42bobo4bo2bo4bobo42bobo4bo2bo4bobo12bobo4bo2bo4bobo12bobo4bo2bo4bobo
50bob2obo46bobo4bo2bo4bobo42bobo4bo2bo4bobo41b2obo4bo2bo4bob2o$37bobo
2bobo58bobo2bobo51bobo2bobo45bo2b8o2bo61bobo2bobo53bobo2bobo20bobo2bob
o44bobo2bobo44bo2b8o2bo16bo2b8o2bo46bo2b8o2bo46bo2b8o2bo46bo2b8o2bo46b
o2b8o2bo46bo2b8o2bo16bo2b8o2bo16bo2b8o2bo51bobo2bobo47bo2b8o2bo46bo2b
8o2bo46bo2b8o2bo$35b4o4b4o54b4o4b4o47b4o4b4o43bobobo4bobobo59b4o4b4o
49b4o4b4o16b4o4b4o40b4o4b4o42bobobo4bobobo16bobobo4bobobo46bobobo4bobo
bo46bobobo4bobobo46bobobo4bobobo46bobobo4bobobo46bobobo4bobobo16bobobo
4bobobo16bobobo4bobobo49b4o4b4o45bobobo4bobobo46bobobo4bobobo46bobobo
4bobobo$35b2o2bo2bo2b2o54b2o2bo2bo2b2o47b2o2bo2bo2b2o42b2o2bo6bo2b2o
58b2o2bo2bo2b2o49b2o2bo2bo2b2o16b2o2bo2bo2b2o40b2o2bo2bo2b2o41b2o2bo6b
o2b2o14b2o2bo6bo2b2o44b2o2bo6bo2b2o44b2o2bo6bo2b2o44b2o2bo6bo2b2o44b2o
2bo6bo2b2o44b2o2bo6bo2b2o14b2o2bo6bo2b2o14b2o2bo6bo2b2o48b2o2bo2bo2b2o
44b2o2bo6bo2b2o44b2o2bo6bo2b2o44b2o2bo6bo2b2o$34bo2b2o4b2o2bo52bo2b2o
4b2o2bo45bo2b2o4b2o2bo40bo2b2ob2o2b2ob2o2bo56bo2b2o4b2o2bo47bo2b2o4b2o
2bo14bo2b2o4b2o2bo38bo2b2o4b2o2bo39bo2b2ob2o2b2ob2o2bo12bo2b2ob2o2b2ob
2o2bo42bo2b2ob2o2b2ob2o2bo42bo2b2ob2o2b2ob2o2bo42bo2b2ob2o2b2ob2o2bo
42bo2b2ob2o2b2ob2o2bo42bo2b2ob2o2b2ob2o2bo12bo2b2ob2o2b2ob2o2bo12bo2b
2ob2o2b2ob2o2bo46bo2b2o4b2o2bo42bo2b2ob2o2b2ob2o2bo42bo2b2ob2o2b2ob2o
2bo42bo2b2ob2o2b2ob2o2bo$33b3o2bo4bo2b3o50b3o2bo4bo2b3o43b3o2bo4bo2b3o
39b3obobo4bobob3o55b3o2bo4bo2b3o45b3o2bo4bo2b3o12b3o2bo4bo2b3o36b3o2bo
4bo2b3o38b3obobo4bobob3o12b3obobo4bobob3o42b3obobo4bobob3o42b3obobo4bo
bob3o42b3obobo4bobob3o42b3obobo4bobob3o42b3obobo4bobob3o12b3obobo4bobo
b3o12b3obobo4bobob3o45b3o2bo4bo2b3o41b3obobo4bobob3o42b3obobo4bobob3o
42b3obobo4bobob3o$33b2o12b2o50b2o12b2o43b2o12b2o42bo10bo58b2o12b2o45b
2o12b2o12b2o12b2o36b2o12b2o41bo10bo18bo10bo48bo10bo48bo10bo48bo10bo48b
o10bo48bo10bo18bo10bo18bo10bo48b2o12b2o44bo10bo48bo10bo48bo10bo$31b2ob
3o8b3ob2o46b2ob3o8b3ob2o39b2ob3o8b3ob2o37b2o2bobo4bobo2b2o53b2ob3o8b3o
b2o41b2ob3o8b3ob2o8b2ob3o8b3ob2o32b2ob3o8b3ob2o36b2o2bobo4bobo2b2o12b
2o2bobo4bobo2b2o42b2o2bobo4bobo2b2o42b2o2bobo4bobo2b2o42b2o2bobo4bobo
2b2o42b2o2bobo4bobo2b2o42b2o2bobo4bobo2b2o12b2o2bobo4bobo2b2o12b2o2bob
o4bobo2b2o43b2ob3o8b3ob2o39b2o2bobo4bobo2b2o42b2o2bobo4bobo2b2o42b2o2b
obo4bobo2b2o$31bo2b2ob2o4b2ob2o2bo46bo2b2ob2o4b2ob2o2bo39bo2b2ob2o4b2o
b2o2bo37bo16bo53bo2b2ob2o4b2ob2o2bo41bo2b2ob2o4b2ob2o2bo8bo2b2ob2o4b2o
b2o2bo32bo2b2ob2o4b2ob2o2bo36bo16bo12bo16bo42bo16bo42bo16bo42bo16bo42b
o16bo42bo16bo12bo16bo12bo16bo43bo2b2ob2o4b2ob2o2bo39bo16bo42bo16bo42bo
16bo$29bobo2b2o2b2o2b2o2b2o2bobo42bobo2b2o2b2o2b2o2b2o2bobo35bobo2b2o
2b2o2b2o2b2o2bobo32b2obo4bo6bo4bob2o48bobo2b2o2b2o2b2o2b2o2bobo37bobo
2b2o2b2o2b2o2b2o2bobo4bobo2b2o2b2o2b2o2b2o2bobo28bobo2b2o2b2o2b2o2b2o
2bobo32bobo3bo8bo3bobo7b2obo4bo6bo4bob2o37bobo3bo8bo3bobo38bobo3bo8bo
3bobo38bobo3bo8bo3bobo38bobo3bo8bo3bobo38bobo3bo8bo3bobo8bobo3bo8bo3bo
bo8bobo3bo8bo3bobo39bobo2b2o2b2o2b2o2b2o2bobo35bobo3bo8bo3bobo38bobo3b
o8bo3bobo38bobo3bo8bo3bobo$29b2o4b2obo4bob2o4b2o42b2o4b2obo4bob2o4b2o
35b2o4b2obo4bob2o4b2o32b2ob2o4bo4bo4b2ob2o48b2o4b2obo4bob2o4b2o37b2o4b
2obo4bob2o4b2o4b2o4b2obo4bob2o4b2o28b2o4b2obo4bob2o4b2o32b2o4b3o4b3o4b
2o7b2ob2o4bo4bo4b2ob2o37b2o4b3o4b3o4b2o38b2o4b3o4b3o4b2o38b2o4b3o4b3o
4b2o38b2o4b3o4b3o4b2o38b2o4b3o4b3o4b2o8b2o4b3o4b3o4b2o8b2o4b3o4b3o4b2o
39b2o4b2obo4bob2o4b2o35b2o4b3o4b3o4b2o38b2o4b3o4b3o4b2o38b2o4b3o4b3o4b
2o$36bob2o2b2obo56bob2o2b2obo49bob2o2b2obo42bo4bo6bo4bo58bob2o2b2obo
51bob2o2b2obo18bob2o2b2obo42bob2o2b2obo47b2o2b2o18bo4bo6bo4bo48b2o2b2o
54b2o2b2o54b2o2b2o54b2o2b2o54b2o2b2o24b2o2b2o24b2o2b2o54bob2o2b2obo50b
2o2b2o54b2o2b2o54b2o2b2o$34bobob2o2b2obobo52bobob2o2b2obobo45bobob2o2b
2obobo40bo3bo8bo3bo56bobob2o2b2obobo47bobob2o2b2obobo14bobob2o2b2obobo
38bobob2o2b2obobo69bo3bo8bo3bo406bobob2o2b2obobo$33bobo10bobo50bobo10b
obo43bobo10bobo38b2ob2obo6bob2ob2o51b2obobo10bobob2o42bobo10bobo12bobo
10bobo36bobo10bobo39b2obo2bo2bo2bob2o12b2ob2obo6bob2ob2o42b2obo2bo2bo
2bob2o44b2obo2bo2bo2bob2o44b2obo2bo2bo2bob2o44b2obo2bo2bo2bob2o44b2obo
2bo2bo2bob2o14b2obo2bo2bo2bob2o14b2obo2bo2bo2bob2o46bobo10bobo42b2obo
2bo2bo2bob2o44b2obo2bo2bo2bob2o44b2obo2bo2bo2bob2o$33bo2b3o4b3o2bo50bo
2b3o4b3o2bo43bo2b3o4b3o2bo37bo2bo4bo4bo4bo2bo50bob2o2b3o4b3o2b2obo42bo
2b3o4b3o2bo12bo2b3o4b3o2bo36bo2b3o4b3o2bo39bo14bo11bo2bo4bo4bo4bo2bo
41bo14bo44bo14bo44bo14bo44bo14bo44bo14bo14bo14bo14bo14bo46bo2b3o4b3o2b
o42bo14bo44bo14bo44bo14bo$32b2o5bo2bo5b2o48b2o5bo2bo5b2o41b2o5bo2bo5b
2o37bo2b5o4b5o2bo55bobo2bo2bo2bobo44b2obobo2bo2bo2bobob2o9b2o5bo2bo5b
2o33b2obobo2bo2bo2bobob2o38b4obo2bob4o13bo2b5o4b5o2bo43b4obo2bob4o46b
4obo2bob4o46b4obo2bob4o46b4obo2bob4o46b4obo2bob4o16b4obo2bob4o16b4obo
2bob4o46b2o5bo2bo5b2o42b4obo2bob4o46b4obo2bob4o46b4obo2bob4o$36b2obo2b
ob2o56b2obo2bob2o44bo4b2obo2bob2o4bo37b2o4bo4bo4b2o56bo2bobo2bobo2bo
43bobobo2bobo2bobo2bobobo12b2obo2bob2o38bobo2bobo2bobo2bobo36b3o5b4o5b
3o11b2o4bo4bo4b2o41b3o5b4o5b3o40b3o5b4o5b3o40b3o5b4o5b3o40b3o5b4o5b3o
40b3o5b4o5b3o10b3o5b4o5b3o10b3o5b4o5b3o47b2obo2bob2o43b3o5b4o5b3o40b3o
5b4o5b3o48b4o$26bo8bobo6bobo8bo45bobo6bobo37b2o4bo3bobo6bobo3bo4b2o33b
4o6b4o59bobo6bobo45bo3bobo6bobo3bo12bobo6bobo36bo2b2obo6bob2o2bo34bo2b
ob4o4b4obo2bo12b4o6b4o42bo2bob4o4b4obo2bo38bo2bob4o4b4obo2bo38bo2bob4o
4b4obo2bo38bo2bob4o4b4obo2bo38bo2bob4o4b4obo2bo8bo2bob4o4b4obo2bo8bo2b
ob4o4b4obo2bo45bobo6bobo41bo2bob4o4b4obo2bo38bo2bob4o4b4obo2bo42b5o4b
5o$24b3o3b2o3bobob4obobo3b2o3b3o33bobo7bobob4obobo7bobo28bo2b2o4bobob
4obobo4b2o2bo30b4o14b4o56bo8bo51bo8bo17bo10bo37b2o2bo8bo2b2o35b2obobo
2bob2obo2bobob2o8b4o14b4o38b2obobo2bob2obo2bobob2o38b2obobo2bob2obo2bo
bob2o38b2obobo2bob2obo2bobob2o38b2obobo2bob2obo2bobob2o38b2obobo2bob2o
bo2bobob2o8b2obobo2bob2obo2bobob2o8b2obobo2bob2obo2bobob2o45bobob4obob
o41b2obobo2bob2obo2bobob2o38b2obobo2bob2obo2bobob2o41bobo2bob2obo2bobo
$23bo6bo2bobo2bo4bo2bobo2bo6bo32b2obo3b2obo2bo4bo2bob2o3bob2o28bobo2b
3obo2bo4bo2bob3o2bobo30bo3b3o3b2o3b3o3bo57b3o2b3o53b3o2b3o17b2o2bo4bo
2b2o38bobobo4bobobo40bo3b2ob2ob2o3bo11bo3b3o3b2o3b3o3bo41bo3b2ob2ob2o
3bo44bo3b2ob2ob2o3bo44bo3b2ob2ob2o3bo44bo3b2ob2ob2o3bo44bo3b2ob2ob2o3b
o14bo3b2ob2ob2o3bo14bo3b2ob2ob2o3bo43bob2obo2bo4bo2bob2obo39bo3b2ob2ob
2o3bo44bo3b2ob2ob2o3bo44bo3b2ob2ob2o3bo$23bo2b3obob2obo4b2o4bob2obob3o
2bo35bo4bobo4b2o4bobo4bo30b2ob3o2bobo4b2o4bobo2b3ob2o32bo3bo2b2o2bo3bo
57b3o2b4o2b3o47b3o2b4o2b3o12bo2bobob4obobo2bo36bobob2o2b2obobo40bo2b2o
6b2o2bo14bo3bo2b2o2bo3bo44bo2b2o6b2o2bo44bo2b2o6b2o2bo44bo2b2o6b2o2bo
44bo2b2o6b2o2bo44bo2b2o6b2o2bo14bo2b2o6b2o2bo14bo2b2o6b2o2bo43b2obobo
4b2o4bobob2o39bo2b2o6b2o2bo44bo2b2o6b2o2bo41b2obo2b2o6b2o2bob2o$20b2ob
obo2bobo2bo2b4o2b4o2bo2bobo2bobob2o29b3ob2o2bo2b4o2b4o2bo2b2ob3o33bobo
2b4o2b4o2bobo38b3obo6bob3o56bo2bob2o2b2obo2bo45bo2bob2o2b2obo2bo11b2o
3bo6bo3b2o33b2obobob2o2b2obobob2o34b2obob3ob4ob3obob2o11b3obo6bob3o41b
2obob3ob4ob3obob2o38b2obob3ob4ob3obob2o38b2obob3ob4ob3obob2o38b2obob3o
b4ob3obob2o38b2obob3ob4ob3obob2o8b2obob3ob4ob3obob2o8b2obob3ob4ob3obob
2o43bo2b4o2b4o2bo39b2obob3ob4ob3obob2o38b2obob3ob4ob3obob2o37bobobob3o
b4ob3obobobo$20bo2bobo5bobo6b2o6bobo5bobo2bo28bo4bobobo6bo7bobobo4bo
26b4o2bobo7bo6bobo2b4o35bob6obo59b2obobob2obobob2o45b2obobob2obobob2o
15b2o6b2o37bo2b2ob3o2b3ob2o2bo34b2obob2o3b2o3b2obob2o9b2o3bob6obo3b2o
39b2obob2o3b2o3b2obob2o38b2obob2o3b2o3b2obob2o38b2obob2o3b2o3b2obob2o
38b2obob2o3b2o3b2obob2o38b2obob2o3b2o3b2obob2o8b2obob2o3b2o3b2obob2o8b
2obob2o3b2o3b2obob2o43bo6b2o6bo39b2obob2o3b2o3b2obob2o38b2obob2o3b2o3b
2obob2o37bobobob2o3b2o3b2obobobo$21b2o4b3obobob5o2b5obobob3o4b2o29b2o
3bobobob5ob6obobobo3b2o26bo5bobob6ob5obobo5bo32b3o2bo4bo2b3o59bobo4bob
o49bobobo4bobobo17b3o2b3o40bo5bo2bo5bo39bo5b4o5bo11bo2b3o2bo4bo2b3o2bo
41bo5b4o5bo44bo5b4o5bo44bo5b4o5bo44bo5b4o5bo44bo5b4o5bo14bo5b4o5bo14bo
5b4o5bo47b2ob2o4b2ob2o43bo5b4o5bo44bo5b4o5bo41bo2bo5b4o5bo2bo$23b4o3b
2o7bo2bo7b2o3b4o36b3o7bo10b3o32b6o8bo9b6o33bo2bobob2obobo2bo59bo2bo2bo
2bo48bo2bo2bo2bo2bo2bo17b2o2b2o40b2ob3obo2bob3ob2o38b2o2bo6bo2b2o12bob
o2bobob2obobo2bobo42b2o2bo6bo2b2o44b2o2bo6bo2b2o44b2o2bo6bo2b2o44b2o2b
o6bo2b2o44b2o2bo6bo2b2o14b2o2bo6bo2b2o14b2o2bo6bo2b2o49b2o6b2o45b2o2bo
6bo2b2o44b2o2bo6bo2b2o44b2o2bo6bo2b2o$23bo3bo4b7o4b7o4bo3bo31b4obo2b6o
bo3b7o2bob4o33b6o2bo3b6o40bo3bob2obo3bo58b2o10b2o46b3o10b3o14bo2bo4bo
2bo35bo2bobo2b2o2b2o2bobo2bo37bo2bo6bo2bo12b2o2bo3bob2obo3bo2b2o42bo2b
o6bo2bo46bo2bo6bo2bo46bo2bo6bo2bo46bo2bo6bo2bo46bo2bo6bo2bo16bo2bo6bo
2bo16bo2bo6bo2bo48b2o10b2o44bo2bo6bo2bo46bo2bo6bo2bo46bo2bo6bo2bo$24b
3o2bobo18bobo2b3o32bo3bo2bo5b2o4bo6bo2bo3bo27b3obobo5bob2obo5bobob3o
32bobobobo4bobobobo55bo2b10o2bo48b10o15b3o3b4o3b3o33b2obo2b2o6b2o2bob
2o34b3o14b3o11bobobobo4bobobobo41b3o14b3o40b3o14b3o40b3o14b3o40b3o14b
3o40b3o14b3o10b3o14b3o10b3o14b3o45bo3b2o2b2o3bo41b3o14b3o40b3o14b3o40b
3o14b3o$26bob2ob2ob2ob2o4b2ob2ob2ob2obo35bo2bobob3o11b4obobo2bo27bo4bo
bo2b4o2bob4o2bobo4bo30bobo2b2ob2obob2o2bobo54bobo2bo4bo2bobo47bo2bo4bo
2bo13bo4b8o4bo35b2obo8bob2o37bo2b3o3b2o3b3o2bo11bobob2ob4ob2obobo41bo
2b3o3b2o3b3o2bo40bo2b3o3b2o3b3o2bo40bo2b3o3b2o3b3o2bo40bo2b3o3b2o3b3o
2bo40bo2b3o3b2o3b3o2bo10bo2b3o3b2o3b3o2bo10bo2b3o3b2o3b3o2bo42b2obo3b
6o3bob2o38bo2b3o3b2o3b3o2bo40bo2b3o3b2o3b3o2bo40bo2b3o3b2o3b3o2bo$26bo
2bobo3bobo6bobo3bobo2bo34b2o3b2obo2bo10bo2bob2o3b2o27bobobobo6bo2bo6bo
bobobo31bo2b2o3bob2o3b2o2bo52b2o2b3obo2bob3o2b2o45b3obo2bob3o13bo2b2ob
o4bob2o2bo35bo2bobo4bobo2bo38b2o4bo4bo4b2o9b2obo2bo3bo2bo3bo2bob2o39b
2o4bo4bo4b2o42b2o4bo4bo4b2o42b2o4bo4bo4b2o42b2o4bo4bo4b2o42b2o4bo4bo4b
2o12b2o4bo4bo4b2o12b2o4bo4bo4b2o43bo2b2o2bo4bo2b2o2bo39b2o4bo4bo4b2o
42b2o4bo4bo4b2o42b2o4bo4bo4b2o$27b2o2bo3bobo6bobo3bo2b2o42bo2b2o14bo
35b2obo2b3ob2o4b2ob3o2bob2o33b2o2b2obo4b2o2b2o52bo2b2o3bo4bo3b2o2bo42b
2o3bo4bo3b2o10b2obo3bo4bo3bob2o36bobobo2bobobo42b2ob2o4b2ob2o12bobo3b
2o6b2o3bobo42b2ob2o4b2ob2o46b2ob2o4b2ob2o46b2ob2o4b2ob2o46b2ob2o4b2ob
2o46b2ob2o4b2ob2o16b2ob2o4b2ob2o16b2ob2o4b2ob2o46b2o3b2o4b2o3b2o42b2ob
2o4b2ob2o46b2ob2o4b2ob2o46b2ob2o4b2ob2o$31b2o3bo8bo3b2o43bobo20bobo36b
2o2bobo6bobo2b2o34b3o2bo3bobob2o3bo2b3o50b2o2b5o2b5o2b2o42bo2b5o2b5o2b
o12bobobo4bobobo35b5obo6bob5o38bo3bo4bo3bo12bob2o4b6o4b2obo42bo3bo4bo
3bo46bo3bo4bo3bo46bo3bo4bo3bo46bo3bo4bo3bo46bo3bo4bo3bo16bo3bo4bo3bo
16bo3bo4bo3bo49b3o6b3o45bo3bo4bo3bo46bo3bo4bo3bo46bo3bo4bo3bo$94b2o22b
2o37bobo2bo6bo2bobo35bo2bobob2o2b2o2b2obobo2bo52bobo10bobo45bobo10bobo
10b2obo2bo2b2o2bo2bob2o31bo8b4o8bo38b4o4b4o14bo2bo2bo6bo2bo2bo44b4o4b
4o48b4o4b4o48b4o4b4o48b4o4b4o48b4o4b4o18b4o4b4o18b4o4b4o47b3o3bo4bo3b
3o43b4o4b4o48b4o4b4o48b4o4b4o$157bo2b2o8b2o2bo37b2obo3b2o3bo3bob2o54bo
2bobob2obobo2bo44b2o2bobob2obobo2b2o10bob5o4b5obo33bob2ob2obo2bob2ob2o
bo36b3o4b4o4b3o12bobo2b2ob2ob2o2bobo42b3o4b4o4b3o42b3o4b4o4b3o42b3o4b
4o4b3o42b3o4b4o4b3o42b3o4b4o4b3o12b3o4b4o4b3o12b3o4b4o4b3o44bo2bobobo
2bobobo2bo40b3o4b4o4b3o42b3o4b4o4b3o42b3o4b4o4b3o$156b2o16b2o38b5o3b2o
b5o57bobo8bobo47bobo8bobo12bo5b2o2b2o5bo32b2obo3bo6bo3bob2o35bo2bo2b6o
2bo2bo11b2ob2o2bob2obo2b2ob2o41bo2bo2b6o2bo2bo42bo2bo2b6o2bo2bo42bo2bo
2b6o2bo2bo42bo2bo2b6o2bo2bo42bo2bo2b6o2bo2bo12bo2bo2b6o2bo2bo12bo2bo2b
6o2bo2bo45bobo10bobo41bo2bo2b6o2bo2bo42bo2bo2b6o2bo2bo42bo2bo2b6o2bo2b
o$212b2o4bo4bobo4b2o54b2obobo4bobob2o46bobobo4bobobo13b5o2b2o2b5o36bo
4bo4bo4bo41bobo6bobo78bobo6bobo48bobo6bobo48bobo6bobo48bobo6bobo48bobo
6bobo18bobo6bobo18bobo6bobo47b2obobo6bobob2o43bobo6bobo48bobo6bobo48bo
bo6bobo$212bo4bo5bo2bo4bo57bobo4bobo48b2obobo4bobob2o64b3obo6bob3o42bo
bo4bobo80bobo4bobo50bobo4bobo50bobo4bobo50bobo4bobo50bobo4bobo20bobo4b
obo20bobo4bobo49bo5b4o5bo45bobo4bobo50bobo4bobo50bobo4bobo$214bo2bobo
4bobo2bo59bobo4bobo48bo2bobo4bobo2bo14b3o6b3o41bobob2obobo48bo2bo26b4o
56bo2bo56bo2bo56bo2bo56bo2bo56bo2bo26bo2bo26bo2bo52bo4bob2obo4bo48bo2b
o56bo2bo56bo2bo$213b2o3b2o5bo3b2o57b2obo4bob2o49b2obo4bob2o16bo2b2o2b
2o2bo36b4obob2o2b2obob4o38b5ob2ob5o76b5ob2ob5o46b5ob2ob5o46b5ob2ob5o
46b5ob2ob5o46b5ob2ob5o16b5ob2ob5o16b5ob2ob5o48b3obob2obob3o44b5ob2ob5o
46b5ob2ob5o46b5ob2ob5o$375bobobo6bobobo34bo2bo4bo2bo4bo2bo37bo4b2o2b2o
4bo15b2obo6bob2o45bo4b2o2b2o4bo44bo4b2o2b2o4bo44bo4b2o2b2o4bo44bo4b2o
2b2o4bo44bo4b2o2b2o4bo14bo4b2o2b2o4bo14bo4b2o2b2o4bo53b2o49bo4b2o2b2o
4bo44bo4b2o2b2o4bo44bo4b2o2b2o4bo$288b2o8b2o49b2o8b2o13bob2o2bo4bo2b2o
bo37b2o2bo2bo2b2o41b2o2bo6bo2b2o15bo12bo45b2o2bo6bo2b2o44b2o2bo6bo2b2o
44b2o2bo6bo2b2o44b2o2bo6bo2b2o44b2o2bo6bo2b2o14b2o2bo6bo2b2o14b2o2bo6b
o2b2o43b2obob4o4b4obob2o39b2o2bo6bo2b2o44b2o2bo6bo2b2o44b2o2bo6bo2b2o$
288bo10bo49bo10bo13bo3bo8bo3bo39bo6bo75b3obo2bob3o405bob2obo10bob2obo$
286bobo2bo4bo2bobo45bobo2bo4bo2bobo12b2obobo4bobob2o36b3o10b3o43bo6bo
82bo6bo52bo6bo52bo6bo52bo6bo52bo6bo22bo6bo22bo6bo53b2ob4ob2o49bo6bo52b
o6bo52bo6bo$286b2o4b4o4b2o45b2o4b4o4b2o14bobobo2bobobo38bo2b2o6b2o2bo
42bobo4bobo19b5o2b5o49bobo4bobo50bobo4bobo50bobo4bobo50bobo4bobo50bobo
4bobo20bobo4bobo20bobo4bobo53bobo2bobo49bobo4bobo50bobo4bobo50bobo4bob
o$293b2o59b2o21bobobo2bobobo39bo12bo46bo2bo22bo10bo52bo2bo56bo2bo56bo
2bo56bo2bo56bo2bo26bo2bo26bo2bo56bob4obo52bo2bo56bo2bo56bo2bo$292b4o
58b2o18b2ob2ob6ob2ob2o34bob5ob2ob5obo41bo2bo2bo2bo16b2obo2b6o2bob2o49b
o2bo53bo2bo2bo2bo50bo2bo2bo2bo50bo2bo2bo2bo53bo2bo26bo2bo23bo2bo2bo2bo
51bobobo2bobobo47bo2bo2bo2bo50bo2bo2bo2bo50bo2bo2bo2bo$291b2o2b2o52b2o
3bo19bobo12bobo33bobo4b2o2b2o4bobo66b2obobo6bobob2o406bobobob2obobobo$
292bo2bo53bo3bobo21b12o36bo2b3obo4bob3o2bo40bo8bo19bobobo2bobobo51bo4b
o52bo8bo50bo8bo50bo8bo52bo4bo24bo4bo22bo8bo49bo2bobo4bobo2bo45bo8bo50b
o8bo50bo8bo$289b3o4b3o51bo3bobo25b2o42bobo12bobo37b2obo2b2o2b2o2bob2o
15bobob4obobo50bobo2bobo50bo2b2o2b2o2bo48bo2b2o2b2o2bo45b2obo2b2o2b2o
2bob2o47bobo2bobo22bobo2bobo20bo2b2o2b2o2bo49b3o2bo2bo2b3o45bo2b2o2b2o
2bo48bo2b2o2b2o2bo48bo2b2o2b2o2bo$289bo8bo52bo4bo22b2o4b2o38b2o2bob2o
4b2obo2b2o37bobo3bo2bo3bobo15b2obob4obob2o50b2o2b2o51bo3bo2bo3bo48bo3b
o2bo3bo46bobo3bo2bo3bobo49b2o2b2o24b2o2b2o21bo3bo2bo3bo52bo6bo48bo3bo
2bo3bo48bo3bo2bo3bo48bo3bo2bo3bo$348b3o5b2o21bo6bo40bobobo6bobobo38bo
2bobo6bobo2bo16bobo4bobo106b2obobo6bobob2o43bobobo6bobobo43bo2bobo6bob
o2bo103bobobo6bobobo47b4o6b4o43bobobo6bobobo43b2obobo6bobob2o43bobobo
6bobobo$348bo31bo4bo41bobobobo2bobobobo38b3obob6obob3o16bobo4bobo52bo
4bo48bobobob6obobobo42bobobob6obobobo42b3obob6obob3o48bo4bo24bo4bo18bo
bobob6obobobo46bo3b2o2b2o3bo42bobobob6obobobo42bobobob6obobobo42bobobo
b6obobobo$379b2o4b2o41bo3b2o2b2o3bo43bo3b2o3bo18b2o10b2o47b2o8b2o47bob
o3b2o3bobo44bobobo3b2o3bobobo46bo3b2o3bo49b2o8b2o18b2o8b2o15bobobo3b2o
3bobobo47b2o2bo2bo2b2o44bo2bo3b2o3bo2bo45bobo3b2o3bobo45bo2bo3b2o3bo2b
o$483b2ob2o4b2ob2o14bo2bobob4obobo2bo44bob4o2b4obo46bo2b2o4b2o2bo45bob
ob2o4b2obobo45b2ob2o4b2ob2o46bob4o2b4obo16bob4o2b4obo15bo3b2o4b2o3bo
45b3o3bob2obo3b3o42b2ob2o4b2ob2o46bo2b2o4b2o2bo46b2ob2o4b2ob2o$484bo2b
o4bo2bo15b2obobob4obobob2o44bo4bo2bo4bo47b2o2bo2bo2b2o48bo2bo4bo2bo48b
o2bo4bo2bo47bo4bo2bo4bo16bo4bo2bo4bo16b3o2bo2bo2b3o46bo2b3o6b3o2bo43bo
2bo4bo2bo48b2o2bo2bo2b2o48bo2bo4bo2bo$483bo2bob4obo2bo17bobobo2bobobo
48b4ob2ob4o45b3o2b2o4b2o2b3o44bo2bob4obo2bo46bo2bob4obo2bo47b2obob2obo
b2o18b2obob2obob2o20bo6bo50b2o12b2o43bo2bob4obo2bo49bo6bo49bo2bob4obo
2bo$483b2obobo2bobob2o17bobo6bobo46bobo2bo4bo2bobo43bo2bobo6bobo2bo44b
2obobo2bobob2o46b2obobo2bobob2o42b2obobob2o4b2obobob2o8b2obobob2o4b2ob
obob2o10b4obob4obob4o47b4o4b4o45b2obobo2bobob2o49bob4obo49b2obobo2bobo
b2o$486bobo2bobo18b2obob6obob2o44b2o4bo2bo4b2o46bo2bob2obo2bo50bobo2bo
bo52bobo2bobo45bob2obo3bo2bo3bob2obo8bob2obo3bo2bo3bob2obo10bo2bobobo
2bobobo2bo45b2o2b2o4b2o2b2o46bobo2bobo46b2ob2obobo2bobob2ob2o46bobo2bo
bo$483b2obob4obob2o15bo2bo8bo2bo51b2o51bob2ob6ob2obo45b2obob4obob2o46b
2obob4obob2o48b2o2b2o2b2o20b2o2b2o2b2o21bo6bo49bo2b2o8b2o2bo40b4obob4o
bob4o42bobob2o6b2obobo42b4obob4obob4o$482bob3o6b3obo16bobobo2bobobo
105bobo2bo6bo2bobo43bob3o6b3obo44bob3o6b3obo42b4obo8bob4o10b4obo8bob4o
14bo2bo4bo2bo48b2o2bo6bo2b2o41bo2bob2o4b2obo2bo41bo2bo2bobo2bobo2bo2bo
41bo2bob2o4b2obo2bo$482bo14bo15b2obob4obob2o104bo2b3obo2bob3o2bo43bo
14bo44bo14bo42bo2bobo8bobo2bo10bo2bobo8bobo2bo12b4obo4bob4o48bob2o4b2o
bo102b2o2b2o2bo2bo2b2o2b2o$483b4o6b4o18bo8bo49bo12bo44b2o12b2o45b4o6b
4o46b4o6b4o48b2o6b2o20b2o6b2o16bo4bo6bo4bo47bo10bo47b2obo2bob2o52bo4bo
52b2obo2bob2o$485bobo4bobo20bobo4bobo48bobo10bobo45bob2o4b2obo49bobo4b
obo50bobo4bobo49bo2b2o2b2o2bo18bo2b2o2b2o2bo15bo2b2o8b2o2bo44b2obo4b2o
4bob2o46b6o51b2obob2obob2o51b6o$480b2o16b2o14b2o8b2o47bo2bo8bo2bo45bob
2o4b2obo168b5o2b5o18b5o2b5o12b2obobobo2bo2bo2bobobob2o41bo2b2o8b2o2bo
101bo2bobob2obobo2bo$480bobo3b2ob2ob2o3bobo13bo2b3o2b3o2bo45b2obob8obo
b2o41b2obo10bob2o47b2ob2ob2o52b2ob2ob2o48b2o4bo2bo4b2o14b2o4bo2bo4b2o
10bob2obo4b4o4bob2obo42b2o2b2o4b2o2b2o47b6o49b2obobob2obobob2o49b6o$
482bo2bobo4bobo2bo15bobo2bo2bo2bobo45bo2b12o2bo41b2ob2o8b2ob2o46bobo4b
obo50bobo4bobo46bo2bobobo2bobobo2bo12bo2bobobo2bobobo2bo13bobo3bo2bo3b
obo48b2ob2o2b2ob2o47b2obo2bob2o50bobo4bobo50b2obo2bob2o$481b2obobo6bob
ob2o12b2o2b3o4b3o2b2o45bo3b6o3bo46bob2o4b2obo48bobo6bobo48bobo6bobo45b
2obo10bob2o12b2obo10bob2o13bobo3b4o3bobo48bo3b4o3bo104b2obobob2obobob
2o$480bo3bob2o4b2obo3bo10bobobo2bo4bo2bobobo45b3o6b3o47bo2bo4bo2bo49bo
8bo48bobo3b2o3bobo45bobo10bobo14bobo10bobo12b2o2b5o2b5o2b2o47bobob2obo
bo44bo2bob2o4b2obo2bo43bo2bobob2obobo2bo43bo2bob2o4b2obo2bo$481bobo2bo
bo2bobo2bobo11bobo2b2o6b2o2bobo47bo6bo46b2obo10bob2o104bo12bo44bo2bobo
bo2bobobo2bo12bo2bobobo2bobobo2bo12bobo2bobo2bobo2bobo45b3o2bo4bo2b3o
41b4obob4obob4o45b2obob2obob2o45b4obob4obob4o$480b2ob2obob4obob2ob2o
11bobobo8bobobo46b2o3b2o3b2o44bo2b2o8b2o2bo42b2o14b2o42b2ob4o4b4ob2o
43b2o4bo2bo4b2o12bob2o4bo2bo4b2obo10bo2b3obo4bob3o2bo43bo3b2o6b2o3bo
45bobo2bobo53bo4bo53bobo2bobo$484bob2o4b2obo16bo2bo8bo2bo47bo3bo2bo3bo
45b2o12b2o43bo2b2o8b2o2bo43bobob2o4b2obobo46b5o2b5o15bo2b5o2b5o2bo11bo
bo3bobo2bobo3bobo42bobobo10bobobo41b2obobo2bobob2o43b2o2b2o2bo2bo2b2o
2b2o43b2obobo2bobob2o$484bo4b2o4bo17b2o10b2o46bobo4b2o4bobo45b2o8b2o
46bobo2b2o2b2o2bobo44bobo4b2o4bobo46bo2b2o2b2o2bo16bobo2b2o2b2o2bobo
11b2ob2ob2obo2bob2ob2ob2o41bobob3o6b3obobo41bo2bob4obo2bo43bo2bo2bobo
2bobo2bo2bo43bo2bob4obo2bo$483b2ob3o2b3ob2o76b2o12b2o45bo10bo45b2obobo
b4obobob2o42b2obob2o4b2obob2o46b2o6b2o16b2o2b2o6b2o2b2o17bobo2bobo49b
2o4b2o2b2o4b2o43bo2bo4bo2bo45bobob2o6b2obobo45bo2bo4bo2bo$485bo2bo2bo
2bo140bo8bo50b2o6b2o45bo2bobobo4bobobo2bo43bobo8bobo16bobo8bobo19bo6bo
51b2obob4obob2o44b2ob2o4b2ob2o43b2ob2obobo2bobob2ob2o43b2ob2o4b2ob2o$
485bobo4bobo139b2o8b2o51b2o2b2o48bobobo8bobobo42b3obo8bob3o14bobo8bobo
16b2obobo2bobob2o48bo2bo6bo2bo46bo3b2o3bo51bob4obo48bo2bo3b2o3bo2bo$
486bo6bo203bo2bobo49bo2bo8bo2bo42bo4b2o6b2o4bo14bo3bo2bo3bo17b2obob4ob
ob2o46bobob2o6b2obobo44bob6obo51bo6bo47bobobob6obobobo$698b2o55b2o6b2o
45bobobo3bo2bo3bobobo15b4o2b4o22bo4bo50b2o2bo8bo2b2o45bo6bo50b2o2bo2bo
2b2o46bobobo6bobobo$811b2ob2ob2o2b2ob2ob2o49bo2bo55bobo4bobo51bo2bo51b
o2b2o4b2o2bo47bo3bo2bo3bo$847b2o2b2o24b2o2b2o55b2o4b2o50bob4obo49bobo
3b2o3bobo47bo2b2o2b2o2bo$847b2o2b2o142bobo4bobo47b2obob6obob2o47bo8bo$
995bo2bo2bo2bo51bo6bo$996b2o4b2o54bo2bo53bo2bo2bo2bo$1056bob4obo54bo2b
o$1055bobo4bobo50bobo4bobo$1055bo2bo2bo2bo51bo6bo$1056b2o4b2o$1112b2o
2bo6bo2b2o$1112bo4b2o2b2o4bo$1113b5ob2ob5o$1118bo2bo$1115bobo4bobo$
1114bobo6bobo$1111bo2bo2b6o2bo2bo$1111b3o4b4o4b3o$1114b4o4b4o$1113bo3b
o4bo3bo$1113b2ob2o4b2ob2o$1111b2o4bo4bo4b2o$1110bo2b3o3b2o3b3o2bo$
1110b3o14b3o$1113bo2bo6bo2bo$1112b2o2bo6bo2b2o$1109bo2bo5b4o5bo2bo$
1108bobobob2o3b2o3b2obobobo$1108bobobob3ob4ob3obobobo$1109b2obo2b2o6b
2o2bob2o$1112bo3b2ob2ob2o3bo$1112bobo2bob2obo2bobo$1113b5o4b5o$1118b4o
$1113b4obo2bob4o$1112bo14bo$1112b2obo2bo2bo2bob2o2$1117b2o2b2o$1109b2o
4b3o4b3o4b2o$1109bobo3bo8bo3bobo$1111bo16bo$1111b2o2bobo4bobo2b2o$
1114bo10bo$1111b3obobo4bobob3o$1111bo2b2ob2o2b2ob2o2bo$1112b2o2bo6bo2b
2o$1113bobobo4bobobo$1113bo2b8o2bo$1110b2obo4bo2bo4bob2o$1110bobob2obo
4bob2obobo$1112bobo10bobo$1112bob2o3b2o3b2obo$1109b2obob2ob6ob2obob2o$
1110bobob2ob2o2b2ob2obobo$1110bobo14bobo$1111bob2o2b2o2b2o2b2obo$1113b
o3b6o3bo$1113bobo3b2o3bobo$1111bobobob6obobobo$1111b2obo4b2o4bob2o$
1114bob3o2b3obo$1111b2o2bob2o2b2obo2b2o$1110bob2obo8bob2obo$1109bo5b2o
6b2o5bo$1110b3obo2b2o2b2o2bob3o$1112bob4ob2ob4obo2$1113b4obo2bob4o$
1108bo5bo2b6o2bo5bo$1108b3o5bo6bo5b3o$1111bo4bob4obo4bo$1110bo2bo2bo6b
o2bo2bo$1108bo2b3o2bo2b2o2bo2b3o2bo$1108b3o5bo6bo5b3o$1111bo16bo$1110b
o2bobob2o2b2obobo2bo$1110b4ob2o6b2ob4o$1115bo8bo$1112b3o4b2o4b3o$1112b
o2b2o2b2o2b2o2bo$1113bo3b2o2b2o3bo$1116bobo2bobo$1117b2o2b2o$1117bo4bo
$1117bo4bo2$1117bo4bo$1119b2o!

Edit 2: I have realized that the 6 triangles approach comes at the cost of translations and now I'm sad.

[Citation needed]

Nikro found a semi-natural 1CPG in my rule Calthrops with ikpx2:
https://catagolue.hatsya.com/census/b2n ... _stdin/yl1

Code: Select all

x = 0, y = 0, rule = B2n3ainy4aijqyz5einy6aci7e/S23-ajkq4cjkrwy5jk6-en7c
3bob3o$2b3ob2o$bo8bo$2o2bo4b2o$bobo$o6bobobo$2o4b5obo$2o3b2o4bo$6b
obo5b3o$3bob2o2b2ob2obo$2b2o2bo2b4obo$5bobo2b4o$6bo2b3o$9bobo$8bob
o$8b2o$8bo!

It's obviously not semi-natural. By the way, are you interested in calculators?

[H. H. P. M. P. Cole]

Do not overwork yourself. If you do so you will fail to see the world beyond your "line": whether it is your profession, your career, your studies, or something else.

Code: Select all

x = 56, y = 28, rule = R3,C2,S2,B3,N+
4obo3bo36bo3bob4o$9bo36bo$2bo4bobo36bobo4bo$9bo36bo$o54bo$9bo36bo$o54b
o$obo4bo40bo4bobo$o54bo$o3bob4o36b4obo3bo4$9bo2b3o3$bo52bo$3b3o5bo32b
o5b3o2$5bo4bo34bo4bo$10bo34bo$8bobo34bobo$bobo48bobo$bo52bo$bo4bo42bo
4bo2$o5b3o38b3o5bo$10bo34bo!

Instead, turn your life in an unexpected direction. Who knows what that will give you?

Code: Select all

x = 26, y = 8, rule = R3,C2,S2,B3,N+
o2b3o4$22bo$25bo$22bo$25bo!

[confocaloid]

I think it should be possible to find a two-state isotropic CA with stable technology for the factorial spaceship (reflectors, shifters, duplicators) but that would "look artificial and arbitrary". Not sure how much is possible with "simple" rules.

edit (unrelated):

I don’t know how Corderman managed to corderize the switch engine, and if it would be even possible to corderize such a messy puffer, [...]

Related post, unfortunately some images appear to be missing/broken:
https://cp4space.hatsya.com/2025/03/18/ ... -computer/ "Charles Corderman’s computer"

[islptng]

Depends on your definition of 'fun' I guess, there are certainly cases when people prefer to do it by hand and eye and sometimes regex. For example, it can be very helpful to follow some algorithm with paper and pencil, instead of immediately trying to code it as a program. Life is about understanding and "doing things by hand" often leads to better understanding of how it works.

I, being the creator of the script, disagree with that.

I like to program, and I think doing the same thing over and over is never interesting and I prefer to write a script even if that takes more time than doing by hand.

Also, writing a script saves time, since doing the same thing again by hand will take more time than just running a script directly.

[confocaloid]

Of course it can be helpful to write a script, when you already understand what the script should do and how it should work. When you already understand the problem and when you already see an implementable algorithm for solving it, coding it makes sense.

My point was different. It can be helpful to think more about a problem, in order to gain better deeper understanding. It can be helpful to "do it by hand and eye", even if you could just run some script or use a calculator, because "doing it by hand and eye" will help you understand a given topic.

Pushing buttons, without understanding what you're really doing, can (and usually does) lead to all kinds of errors/mistakes/fallacies.

Depends on your definition of 'fun' I guess, there are certainly cases when people prefer to do it by hand and eye and sometimes regex. For example, it can be very helpful to follow some algorithm with paper and pencil, instead of immediately trying to code it as a program. Life is about understanding and "doing things by hand" often leads to better understanding of how it works.

I, being the creator of the script, disagree with that.

I like to program, and I think doing the same thing over and over is never interesting and I prefer to write a script even if that takes more time than doing by hand.

Also, writing a script saves time, since doing the same thing again by hand will take more time than just running a script directly.

[b-engine]

Terms in most problematic sandbox threads:

"Ban": not actual ban, but to "exclude" someone from a thread for some reason. This won't actually work and only cause more conflicts. A type of abuse.

I think these only exist in roleplay threads:
"Zeration": an "antagonist" that could "possess" patterns using the 15th state of LifeSuper. I don't know how is it on-topic, and why it was even introduced at the first place. Another similar antagonist is "Ice monster".
"Dimensions": "alternative" RLEs, often in different CA rules, where some different events could happen. "Portals" are apparently linked to "dimensions", but doesn't actually do anything.
"Fork": described as a "different timeline". Usually a result of a conflict or abuse.
"'94470589!": I had tried to save the old storytelling thread by removing an antagonist called "corruption", but unname4798 renames it to '94470589! and continue. I don't see how this is related to CA.


I'm still trying to find more problematic terms. Anyone could help me?
(Uh, maybe it's me who had caused the sandbox to descend into chaos?)

[Aleph]

"'94470589!": I had tried to save the old storytelling thread by removing an antagonist called "corruption", but unname4798 renames it to '94470589! and continue.

Please tell me how this is problematic. Trying to cut out Mysterious Fragments is a very difficult process, requiring me to put in a lot of thought and effort to make a single post. I have even posted my notes at least once to demonstrate this.