Challenges

A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.
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dvgrn
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Re: Challenges

Post by dvgrn » May 23rd, 2020, 10:13 pm

otismo wrote:
April 23rd, 2020, 4:23 pm
This "Mystery" Pattern is in my collection
...
@ Adam P. Goucher, what is it - I give up...
Wait, don't give up so easily! I bet someone here can figure out the mystery (previously posted here) pretty quickly, especially with these optional hints:

Code: Select all















The input seems to be 12 bits encoded as incoming gliders from the NE, on the right.

The output seems to be 24 bits encoded as outgoing NW-ward gliders, on the left side.

Code: Select all















Assume that the input is a binary number read from left to right, and
the output is also a binary number read from top to bottom.

What could it be doing that converts 12 bits into 24 bits?
Is it taking the square of the input number?

Try putting in "000000000001" (just one rightmost glider as input)
and see if you get "000000000000000000000001" as output.

Code: Select all















Okay, it's not squaring the number.

Calculate the numbers that "000000000001" and "000000000010" produce, converted to decimal.

That's an integer sequence... a short one, but good enough for an identifying fingerprint!

Look it up on https://oeis.org/
and then
test the resulting hypothesis by feeding in a few more binary inputs.

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toroidalet
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Re: Challenges

Post by toroidalet » May 24th, 2020, 3:34 pm

It seems to be some sort of error-correcting code on 12 bits (a Hamming code?). The original message can be recovered if there are one or probably even 2 errors (EDIT: the Hamming distance between codewords is 8, so it can correct errors of up to 3 bits and detect 4-bit errors).
Any sufficiently advanced software is indistinguishable from malice.

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Re: Challenges

Post by dvgrn » May 24th, 2020, 5:08 pm

Hunting wrote:
April 23rd, 2020, 12:56 pm
dvgrn wrote:
April 23rd, 2020, 11:59 am
Then again, why not make the self-documenting pattern a little more readable? I can dig out the code I used to make that unimpressive length-13055 cyclical sample, if anyone is interested in adapting it.
Or the RLE, or the apgcode, etc. There are just too many ways to represent a constellation.
This reminded me to go back and find the script I was running a couple of years ago to try and find a self-documenting Life pattern.
census_permute_v1.4.zip
(12.97 KiB) Downloaded 172 times
The closest I've come so far is this pattern, which gets a score of 6 where the ideal score is zero:

Code: Select all

x = 117, y = 47, rule = B3/S23
5obo3bob3o2b4o5b4o3b3o2b5ob5ob5ob4o2bo3bob2o2b4o6b3o3b4obo3bo$2bo3bo3b
o2bo2bo9bo3bobo3bo3bo5bo3bo5bo3bobo3bo2bobo9bo3bobo5bo3bo$2bo3bo3bo2bo
2bo9bo3bobo3bo3bo5bo3bo5bo3bob2o2bobo2bo9bo3bobo5bo3bo$2bo3b5o2bo3b3o
6b4o2bo3bo3bo5bo3b4o2b4o2bobobo5b3o6bo3bo2b3o2b5o$2bo3bo3bo2bo6bo5bo5b
5o3bo5bo3bo5bobo3bo2b2o8bo5b5o5bobo3bo$2bo3bo3bo2bo6bo5bo5bo3bo3bo5bo
3bo5bo2bo2bo3bo8bo5bo3bo5bobo3bo$2bo3bo3bob3ob4o6bo5bo3bo3bo5bo3b5obo
3bobo3bo4b4o6bo3bob4o2bo3bo4$b3o3b3o2bo3bob5o2b3o2b3obo3bo2b4o6b2o3b2o
6b4o2b5ob5obo3bob3obo3bob5o2b4o$o3bobo3bobo3bo3bo3bo3bo2bo2bo3bobo9bo
2bobo2bo5bo3bobo5bo5bo3bo2bo2bo3bobo5bo$o5bo3bob2o2bo3bo3bo3bo2bo2b2o
2bobo12bo4bo5bo3bobo5bo5bo3bo2bo2bo3bobo5bo$o5bo3bobobobo3bo3bo3bo2bo
2bobobo2b3o8bo4bo6b4o2b4o2b4o2b5o2bo2bo3bob4o3b3o$o5bo3bobo2b2o3bo3b5o
2bo2bo2b2o5bo6bo4bo7bo3bobo5bo5bo3bo2bo2bo3bobo9bo$o3bobo3bobo3bo3bo3b
o3bo2bo2bo3bo5bo5bo4bo8bo3bobo5bo5bo3bo2bo3bobo2bo9bob2o$b3o3b3o2bo3bo
3bo3bo3bob3obo3bob4o6b4ob4o5b4o2b5ob5obo3bob3o3bo3b5ob4o3bo$110bo3$3o
7b4obo3bob3ob4o3b4o9b3o6b3o2bo5b3ob3o3b5ob4o3b4o$3bo5bo5bo3bo2bo2bo3bo
bo12bo8bo3bobo6bo2bo2bo2bo5bo3bobo$3bo5bo5bo3bo2bo2bo3bobo12bo8bo5bo6b
o2bo3bobo5bo3bobo$b2o7b3o2b5o2bo2b4o3b3o9b3o6bob3obo6bo2bo3bob4o2b4o3b
3o$3bo9bobo3bo2bo2bo9bo8bo2bo5bo3bobo6bo2bo3bobo5bobo7bo$3bo9bobo3bo2b
o2bo9bob2o5bo2bo5bo3bobo6bo2bo2bo2bo5bo2bo6bob2o$3o6b4o2bo3bob3obo5b4o
3bo6b2o7b4ob5ob3ob3o3b5obo3bob4o3bo$37bo55bo3$4o5bo6b3o3b3o2bo3bob5o2b
4o8bo2bo2b2o6b4o2bo5b3obo3bobo3bob5ob4o3b4o$3bo5bo5bo3bobo3bobo3bobo5b
o12bo2bobo2bo5bo3bobo6bo2bo3bobo2bo2bo5bo3bobo$2bo6bo5bo3bobo3bobo3bob
o5bo12bo2bobo2bo5bo3bobo6bo2b2o2bobobo3bo5bo3bobo$2bo6bo5bo3bobo3bobo
3bob4o3b3o9b4obo2bo5b4o2bo6bo2bobobob2o4b4o2b4o3b3o$bo7bo5bo3bob5obo3b
obo9bo11bobo2bo5bo3bobo6bo2bo2b2obobo3bo5bobo7bo$bo7bo5bo3bobo3bo2bobo
2bo9bob2o8bobo2bo5bo3bobo6bo2bo3bobo2bo2bo5bo2bo6bob2o$bo7b5o2b3o2bo3b
o3bo3b5ob4o3bo8bo2b2o6b4o2b5ob3obo3bobo3bob5obo3bob4o3bo$45bo66bo3$4o
5b4o3b3o3b3o2b5o2b4o6b3o2bo3bob3o7b3o3b2o6b4o2bo6b3o3b3o2bo3bo2b4o$3bo
5bo3bobo3bobo3bo3bo3bo9bo3bobo3bobo2bo9bobo2bo5bo3bobo5bo3bobo3bobo2bo
2bo$2bo6bo3bobo3bobo3bo3bo3bo9bo3bob2o2bobo3bo8bobo2bo5bo3bobo5bo3bobo
5bobo3bo$2bo6b4o2bo3bobo3bo3bo4b3o6bo3bobobobobo3bo6b2o3b3o5b4o2bo5bo
3bobo5b2o5b3o$bo7bo3bobo3bob5o3bo7bo5b5obo2b2obo3bo8bo4bo5bo3bobo5bo3b
obo5bobo7bo$bo7bo3bobo3bobo3bo3bo7bo5bo3bobo3bobo2bo9bo4bo5bo3bobo5bo
3bobo3bobo2bo6bob2o$bo7b4o3b3o2bo3bo3bo3b4o6bo3bobo3bob3o7b3o2b3o6b4o
2b5o2b3o3b3o2bo3bob4o2b2o!
The pattern really does produce seven loaves, 40 blinkers, and 22 beehives, but its self-prediction is one off on number of ponds, ships, boats, tubs, gliders, and blocks. The score is the sum of the squares of the difference between actual object counts and predicted object counts, with "unknown cell" being a catchall kind of defined object whenever rare stuff pops up.

The average number of tubs and ponds in each final constellation for a sentence of this size (with seven objects listed) is a little bit over 1. The idea here was to try a search run with a shorter sentence, which produces less ash on average. I'll probably go back to including "1 tub, 1 pond" in the next round of searches, since that prediction is more likely to be correct... even though it also increases the average count of all the other object types slightly, and thus makes it a little less likely that any given prediction will actually come true.

Operator's Manual
I won't spend too much time documenting the script, since the right thing to do next is probably to rewrite it using lifelib to get it running an order of magnitude or two faster. But if anyone wants to try running it, the key points are

1) replace text.py in your copy of Golly, in Scripts/Python/glife/, with the version in the archive.
2) Maybe think of some unique wording for the beginning or end of the sentence, so you're guaranteed not to be running a search I've already tried. Change the standardtext variable appropriately.
3) First temporarily set the countfirstN variable to 1000 or 10000 or something, to find out what the average counts are for each still life being named.
4) Once you have those averages (they're copied to the clipboard when the cycle count hits countfirstN) ... set countfirstN back to 0, set up appropriate search ranges for each variable in the minimaltarget dictionary, and re-run the script.

The script reports the count of population matches in the status bar, the average distance between population matches, and the best score seen so far for patterns with a population match. (If the final ash's population doesn't match the target population, the script doesn't bother doing a slow census of the final ash, since it can't possibly be right anyway.)

The script runs through all permutations of the objects listed in the minimaltarget dictionary, and all the sizes of spaces between words implied by the setting of the maxspace variable, and all the object counts between the minimum and maximum values given in the minimaltarget dictionary. The script can go through several million candidates a day, but the number of permutations can quickly get up into the millions, so set ranges accordingly. If you want to stop a search before all permutations have been tested, hit the "k" key.

These Are A Few Of The Changeable Things
Other things that could be permuted include
  • The text wrap width, currently hard-coded to 144 in the addnewlines() call. Text that's roughly as tall as it is wide seems to produce the least ash. However, it's possible that text with no wrap might have much lower standard deviations on its object counts, in which case it might be possible to target the average count more precisely and get a correct self-documenting sentence sooner.
    -- It doesn't seem worth trying every possible wrap width, though, since some wrap-width changes don't actually result in a different pattern.
  • Distance between lines. Currently this is hard-coded in the "width" of a newline character in text.py, so it would take some more serious fiddling around with the script to make this adjustable.
  • Justification. Text is currently left-justified, but maybe it would look better centered.
  • Presence or absence of a comma before the final "and".
  • Custom adjustment of spaces between individual words. Not sure I like this option, though, because the pattern then can't be regenerated just by knowing the words in its text. A self-documenting sentence like that wouldn't necessarily be invalid, but it seems like a short step to just adding a bunch of gliders and still lifes to the initial pattern, to make the count come out exactly right -- and that does seem like cheating.

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EvinZL
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Re: Challenges

Post by EvinZL » May 29th, 2020, 8:08 pm

Related to self-describing pattern: make a self describing apgcode. "xp0_nogliders" works but its kind of cheating

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Re: Challenges

Post by Saka » May 30th, 2020, 12:03 am

EvinZL wrote:
May 29th, 2020, 8:08 pm
Related to self-describing pattern: make a self describing apgcode. "xp0_nogliders" works but its kind of cheating
Does xp0_blinker work?
I didn't find this, I remembered this from another thread, but I forgot where...

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Re: Challenges

Post by Moosey » June 9th, 2020, 8:08 pm

Find a c/137 in a nontotalistic rule which contains two pis and two rs
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Re: Challenges

Post by Hdjensofjfnen » July 13th, 2020, 12:44 pm

Saka wrote:
May 30th, 2020, 12:03 am
EvinZL wrote:
May 29th, 2020, 8:08 pm
Related to self-describing pattern: make a self describing apgcode. "xp0_nogliders" works but its kind of cheating
Does xp0_blinker work?
I didn't find this, I remembered this from another thread, but I forgot where...
After xp0_blinker, there are no more apgcodes in which a stable object's name yields the original object, let alone yield it cleanly. I did this a while ago and got to xp0_cismirroredrbee before giving up.

Code: Select all

x = 5, y = 9, rule = B3-jqr/S01c2-in3
3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo!

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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Re: Challenges

Post by Moosey » July 14th, 2020, 3:04 pm

Trivial counterexample:
name a large still life the apgcode of itself (perhaps with an additional spark).

For instance, name xs33_259e0ehu0uhe0e96 "259e0ehu0uhe0e96z1". x0_259e0ehu0uhe0e96z1 stabilizes into a so-called 259e0ehu0uhe0e96z1.
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Re: Challenges

Post by gameoflifemaniac » July 16th, 2020, 10:55 am

Make this in 3G

Code: Select all

x = 12, y = 13, rule = B3/S23
b2o$o2bo$obo$bo8$10b2o$10b2o!
I was so socially awkward in the past and it will haunt me for the rest of my life.

Code: Select all

b4o25bo$o29bo$b3o3b3o2bob2o2bob2o2bo3bobo$4bobo3bob2o2bob2o2bobo3bobo$
4bobo3bobo5bo5bo3bobo$o3bobo3bobo5bo6b4o$b3o3b3o2bo5bo9bobo$24b4o!

wwei23

Re: Challenges

Post by wwei23 » September 1st, 2020, 6:11 pm

About that still life tree thing:

Code: Select all

x = 115, y = 95, rule = LifeHistory
11.A18.2A38.2A28.2A$10.A.A17.A.A37.A2.A26.A.A.A$11.A19.2A39.2A29.2A2$
11.D19.D40.D30.D$11.D19.D40.D30.D$9.D.D.D15.D.D.D36.D.D.D26.D.D.D$10.
3D17.3D38.3D28.3D$11.D19.D40.D30.D$D3.D.3D11.D3.D.3D62.D3.D.3D$2D2.D.
D.D2.A8.2D2.D.D.D.2AC3.2AC21.D3.D.3D3.C18.2D2.D.D.D3.C$D.D.D.D.D.A.BC
6.D.D.D.D.D.A.BC2.ACB21.2D2.D.D.D2.CBA17.D.D.D.D.D2.CBA$D2.2D.D.D2.AC
7.D2.2D.D.D2.2A4.2A21.D.D.D.D.D3.A2.A15.D2.2D.D.D3.A.A.A$D3.D.3D11.D
3.D.3D31.D2.2D.D.D5.2A15.D3.D.3D6.2A$60.D3.D.3D$78.C$71.ABC3.ABC23.2A
5.2A$71.AC.A2.A2.A21.CB.A.A2.BCA.A$73.2A4.2A22.C2.2A2.C2.2A$18.D.D.3D
.3D$18.D.D.D3.D3.2A$18.3D.3D.3D.A.A38.2A5.2A30.C$19.D2.D5.D2.ABC36.CB
2.A3.BC.A20.ABC4.ABC$19.D2.3D.3D3.C38.C.2A3.C.2A20.ACA.A2.A.A.A$105.
2A5.2A$32.D$32.D$30.D.D.D67.2AC4.2AC$31.3D68.A.BCA2.ACB.A$32.D72.2A5.
2A$70.2A.A$20.D3.D.3D3.C37.A.2A$20.2D2.D.D.D2.ABC3.ABC$20.D.D.D.D.D2.
A.A3.ACA20.D3.D.3D3.D$20.D2.2D.D.D3.A.A3.A.A19.2D2.D.D.D3.D$20.D3.D.
3D4.A5.A20.D.D.D.D.D.D.D.D$60.D2.2D.D.D2.3D$60.D3.D.3D3.D$31.2AC3.2AC
3.2A4.2A$31.A.BC2.ACB3.ACB3.A.BC19.C$32.A.A3.A.A3.ACA3.ACA18.CBA.A24.
2A$33.A5.A5.A5.A20.A.2A24.A.A$102.E$78.C23.2A$31.2A5.2A4.2A4.2A19.ABC
A2.ABCA$31.A.AC3.A.AC2.A.A3.A.AC17.AC2A2.A.2A21.D$32.A.BC3.ACB3.ACB3.
ACB48.D$33.A6.A5.AC4.A47.D.D.D$71.2A.A3.2A.A19.3D$70.CB.2A3.BC2A20.D$
18.D.D.3D.3D2.C39.C6.C$18.D.D.D3.D3.CBA57.D3.D.3D3.C$18.3D.3D.3D2.A.A
56.2D2.D.D.D2.ABC3.ABC$19.D2.D5.D3.A.A55.D.D.D.D.D2.A.A3.ACA$19.D2.3D
.3D4.A56.D2.2D.D.D4.A5.A$90.D3.D.3D4.2A4.2A$33.D$33.D$31.D.D.D65.2A5.
2A$32.3D65.CB.A4.BCA$33.D67.C.A4.C.A$103.2A5.2A$20.D3.D.3D4.C6.C$20.
2D2.D.D.D4.BC4.CB5.CB6.BC$20.D.D.D.D.D3.A.A4.A.A4.ACA4.ACA45.2AC3.2AC
$20.D2.2D.D.D4.A.A4.A.A4.A.A4.A.A44.A.BC2.ACB$20.D3.D.3D5.A.A4.A.A4.A
.A4.A.A45.A5.A$35.A6.A6.A6.A46.2A4.2A3$33.AC5.AC5.A6.A46.2A$32.A.BC3.
ACB4.ACB4.A.BC44.A.A$33.A.A4.A.A4.ACA4.ACA46.A$34.A.A4.A.A4.A.A4.A.A
44.CBA$35.A6.A6.A6.A46.C3$101.2A5.2A$101.A.A4.A.A$103.AC5.A$103.ABC4.
ABC$111.C9$88.D.D.3D.3D2.C$88.D.D.D3.D3.CBA$88.3D.3D.3D2.A.A$89.D2.D
5.D4.A$89.D2.3D.3D4.2A!
(I didn't bother with the tub with tail because that's a lot of branching possibilities to write down.)
(I skipped still lives that were in other trees.)

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Re: Challenges

Post by Moosey » September 6th, 2020, 8:44 am

Challlenge: find a rule where the SL from Snowflakes is common, but GoL's glider is supported (and you know, works like it would normally).
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Re: Challenges

Post by wwei23 » September 6th, 2020, 11:10 am

I don't think that's possible. The evolution of the snowflake from the 2-cell seed relies on B2c, but that kills the glider.

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Re: Challenges

Post by Moosey » September 6th, 2020, 3:34 pm

wwei23 wrote:
September 6th, 2020, 11:10 am
I don't think that's possible. The evolution of the snowflake from the 2-cell seed relies on B2c, but that kills the glider.
I didn't say it would have to evolve from a two-cell seed. I just said that that still life has to be common.
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Re: Challenges

Post by toroidalet » September 6th, 2020, 3:58 pm

Snowflake evolves from the traffic light in B3-qy4e/S23-c4yz, and is reasonably common:

Code: Select all

x = 3, y = 2, rule = B3-qy4e/S023-c4yz
3o$bo!
Bakery also evolves into a nice p2:

Code: Select all

x = 5, y = 5, rule = B3-qy4e/S023-c4yz
2b3o$bo2bo$o3bo$bobo$2bo!
Unsurprisingly, weird still lives are more common, but otherwise it's not too interesting.
Any sufficiently advanced software is indistinguishable from malice.

wwei23

Re: Challenges

Post by wwei23 » September 12th, 2020, 8:40 pm

Insert a switch engine into this gap to make it a spaceship. (I don't know if there is a solution or not.)

Code: Select all

x = 151, y = 151, rule = B3/S23
24b3o$24b3o$25bo$23b2o$23bo$8b2o14bo$8b2o3$25b2o$25b2o$25bo$9bo15bo$2o
5b2o15bobo$2o6bobo16bo$10bo11b2o2bo$10bo10bo3bo$8b2o12b2o$23bo2$11bo3b
o$10bo4bo$10bo4b2o15bo$12bo2bo15bobo$12bo2bo$12bobo15bo2bo$7b3o20b2o$
7bo22bo$8bo12$48bobo$51bo$47bo2bo$46b3o5$58bo$57bobo2$56bo2bo$56b2o$
56bo13$74bobo$77bo$73bo2bo$72b3o22$99bobo$102bo$98bo2bo$97b3o5$109bo$
108bobo2$107bo2bo$107b2o$107bo13$125bobo$128bo$124bo2bo$123b3o3$136bo$
135bobo2b2o7b2o$134bo3b4o6b3o$137bo7bobob2o$132b2obo10b2o$133bobo$134b
o5$128bo$126b5o$125bo2$125b3o$130bo$128b2o4b3o$124bo8bo4bo5b2o$122bobo
8bo2b2o6b2o$123b2o12bo6$136b2o$136b2o!

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Re: Challenges

Post by pzq_alex » August 6th, 2021, 11:17 pm

\sum_{n=1}^\infty H_n/n^2 = \zeta(3)

How much of current CA technology can I redevelop "on a desert island"?

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Re: Challenges

Post by ColorfulGabrielsp138 » August 7th, 2021, 12:59 am

pzq_alex wrote:
August 6th, 2021, 11:17 pm
https://catagolue.hatsya.com/object/xs0 ... lock/b3s23
makes exactly one block.
itisblock makes a clean block.
blinker is a clean blinker.

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

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Alexander Yu
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Re: Challenges

Post by Alexander Yu » September 29th, 2021, 5:45 pm

Find a still life (or oscillator) that will make multiple copies of itself if one cell is altered, and is also larger than this by bounding box:

I didn't find any yet, so it could be impossible...

Code: Select all

x = 8, y = 13, rule = B3/S23
6bo$5bobo$5bobo$6bo2$b2o$ob2o$b2o2$6bo$5bobo$5bobo$6bo!

hi.

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Re: Challenges

Post by Tropylium » September 30th, 2021, 5:17 pm

wwei23 wrote:
September 1st, 2020, 6:11 pm
About that still life tree thing:
Any corner-hook can be turned into a tub (the integral > integral with tub relationship), which means that a still life with N distinct hooks gives a tree with N layers and 2^N still lives (we will ignore still lifes with indistinguishable hooks, which give rise to symmetry complications out of Combinatorics Hell). Here are the 1st, 2nd and 5th layers of a 32-still-life tree:

Code: Select all

x = 94, y = 105, rule = B3/S23
28bo50bo$2o25bobo48bobo$o27bo50bo$b3o25b3o48b3o$4bo27bo50bo5bo$b3obo3b
2o18b3obo3b2o41b3obo3bobo$o4bo4bo17bo4bo4bo40bo4bo4bo$2o3bob3o11bo6b2o
3bob3o11bo22bo5bobo3bob3o$6bo15bo11bo15bo22bo5bo5bo$7bo27bo50bo5bo$4b
3obo3b2o3bobobo2bo7b3obo3b2o3bobobo2bo4bo2bo2bo4bobobo2bo7b3obo3bobo$
3bo4bo4bo17bo4bo4bo40bo4bo4bo$3b2o3bob3o9bo8b2o3bob3o9bo22bo7bobo3bob
3o$9bo11bo15bo11bo22bo9bo5bo$10bo27bo50bo$7b3o25b3o48b3o$6bo27bo50bo$
6b2o26b2o48bobo$12bo72bo$28b2o$13bo14bo$29b3o$14bo17bo5bo$29b3obo3bobo
$28bo4bo4bo$28b2o3bob3o$34bo$35bo$32b3obo3b2o$31bo4bo4bo$31b2o3bob3o$
37bo$38bo$35b3o$34bo$34b2o$28b2o$28bo$29b3o$32bo$29b3obo3b2o$28bo4bo4b
o$27bobo3bob3o$28bo5bo$35bo$32b3obo3b2o$31bo4bo4bo$31b2o3bob3o$37bo$
38bo$35b3o$34bo$34b2o$28b2o$28bo$29b3o$32bo$29b3obo3b2o$28bo4bo4bo$28b
2o3bob3o$34bo$35bo5bo$32b3obo3bobo$31bo4bo4bo$31b2o3bob3o$37bo$38bo$
35b3o$34bo$34b2o$28b2o$28bo$29b3o$32bo$29b3obo3b2o$28bo4bo4bo$28b2o3bo
b3o$34bo$35bo$32b3obo3b2o$31bo4bo4bo$30bobo3bob3o$31bo5bo$38bo$35b3o$
34bo$34b2o$28b2o$28bo$29b3o$32bo$29b3obo3b2o$28bo4bo4bo$28b2o3bob3o$
34bo$35bo$32b3obo3b2o$31bo4bo4bo$31b2o3bob3o$37bo$38bo$35b3o$34bo$33bo
bo$34bo!
hence there exist arbitrarily long still life trees.

True enough this is sort of unsatisfying insofar as it's just iterating one transformation over and over. We might be interested in how many versions of this there are that are that are different with regards to the 15-cell environment of the tree operation, and then ask how many different ones can occur in one tree. With regards to the environment of the parent stage, there seem to be 9 possible variants of which OP's initial tree covers 6:

Code: Select all

x = 61, y = 46, rule = LifeHistory
.5B2.5B$2B3.B.2B3.B$B4.B.B2.C.B$B2.C.B.B.C2.B$B4.B.B4.B$6B.6B2$.5B2.
5B4.5B2.5B4.5B2.5B4.5B2.5B$2B3.B.2B3.B3.2B3.B.2B3.B3.2B3.B.2B3.B3.2B
3.B.2B3.B$B2.B.B.B2.C.B3.B3.EB.B2.CEB3.B3.EB.B2.CEB3.B.E2.B.B.EC.B$B.
BCEB.B.C.EB3.B2.C.A.B.C2.A3.B2.C.A.B.C2.A3.B.FC.B.B.D2.B$B2.2EB.B2.2E
B3.B2.2EB.B2.2EB3.B.E.EB.B.E.EB3.B.E.EB.B.E.EB$6B.6B3.6B.6B3.3BA2B.3B
A2B3.6B.6B4$.5B2.5B4.5B2.5B4.5B2.5B4.5B2.5B$2B3.B.2B3.B3.2B3.B.2B3.B
3.2B3.B.2B3.B3.2B3.B.2B3.B$B4.B.B2.C.B3.B3.EB.B2.CEB3.B3.EB.B2.CEB3.B
.EF.B.B.ED.B$B2.CEB.B.C.EB3.B2.C.A.B.C2.A3.B2.C.A.B.C2.A3.B.FCEB.B.D.
EB$B2.E.A.B2.E.A3.B2.E.A.B2.E.A3.B.E2.A.B.E2.A3.B2.E.B.B2.E.B$4BAB.4B
AB3.4BAB.4BAB3.3B2AB.3B2AB3.6B.6B4$.5B2.5B9.5B5.5B12.5B2.5B$2B3.B.2B
3.B8.2B3.B4.2B3.B11.2B3.B.2B3.B$B3.EB.B2.CEB8.B4.B4.B2.C.B11.B2.FEB.B
2.DEB$B2.C.A.B.C2.A8.B2.CEB4.B.C.EB11.B2.CEB.B.C.EB$BA2.EB.BA2.EB8.BA
2.EB4.BA2.EB11.B4.B.B4.B$B3A2B.B3A2B8.B2ABAB2A2.B2ABAB2A9.6B.6B$25.A
2.A6.A2.A$.2A.A3.2A.A13.2A8.2A$.A.2A3.A.2A4$8.2A.A11.2A.A$8.A.2A11.A.
2A2$8.B3AB10.B3AB$7.BA3.A9.BA3.A$7.A.E2.A9.A.EC.A$7.A2.C.A.2A6.A.C2.A
.2A$4.2A.A3.EA.2A3.2A.A3.EA.2A$4.2A.2A4B6.2A.2A4B!
The variants at the right and a couple of similar ones are impossible to stabilize: the grey cells would require a neighbor for birth suppression in the parent still life, while in the child still life any such neighbor would leave the red cells overcrowded.

(I don't claim the stabilizations for the other 3 stable options to be minimal.)

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Re: Challenges

Post by breaker's glider gun » June 5th, 2022, 2:02 pm

Challange: make an RRO that is 1/3/4 fold.
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Re: Challenges

Post by Moosey » June 6th, 2022, 11:04 am

breaker's glider gun wrote:
June 5th, 2022, 2:02 pm
Challange: make an RRO that is 1/3/4 fold.
I'm not sure if this is even possible -- you can have a 1/3 fold rro, because two copies opposite each other might somehow interact, but rros that can be mn fold without being n fold seem quite unlikely

in particular, if you have a 4-fold but not 2-fold rro then it means that two copies must interact, so the opposed copies in the four-fold version would have to interact as well -- the only way to prevent it from breaking in the same way is if the other "side" copies prevent the breaking. This is definitely possible, but since that's still interacting, the four copies definitely wouldn't be non-interacting, so it's debatable whether this would qualify as a 4-fold rro depending on exactly how strict you want to be in terms of the definition of an n-fold rro (if the copies have to not interact).

However, four copies of a period-p rro, spaced as it is every p/4 generations, forming a period-p/4 oscillator, may be possible afaik.
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Re: Challenges

Post by HotWheels9232 » July 14th, 2022, 12:40 am

Find a path in CGoL from the block to the 1)blinker 2)tub or prove that it is impossible.
A path is a line of single objects where you can go along the line, and the next object you encounter must be made from adding a cell to the last object that you encounter. The only thing you can use LifeHistory for is to draw arrows. You can only use state 1 for the adding part.
Edit 1:I did blinker but won't tell you. I needed 2 arrows.
My rules:
B34q/S23-k(ObliquePufferLife) and
B2n3-n4c5c/S234cz5cPM me to get some help on making rules!

Code: Select all

x = 8, y = 5, rule = B3-k/S23
2o3b2o$obo2bobo$2bo2bo$bo$b2o!

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Re: Challenges

Post by breaker's glider gun » November 6th, 2022, 11:39 am

Challenge:
in a non-alternating, non-B0 rule, find a spaceship/oscillator that has at least 1 generation of no birth and no death AT THE SAME TIME.
(Hint:this must be a generations rule.)
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Re: Challenges

Post by hotdogPi » November 6th, 2022, 11:42 am

breaker's glider gun wrote:
November 6th, 2022, 11:39 am
Challenge:
in a non-alternating, non-B0 rule, find a spaceship/oscillator that has at least 1 generation of no birth and no death AT THE SAME TIME.
(Hint:this must be a generations rule.)
Life generations beacon: functions like the regular Life beacon except the rotor cells turn on only when the center cells turn to state 0.

Code: Select all

x = 4, y = 4, rule = 23/3/7
2.2A$3.A$A$2A!
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉞㉟㊱㊳㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,68,70,73,74S,75,76S,80,84,88,90,96
100,02S,06,08,10,12,14G,16,17G,20,26G,28,38,47,48,54,56,72,74,80,92,96S
217,486,576

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G: gun

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Re: Challenges

Post by breaker's glider gun » November 6th, 2022, 11:50 am

hotdogPi wrote:
November 6th, 2022, 11:42 am
breaker's glider gun wrote:
November 6th, 2022, 11:39 am
Challenge:
in a non-alternating, non-B0 rule, find a spaceship/oscillator that has at least 1 generation of no birth and no death AT THE SAME TIME.
(Hint:this must be a generations rule.)
Life generations beacon: functions like the regular Life beacon except the rotor cells turn on only when the center cells turn to state 0.

Code: Select all

x = 4, y = 4, rule = 23/3/7
2.2A$3.A$A$2A!
*facepalm*
It is interesting tho!
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