Thread for advanced questions

[Gustone]

Is there a thread for advanced questions?

[dvgrn]

There is now! (I just split the above post off of the "Thread for basic questions".)

[confocaloid]

I think this 'rough "hierarchy" of problem types' needs to be crossposted near the beginning:

I wanted to get my thoughts out about what kinds of things things CGOL people work on (note: I usually dislike acronyms, but "life" and even "game of life" are so overloaded that CGOL is growing on me). I hope this is an appropriate thread for such thoughts (and there appears to be a culture of avoiding new threads around here).

The reason this is connected to a "broader audience" is that I feel the CGOL community in general and on this website really likes to keep to the top level of the hierarchy I propose below and becomes dismissive as the discussion moves further down the rungs of the ladder. This is understandable for maintaining focus and quality, but a team working on outreach may need a different approach. This is by no means intended as an exhaustive list. Criticism is welcome. It is just to get the ball rolling.

Rough "hierarchy" of problem types.
Research: Some doubt about whether it is possible at all. New approaches and (usually) expertise needed to solve it.
Engineering: Believed to be possible, but no working example shown. Path may be sketched out, but work and skill are needed to complete it (nagging uncertainties about spacing and phasing may remain but are assumed resolvable).
Cataloging: Finding any one solution is a routine task, but solution space has not been fully explored. Solution takes the form of “list all”, “determine how many”, “find fastest/smallest”. This could be either an automated or manual process.
Known method: Finding the solution is a routine task for at least one member of the CGOL community.
Widely known method: Many experienced CGOL hobbyists can accomplish the task.
Scripted method: There is software that solves the problem and can be used without much CGOL experience (but it may require software engineering skills).
Novice: Simple constructions that require some understand[ing] of what CGOL can do. Pairing up guns or rakes for collisions, adding and removing eaters, etc.
Trivial: Shows up in early exploration “Whoa, that 5-cell pattern is moving.” “This small pattern makes a big explosion.” “When I start with a line, the result is always symmetrical.”

An orthogonal axis is level of interest. This varies from “Obviously interesting to anyone who sees it.” to “Only of interest to its discoverer.” The above categories can fall anywhere on this axis. E.g., completing some obscure oscillator of known period may be research-level difficulty, but still not very interesting. Gliders are trivial and well known, but obviously interesting.

(Actually it’s not completely orthogonal, because a research problem can grow in interest as it is perceived to be more challenging and many people try and fail to solve it, much like the trajectory of FLT in pure mathematics.)

EDIT by dvgrn: side note on the last parenthetical remark -- "FLT" is "Fermat's Last Theorem", not "faster than light [travel]".

This list doesn't give any definite guidance as to what types of questions belong here vs. in the Thread for basic questions. It's possible to ask either basic or advanced questions related to most of the above categories. That's okay -- just pick the thread that seems to fit the question better.

[WhiteHawk]

I hope this counts as an "advanced" question. If not, I will move it elsewhere.

Is it possible to modify the recent H-to-MWSS to work in Pedestrian Life (B38/S23)? At gen 131, B8 is triggered, which damages the conduit supports. However, perhaps some novel support mechanism can eat the new waste, and neither of the catalysts at the end are touched when the evolution changes.

Code: Select all

x = 102, y = 55, rule = B38/S23
41b2o3bo$42bo2bobo41b2o3bo$40bo4bobo42bo2bobo$40b5obo41bo4bobo$44bo43b
5obo$36bo3b2o3bo46bo$35bobo2b2o4bo37bo3b2o3bo$36bo8b2o36bobo2b2o4bo$84b
o8b2o3$13b2o$12b2ob3o28b2o$13b5o28b2o46b2o$14b3o36bo40b2o$51b3o47bo$50b
o48b3o$50b2o46bo$98b2o3$45b3o$45bobo$43b6o$40bo3b2o$39bo4b2o$39bo3bo3b
o27bo$42bo3bobo2b2o22bo$39bob2o3bobo2b2o22b3o21b2o$39bo2bo4b2o28bo21b
2o3$47bobo$47b2obo44bobo$50bo44b2obo$50b2o46bo$98b2o3$43b2o$43bo47b2o
$44b3o44bo$46bo45b3o$94bo9$o$obo$2o!

[confocaloid]

[...] Is it possible to modify the recent H-to-MWSS to work in Pedestrian Life (B38/S23)? At gen 131, B8 is triggered, [...]

Enough of the H-to-MWSS conversion reaction appears to be preserved (an output MWSS does escape if you feed in the input Herschel). That gives hope of completion.
Further, at the time when the MWSS escapes, two catalysts are not yet touched, which also gives hope of finding a replacement for them.

I think this is (more or less) as far as one can get, without/before actually trying various possibilities (manually or by a search program) and hoping for a lucky completion.

Code: Select all

x = 27, y = 43, rule = B38/S23
14b2o3bo$15bo2bobo$13bo4bobo$13b5obo$17bo$9bo3b2o3bo$8bobo2b2o4bo$9bo
8b2o5$19b2o$19b2o$26bo$24b3o$23bo$23b2o8$o$obo$3o21b2o$2bo21b2o4$20bo
bo$20b2obo$23bo$23b2o4$16b2o$16bo$17b3o$19bo!
#C [[ GRID THEME Catagolue STOP 100 ]]

[WhiteHawk]

I think this is (more or less) as far as one can get, without/before actually trying various possibilities (manually or by a search program) and hoping for a lucky completion.

Code: Select all

Better result (But not yet complete) with stable ash based on the new reduction

Code: Select all

x = 71, y = 43, rule = B38/S23
14b2o3bo37b2o3bo$15bo2bobo37bo2bobo$13bo4bobo35bo4bobo$13b5obo36b5obo
$17bo42bo$9bo3b2o3bo33bo3b2o3bo$8bobo2b2o4bo31bobo2b2o4bo$9bo8b2o32bo
8b2o5$19b2o41b2o$19b2o41b2o$26bo42bo$24b3o40b3o$23bo42bo$23b2o41b2o3$
63b2o$62bo2bo$63b2o3$o26bo42bo$obo22b3o40b3o$3o21bo42bo$2bo20bobo40bo
bo$24bo42bo3$22b2o41b2o$22b2o41b2o6$16b2o41b2o$16bo25b2o15bo$17b3o23b
2o15b3o$19bo22bo19bo!

Either the preceding conduit would need to produce a glider and herschel, or the FNG could be chained to some stable reflectors and create an H-to-MWSS with an atrocious repeat time.

[dvgrn]

Looks like this works:

Code: Select all

x = 50, y = 43, rule = B38/S23
35b2o3bo$36bo2bobo$34bo4bobo$34b5obo$38bo$30bo3b2o3bo$29bobo2b2o4bo$30b
o8b2o4$5o$o4bo34b2o$o39b2o$bo3bo41bo$3bo41b3o$44bo$44b2o8$21bo24b2o$21b
obo22bobo$21b3o24bo$23bo24b2o2$43b2o$43bo$44b3o$46bo6$37b2o$37bo$38b3o
$40bo!

For comparison, it produces an Annoying Beehive in plain old Life:

Code: Select all

x = 50, y = 43, rule = B3/S23
35b2o3bo$36bo2bobo$34bo4bobo$34b5obo$38bo$30bo3b2o3bo$29bobo2b2o4bo$30b
o8b2o4$5o$o4bo34b2o$o39b2o$bo3bo41bo$3bo41b3o$44bo$44b2o8$21bo24b2o$21b
obo22bobo$21b3o24bo$23bo24b2o2$43b2o$43bo$44b3o$46bo6$37b2o$37bo$38b3o
$40bo!

[WhiteHawk]

For comparison, it produces an Annoying Beehive in plain old Life:

Code: Select all

What is funny is that the most recent reduction of the reflector in life above leaves a beehive in Pedestrian Life but is clean in Life.

Code: Select all

x = 32, y = 47, rule = B38/S23
3$15b2o3bo$16bo2bobo$14bo4bobo$14b5obo$18bo$10bo3b2o3bo$9bobo2b2o4bo$
10bo8b2o5$20b2o$20b2o$27bo$25b3o$24bo$24b2o8$bo26bo$bobo22b3o$b3o21bo
$3bo20bobo$25bo3$23b2o$23b2o6$17b2o$17bo$18b3o$20bo!

EDIT: The Pedestrian Life page should be changed since there is now an H-to-MWSS in the rule.

EDIT 2: any hope for a connection for it's p120 Repeat time? The H-to-R used in Life doesn't work in B38/S23, though the R-to-H does.

[confocaloid]

Crossposting my recent question, which is certainly beyond "basic", but was posted before this thread existed. Unlike earlier questions, it was not yet followed by a discussion in the same thread.

Question: is there a strict still life X with all of the following properties?

1. The bounding box of the still life X is a N-by-N square.
2. Multiple copies of the still life X can be arranged in a two-dimensional lattice, with precisely M empty rows of cells between consecutive rows of copies of X, and with precisely M empty columns of cells between consecutive columns of copies of X.
3. In a two-dimensional arrangement described above, any two "side-by-side adjacent" copies of X can be either left unchanged, or joined together into a single strict still life by a particular "isthmus" connection across the M-cell-thick gap. This way, there are multiple different modifications of any rectangular arrangement of copies of X, where some "isthmuses" are present and other are absent. Every such choice (between adding or not adding an "isthmus") is independent from all other such choices.
4. Every such modified rectangular arrangement has a glider synthesis, for all sizes, and regardless of which "isthmuses" are present and which are absent.

Other things being equal, larger values of N are better.
Other things being equal, smaller values of M are better.
If both N and M are equal in two solutions, then denser still lives are better.

The following would be a solution (with N = 9 and M = 2), if only there was a proof that all possible resulting finite arrangements are glider-constructible. (I don't have either a proof or a disproof of glider-constructibility of these.)

Code: Select all

x = 87, y = 53, rule = B3/S23
36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$37bobo8bobo8bobo8bobo8bobo$34bo2b
obo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$2b2ob2o6b2ob2o16b4o
b4o2b4ob4o2b4ob4o2b4ob4o2b4ob4o$3bobo8bobo$o2bobo2bo2bo2bobo2bo14b4ob
4o2b4ob4o2b4ob4o2b4ob4o2b4ob4o$4ob4o2b4ob4o14bo2bobo2bo2bo2bobo2bo2bo
2bobo2bo2bo2bobo2bo2bo2bobo2bo$37bobo8bobo8bobo8bobo8bobo$4ob4o2b4ob4o
16b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$o2bobo2bo2bo2bobo2bo$3bobo8bobo$
2b2ob2o6b2ob2o18b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$37bobo8bobo8bobo8bo
bo8bobo$34bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$34b4o
b4o2b4ob10ob10ob4o2b4ob4o2$34b4ob4o2b4ob10ob10ob4o2b4ob4o$34bo2bobo2bo
2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$37bobo8bobo8bobo8bobo8bob
o$36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$48bobo8bobo8bobo$48bobo8bobo8bo
bo$36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$2b2ob2o6b2ob2o19bobo8bobo8bobo
8bobo8bobo$3bobo8bobo17bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo
2bobo2bo$o2bobo2bo2bo2bobo2bo14b4ob4o2b4ob10ob10ob4o2b4ob4o$4ob10ob4o$
34b4ob4o2b4ob10ob10ob4o2b4ob4o$4ob10ob4o14bo2bobo2bo2bo2bobo2bo2bo2bob
o2bo2bo2bobo2bo2bo2bobo2bo$o2bobo2bo2bo2bobo2bo17bobo8bobo8bobo8bobo8b
obo$3bobo8bobo19b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$2b2ob2o6b2ob2o30bob
o8bobo8bobo$48bobo8bobo8bobo$36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$37bo
bo8bobo8bobo8bobo8bobo$34bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2b
o2bobo2bo$34b4ob4o2b4ob10ob10ob4o2b4ob4o2$34b4ob4o2b4ob10ob10ob4o2b4ob
4o$34bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$37bobo8bob
o8bobo8bobo8bobo$36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o3$36b2ob2o6b2ob2o
6b2ob2o6b2ob2o6b2ob2o$37bobo8bobo8bobo8bobo8bobo$34bo2bobo2bo2bo2bobo
2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$34b4ob4o2b4ob4o2b4ob4o2b4ob4o2b4o
b4o2$34b4ob4o2b4ob4o2b4ob4o2b4ob4o2b4ob4o$34bo2bobo2bo2bo2bobo2bo2bo2b
obo2bo2bo2bobo2bo2bo2bobo2bo$37bobo8bobo8bobo8bobo8bobo$36b2ob2o6b2ob
2o6b2ob2o6b2ob2o6b2ob2o!