Challenge: Linear Growth

[rokicki]

Here's one that might be easy, maybe not.

Construct a pattern for Conway's Game of Life that, in all generations g > t (for some t),
the population count p is equal to g.

If that's possible, then try to minimize t.

I've tried this and figured out some possible ways to do it, but they aren't particularly
nice.

There's a reason I want this: I want to use this to help testing Golly (and other Life
programs).

-tom

[Ian07]

My first idea was to create a glider synthesis for one per generation (t = 44) but I'm not sure how difficult that would be.

[calcyman]

My first idea was to create a glider synthesis for one per generation (t = 44) but I'm not sure how difficult that would be.

Good idea. I'll set the ball rolling with a t = 94 solution:

Code: Select all

x = 168, y = 111, rule = B3/S23
53bo94bobo$51b2o95b2o$52b2o95bo$109bo$14bo95bo46bo$12bobo45bo47b3o45bo
$13b2o45bobo93b3o$60b2o2$159bo$61bobo93b2o$61b2o95b2o$4bo6bo50bo37bo5b
obo$5bo6b2o84bobo6b2o$3b3o5b2o86b2o6bo$69bo95bo$68bo96bobo$68b3o94b2o$
132bo$34bobo93b2o$34b2o95b2o$35bo$100bo9bo$5bo9bo85bo9bo$3bobo7bobo83b
3o7b3o$4b2o8b2o$33bo$30bo97b3o$23bo5bo3bob2o82bo6b2o4bo2bo$24bo9b2o81b
obo5bo6b4o$22b3o4bo2bo3bo81b2o4bo3bo3b3obo$31bo94b2o2$35bo95bo$34bobo
78bo14bobo$20bo13b2o80bo13b2o$18bobo93b3o$19b2o13b2o94b2o$34b2o94b2o2$
34b2o94b2o$33bobo93bobo$33bo95bo$11b2o19b2o94b2o$10bobo10b3o80b3o10b2o
$12bo12bo82bo9bobo$24bo82bo12bo$8bo$8b2o48b2o43b2o$7bobo48bobo43b2o48b
3o$58bo44bo50bo$155bo2$61b2o95bo$60b2o95b2o$62bo94bobo2$2o94bo$b2o39b
2o21bo30b2o$o41bobo12b3o4b2o29bobo40b3o13b2o5b2o$42bo14bo6bobo71bo15bo
bo3b2o$58bo80bo14bo7bo$61b2o$18b2o41bobo50bo42b3o$19b2o40bo52b2o41bo$
13b3o2bo90b2o2bobo42bo$15bo42b2o48bobo44bo$14bo42b2o51bo43b2o$54bo4bo
94bobo$53b2o95b2o$53bobo93b2o$151bo31$36b4o$35bo3bo$39bo$35bo2bo2$118b
4o$117bo3bo$121bo$117bo2bo!

[chris_c]

Population == generation when generation >= 85:

Code: Select all

x = 182, y = 85, rule = B3/S23
52bo95bo$51bo96bobo$51b3o94b2o2$13bo94bobo$14b2o45bo47b2o45bobo$13b2o
44b2o48bo46b2o$60b2o95bo2$158bo$61bo95bo$61bobo93b3o$12bo48b2o36bo8bo$
3bobo7bo86b2o4bobo$4b2o5b3o85b2o6b2o$4bo3$131bo$34bo95bo$34bobo93b3o$
34b2o2$4bo9bo84bobo7bobo$5b2o8b2o83b2o8b2o$4b2o8b2o84bo9bo$129bo$34bo
92b3o$35b2o81bo7b4ob2o2bo$22bobo8b2o84b2o4b3o3bo4bo$23b2o10bo82b2o5b3o
4bo$23bo103bo5bo2$35bo95bo$34bobo93bobo$19bo14b2o78bobo13b2o$20b2o93b
2o$19b2o13b2o79bo14b2o$34b2o94b2o2$34b2o94b2o47b2o$33bobo45b2o46bobo
46b4o$33bo46b2ob2o44bo47b2ob2o$11b2o11bo7b2o47b4o22bo20b2o48b2o$12b2o
10b2o56b2o23b2o10b2o$11bo11bobo80bobo11b2o$119bo$8b2o$7bobo48b2o43b3o
49bo$9bo47b2o46bo48b2o$59bo44bo49bobo3$60b3o94b2o$60bo96bobo$61bo95bo
2$3o93b2o$2bo39b2o14bo36bobo41bo$bo39b2o14b2o38bo40b2o14b2o$43bo13bobo
78bobo12b2o$155bo2$18b3o93b2o$14bo5bo92bobo$14b2o3bo89b2o4bo$13bobo41b
3o50b2o42b2o$57bo51bo44bobo$53b2o3bo95bo$53bobo93b3o$53bo95bo$150bo9$
48b2o$48b2o10b2o$50b2o5b3ob2o$50b2o5b5o$58b3o!

[rokicki]

Wow, amazing! Thanks! I can't help but giggle watching the numbers increase
completely identically to astronomical values . . . this will be very useful.

What's a good name for this?

How did you manage to make glider constructions so quickly? I know there
are databases for such things but even so . . .

-tom

[gameoflifemaniac]

I saw that somewhere...

[gameoflifemaniac]

I saw that somewhere...
Edit: Oh, got it

Code: Select all

x = 17, y = 15, rule = B3/S23
8b2o$7b2o$9bo$11b2o$10bo2$9bo2b2o$b2o5b2o4bo$2o5bo5bo$2bo4bobo3b2o$4bo
2bo4b2obo$4b2o7b2o$8bo4bob2o$7bobo2bob2o$8bo!

I know they're not equal, but

[dvgrn]

I saw that somewhere...
Edit: Oh, got it

Code: Select all

x = 17, y = 15, rule = B3/S23
8b2o$7b2o$9bo$11b2o$10bo2$9bo2b2o$b2o5b2o4bo$2o5bo5bo$2bo4bobo3b2o$4bo
2bo4b2obo$4b2o7b2o$8bo4bob2o$7bobo2bob2o$8bo!

I know they're not equal, but

Yes, Ian07 linked to One_per_generation several posts back. The initial population count is smaller, so it might well produce a pop-equals-age pattern with a smaller initial value -- but only if someone can come up with a glider synthesis for the pattern, or more likely for the the double tubstretcher that it turns into after one tick.

[chris_c]

Here is a T=47 solution using a different idea:

Code: Select all

x = 53, y = 54, rule = b3/s23
41bo$40bo$36bo3b3o$34b2o$35b2o11$47bobo$47b2o$48bo3$27b2o$26b2o$28bo
22bo$30b2o5bo7bo4bo$29bo6b2o6bo5b3o$36bobo5b3o$28bo2bo$20b2o5b2o2bobo$
19b2o5bo5bobo$21bo4bobo4bobo$23b2o2bo6bo$23b2o$27bo$26bobo$27bobo$3bo
24bobo$3b2o24bo$2bobo19b2o$23b2o21b3o$25bo20bo$47bo$b2o$obo$2bo2$24b2o
21b2o$23bobo19b2ob2o$15b2o8bo12b2o5b4o$14bobo21bobo5b2o$16bo21bo2$23b
2o$22bobo$24bo!