## Challenge: Linear Growth

For general discussion about Conway's Game of Life.
rokicki
Posts: 54
Joined: August 6th, 2009, 12:26 pm

### Challenge: Linear Growth

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
Posts: 480
Joined: September 22nd, 2018, 8:48 am

### Re: Challenge: Linear Growth

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
Posts: 2127
Joined: June 1st, 2009, 4:32 pm

### Re: Challenge: Linear Growth

Ian07 wrote: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!``````
What do you do with ill crystallographers? Take them to the mono-clinic!

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

### Re: Challenge: Linear Growth

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
Posts: 54
Joined: August 6th, 2009, 12:26 pm

### Re: Challenge: Linear Growth

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
Posts: 852
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Challenge: Linear Growth

I saw that somewhere...
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac
Posts: 852
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Challenge: Linear Growth

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
One big dirty Oro. Yeeeeeeeeee...

dvgrn
Moderator
Posts: 6277
Joined: May 17th, 2009, 11:00 pm
Contact:

### Re: Challenge: Linear Growth

gameoflifemaniac wrote: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
Posts: 940
Joined: June 28th, 2014, 7:15 am

### Re: Challenge: Linear Growth

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!
``````