Totally periodic pattern

[dvgrn]

Wow, I never new methuselahs had any use for making a pattern. Say hi to 35201M!

It doesn't meet the stipulation that every cell should die and remain dead after some number of generations.

What's needed is a good expanding diehard as opposed to a methuselah, I suspect this is a perfect problem for LifeAPI or an adaptation of apgsearch. Just fill most of the center of the nonfiller with random patterns of mostly ON cells, run for a few dozen ticks to make sure the nonfiller survives, then maybe remove the nonfiller and run each pattern to stability.

Sort the resulting ash by final population -- every now and then one will happen to be a diehard. If so, re-run it in LifeHistory (or equivalent), chop the original nonfiller bounding box out, and see if it matches an all-state-2 rectangle.

Again a later generation of the nonfiller can be used to increase the search space. I tried this with a later generation of die658.rle, but not surprisingly it left too many holes to be reasonably patched up:

Code: Select all

x = 51, y = 45, rule = LifeHistory
26.3A$26.A2.A$19.3A4.A6.3A$18.A2.A4.A3.A.A2.A$18.A2.A4.A3.A.A2.A$17.
3A.A.A2.A10.A$16.A5.A4.A.A2.2A2.2A$16.3A2.2A16.A$14.A6.A10.2A.A.3A$
14.3A3.A.A9.A8.A$12.A9.A10.A5.3A$12.3A12.2A14.A$10.A15.A2.A11.3A$10.
3A14.2A16.A$8.A34.3A$8.3A36.A$6.A38.3A$6.3A39.A$3.A.A30.2A7.A.3A$2.5A
.A26.A.A11.A$.2A6.A25.2A8.5A$2A4.2A25.2A5.A.A$.A.A3.A2.A21.A.A5.A2.A
3.A.A$8.A.A21.2A9.2A4.2A$.5A35.A6.2A$.A40.A.5A$.3A.A7.A7.2A2.2A18.A.A
$2.A10.A8.A3.A15.3A$3.3A7.A30.A$3.A14.A21.3A$5.3A10.A23.A$5.A11.3A18.
3A$7.3A30.A$7.A28.3A$9.3A5.A10.A9.A$9.A8.A9.A.A3.3A$11.3A.A.2A10.A6.A
$11.A16.2A2.3A$13.2A2.2A2.A.A4.A5.A$13.A10.A2.A.A.3A$15.A2.A.A3.A4.A
2.A$15.A2.A.A3.A4.A2.A$15.3A6.A4.3A$21.A2.A$22.3A!

[calcyman]

The die743 is slightly better, but I found that it's easiest to just do it with waves of *WSSes and gliders:

Code: Select all

x = 99, y = 132, rule = LifeHistory
37.A$38.A$36.3A3$38.A$39.A$37.3A3$39.A$40.A$38.3A$50.3A$50.A2.A$40.A
9.A$41.A8.A$39.3A8.A$50.A$51.A4.3A$41.A14.A2.A$42.A13.A$40.3A13.A$56.
A$56.A$42.A14.A4.3A$43.A18.A2.A$41.3A18.A$62.A$62.A$43.A18.A$44.A18.A
4.3A$42.3A23.A2.A$68.A$68.A$44.A23.A$45.A22.A$43.3A23.A4.3A$59.6A9.A
2.A$37.3A18.A5.A9.A6.3A$36.A2.A5.A18.A9.A3.A.A2.A$30.3A6.A6.A16.A10.A
3.A.A2.A$30.A2.A.A3.A4.3A27.A10.A$30.A2.A.A3.A35.A4.2A2.2A$28.A10.A
12.A12.6A16.A$28.2A2.2A4.A14.A10.A5.A9.2A.A.3A$26.A26.A16.A9.A8.A$26.
3A.A.2A19.A15.A7.A3.A5.3A$24.A8.A19.A24.A12.A$24.3A5.A17.A2.A24.A6.A
3.3A$22.A28.3A5.6A13.A5.A8.A$22.3A33.A5.A13.A5.A6.3A$20.A43.A10.A2.A
5.A10.A$20.3A40.A7.A4.3A5.A8.3A$18.A53.A11.A2.A8.A$18.3A51.A11.3A6.A.
3A$16.A36.6A13.A24.A$16.3A33.A5.A13.A20.5A$14.A43.A10.A2.A15.A.A$14.
3A40.A7.A4.3A15.A2.A3.A.A$12.A25.3A25.A24.2A4.2A$12.3A23.A2.A24.A22.A
6.2A$10.A27.A8.6A13.A18.A4.A.5A$10.3A25.A3.A3.A5.A13.A19.A6.A.A$8.A
29.A3.A9.A10.A2.A17.3A3.3A$8.3A27.A12.A5.A.A4.3A25.A$6.A25.3A4.A.A5.A
12.A27.3A$6.3A3.3A17.A2.A10.A9.A3.A29.A$3.A.A6.A19.A13.A5.A3.A3.A25.
3A$2.5A.A4.A18.A13.6A8.A27.A$.2A6.A22.A24.A2.A23.3A$2A4.2A24.A25.3A
25.A$.A.A3.A2.A15.3A4.A7.A40.3A$8.A.A15.A2.A10.A43.A$.5A20.A13.A5.A
33.3A$.A24.A13.6A36.A$.3A.A6.3A11.A51.3A$2.A8.A2.A11.A53.A$3.3A8.A5.
3A4.A7.A40.3A$3.A10.A5.A2.A10.A43.A$5.3A6.A5.A13.A5.A33.3A$5.A8.A5.A
13.6A5.3A28.A$7.3A3.A6.A24.A2.A17.A5.3A$7.A12.A24.A19.A8.A$9.3A5.A3.A
7.A15.A19.2A.A.3A$9.A8.A9.A16.A26.A$11.3A.A.2A9.A5.A10.A14.A4.2A2.2A$
11.A16.6A12.A12.A10.A$13.2A2.2A4.A35.A3.A.A2.A$13.A10.A27.3A4.A3.A.A
2.A$15.A2.A.A3.A10.A16.A6.A6.3A$15.A2.A.A3.A9.A18.A5.A2.A$15.3A6.A9.A
5.A18.3A$21.A2.A9.6A$22.3A4.A23.3A$30.A22.A$30.A23.A$30.A$30.A$27.A2.
A23.3A$28.3A4.A18.A$36.A18.A$36.A$36.A$36.A18.3A$33.A2.A18.A$34.3A4.A
14.A$42.A$42.A$42.A13.3A$42.A13.A$39.A2.A14.A$40.3A4.A$48.A$48.A8.3A$
48.A8.A$48.A9.A$45.A2.A$46.3A$58.3A$58.A$59.A3$59.3A$59.A$60.A3$60.3A
$60.A$61.A!

What are we trying to optimise? Population count or bounding box?

[lukebradford]

Surely that doesn't work if you delete the blue cells at generation 0.

D'oh, sorry for the foolishness...

These patterns are going in very interesting directions. I was thinking about minimizing population, but bounding box is interesting too.

[simsim314]

I guess those patterns are relevant to this topic, because if we can make synth, and use a breader to have them as trace this will yield a total periodic... if I'm right the next step is to find synthesis for those stretchers. Year ago it would sound science fiction, but with latest discoveries it sounds pretty attainable.

[Scorbie]

I guess those patterns are relevant to this topic, because if we can make synth, and use a breader to have them as trace this will yield a total periodic...

Isn't this pattern enough to become total periodic (with period 1) ? Also, I may have understood wrong, but I think two or more nonfillers would collide in one Life plane.

[simsim314]

Hmm period 1? Isn't empty universe is period 1? Otherwise you don't need a stretcher, simply couple of breeders will suffice.

I guess Total period should mean every cell becomes periodic with P>1.

It's also an interesting question to investigate is there a way to make each cell periodic, but for each period, there would be a rectangle in which the period will not hold (globally a-periodic, but locally totally periodic).

[lukebradford]

Re: calcyman, you can delete a couple of gliders:

Code: Select all

x = 99, y = 132, rule = LifeHistory
37.A$38.A$36.3A3$38.A$39.A$37.3A3$39.A$40.A$38.3A$50.3A$50.A2.A$40.A
9.A$41.A8.A$39.3A8.A$50.A$51.A4.3A$41.A14.A2.A$42.A13.A$40.3A13.A$56.
A$56.A$42.A14.A4.3A$43.A18.A2.A$41.3A18.A$62.A$62.A$43.A18.A$44.A18.A
4.3A$42.3A23.A2.A$68.A$68.A$44.A23.A$45.A22.A$43.3A23.A4.3A$59.6A9.A
2.A$37.3A18.A5.A9.A6.3A$36.A2.A5.A18.A9.A3.A.A2.A$30.3A6.A6.A16.A10.A
3.A.A2.A$30.A2.A.A3.A4.3A27.A10.A$30.A2.A.A3.A35.A4.2A2.2A$28.A10.A
12.A12.6A16.A$28.2A2.2A4.A14.A10.A5.A9.2A.A.3A$26.A26.A16.A9.A8.A$26.
3A.A.2A19.A15.A7.A3.A5.3A$24.A8.A19.A24.A12.A$24.3A5.A17.A2.A24.A6.A
3.3A$22.A28.3A5.6A13.A5.A8.A$22.3A33.A5.A13.A5.A6.3A$20.A43.A10.A2.A
5.A10.A$20.3A40.A7.A4.3A5.A8.3A$18.A53.A11.A2.A8.A$18.3A51.A11.3A6.A.
3A$16.A36.6A13.A24.A$16.3A33.A5.A13.A20.5A$14.A43.A10.A2.A15.A.A$14.
3A40.A7.A4.3A15.A2.A3.A.A$12.A25.3A25.A24.2A4.2A$12.3A23.A2.A24.A22.A
6.2A$10.A27.A8.6A13.A23.A.5A$10.3A25.A3.A3.A5.A13.A26.A.A$8.A29.A3.A
9.A10.A2.A23.3A$8.3A27.A12.A5.A.A4.3A25.A$6.A25.3A4.A.A5.A12.A27.3A$
6.3A23.A2.A10.A9.A3.A29.A$3.A.A26.A13.A5.A3.A3.A25.3A$2.5A.A23.A13.6A
8.A27.A$.2A6.A22.A24.A2.A23.3A$2A4.2A24.A25.3A25.A$.A.A3.A2.A15.3A4.A
7.A40.3A$8.A.A15.A2.A10.A43.A$.5A20.A13.A5.A33.3A$.A24.A13.6A36.A$.3A
.A6.3A11.A51.3A$2.A8.A2.A11.A53.A$3.3A8.A5.3A4.A7.A40.3A$3.A10.A5.A2.
A10.A43.A$5.3A6.A5.A13.A5.A33.3A$5.A8.A5.A13.6A5.3A28.A$7.3A3.A6.A24.
A2.A17.A5.3A$7.A12.A24.A19.A8.A$9.3A5.A3.A7.A15.A19.2A.A.3A$9.A8.A9.A
16.A26.A$11.3A.A.2A9.A5.A10.A14.A4.2A2.2A$11.A16.6A12.A12.A10.A$13.2A
2.2A4.A35.A3.A.A2.A$13.A10.A27.3A4.A3.A.A2.A$15.A2.A.A3.A10.A16.A6.A
6.3A$15.A2.A.A3.A9.A18.A5.A2.A$15.3A6.A9.A5.A18.3A$21.A2.A9.6A$22.3A
4.A23.3A$30.A22.A$30.A23.A$30.A$30.A$27.A2.A23.3A$28.3A4.A18.A$36.A
18.A$36.A$36.A$36.A18.3A$33.A2.A18.A$34.3A4.A14.A$42.A$42.A$42.A13.3A
$42.A13.A$39.A2.A14.A$40.3A4.A$48.A$48.A8.3A$48.A8.A$48.A9.A$45.A2.A$
46.3A$58.3A$58.A$59.A3$59.3A$59.A$60.A3$60.3A$60.A$61.A!