Proving Life "Omni-subperiodic"

For discussion of specific patterns or specific families of patterns in Conway's Game of Life, both newly-discovered and well-known.
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Rhombicubocta
Posts: 80
Joined: May 27th, 2026, 9:44 am

Proving Life "Omni-subperiodic"

Post by Rhombicubocta »

The list of oscillators with subperiod combinations page on the wiki is a good source expanation subperiod combinations. I conjecture that all sub-period combinations are possible. It is a large undertaking to prove and may like proving life omniperiodic will take a long time. Here is a start though. Using the glider gun adjustable to all periods above 80 we can construct an oscillator for every period of the form 2q where q is a greater than or equal to 83. Using a semi-snark once gives us an infinite family of oscillators with the subperiod combination 1,q,2q. The example below has q=81.

Code: Select all

x = 127, y = 141, rule = B3/S23
15$30b2o11bo$30b2o10bobo$42bobo2b2o3bo$41b2ob2o2bo2bobo$45bobo3bobo$
41b2obo2b4obo$41b2obobo3bo$45bobo3bo$46bobo3bo$47bo3b2o47b2o$35b2o29bo
33b2o$35b2o27b3o13bo$39b2o22bo16b3o$38bo2bo21b2o18bo$37b2ob2o40b2o$23b
2o14bo$22bo2bo$21bob2o$21bo$20b2o6b2o38b2o$29b2o4b2o32b2o18b2o$28bo6bo
32b2o2b2o14b2o$36b3o29bo3b2o16bo3b2o$38bo10b2o42b2ob2o$48bobo42b2o2bo
12b2o$48bo44bo3bo12b2o$47b2o10b2o32bob2o$60bo33bo$57b3o9b2o$57bo11bo
19b2o$67bobo18bobo$67b2o19bo$87b2o4$34b2o$34bo19b2o$32bobo18bobo$32b2o
19bo11bo$52b2o9b3o$28bo33bo$26b2obo32b2o10b2o$11b2o12bo3bo44bo$11b2o
12bo2b2o42bobo$25b2ob2o42b2o10bo$27b2o3bo16b2o3bo29b3o$33b2o14b2o2b2o
32bo6bo$32b2o18b2o32b2o4b2o$53b2o38b2o6b2o$101bo$98b2obo$97bo2bo$83bo
14b2o$81b2ob2o$58b2o21bo2bo$59bo22b2o$56b3o27b2o$21b2o33bo29b2o$21b2o
47b2o3bo$70bo3bobo$71bo3bobo$72bo3bobob2o$70bob4o2bob2o$69bobo3bobo$
69bobo2bo2b2ob2o$70bo3b2o2bobo$54bo23bobo10b2o$52bobo24bo11b2o$53b2o
15$89b2o$89bo$87bobo$87b2o$73bobo$74b2o$74bo2$89b2o$89bo$87bobo$87b2o
2$72b2o$72b2o3$89b2o$82b2o5b2o$82b2o2$77bo$76bobo$76b2o6b2o$84bo$85b3o
$87bo!

Using n semi-snarks would allow give a family of period (2^n)p with subperiod combinations of 1,q,2q,4q...,(2^n)q.
Using n tremi-snarks would allow give a family of period (3^n)p with subperiod combinations of 1,q,3q,9q...,(3^n)q.
I have yet to deal with combinations of them.
edit: Also the gun this is based off of can be adjusted to any period above 80 as state life wiki status page.
edit2: Fixed Grammar and changed notation to fit with wiki page. Thanks to glider-rider's code for constructing strictly volatile oscillators we have with 928 periods left without strictly volatile oscillator know or shown to be constructible using self construction.
glider_rider wrote: December 2nd, 2022, 4:37 pm ...
If someone can modify the code or construct least common multiples oscillators based off the strictly volatile oscillators that would be a start. Long term a code should be constructed for arbitrary combinations of common-multiples of those oscillators bringing the number of missing subperiods to a finite amount. Glider synthesized sparks may be the best way to go about this.
edit 3: There is no rush, but finishing in the list of oscillators with subperiod combinations page on the wiki would helpful.
The smallest missing sub-period combination is 2,6. The statorless volatile p6 page does not have one. I can't seem to find one on catagolue. If we can find a way to support the p6 worker be with a combination phoenices and the stricly volatile p6 that would work.
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