Strict definitions

[g0t0]

I found that there are no strict definition of one oscillator.

Is this one oscillator?

Code: Select all

x = 15, y = 14, rule = B3/S23
b2o9b2o$o2bo7bo2bo$3o9b3o$3b9o$2bo2b5o2bo$2b2o2b3o2b2o3$2b2o2b3o2b2o$
2bo2b5o2bo$3b9o$3o9b3o$o2bo7bo2bo$b2o9b2o!

What about this?

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x = 17, y = 17, rule = B3/S23
2b2o$o2bo3$2obo$2bobo2b2o$3bo4bo$4bo$4bo2bo2b2o$8bo2bo3$8b2obo$10bobo
2b2o$11bo4bo$12bo$12bo2bo!

I think the first is and the second not.

[NNlk05]

You can use Catagolue's object page to find if two patterns are interacting or not. If they are interacting, then its one object.

[Disaster16439]

You can use Catagolue's object page to find if two patterns are interacting or not. If they are interacting, then its one object.

Catagolue is not fool-proof. Go to say D2_+2 and xp15. There’ll be a lot of bi-pentadecathons, but a lot of them simply don’t interact, however their envelopes do so Catagolue does not separate them.

Edit 1:

Here’s an example:

https://catagolue.hatsya.com/object/xp1 ... zcfc/b3s23

Even worse, the envelopes don’t even overlap, they just touch.

[SecondTypist]

You can use Catagolue's object page to find if two patterns are interacting or not. If they are interacting, then its one object.

Catagolue is not fool-proof. Go to say D2_+2 and xp15. There’ll be a lot of bi-pentadecathons, but a lot of them simply don’t interact, however their envelopes do so Catagolue does not separate them.

Edit 1:

Here’s an example:

https://catagolue.hatsya.com/object/xp1 ... zcfc/b3s23

Even worse, the envelopes don’t even overlap, they just touch.

Code: Select all

#CSYNTH xp15_3v3y24r4z9g9y24r4zcfc costs 7 gliders (pseudo).

[g0t0]

You can use Catagolue's object page to find if two patterns are interacting or not. If they are interacting, then its one object.

Catagolue is not fool-proof. Go to say D2_+2 and xp15. There’ll be a lot of bi-pentadecathons, but a lot of them simply don’t interact, however their envelopes do so Catagolue does not separate them.

Edit 1:

Here’s an example:

https://catagolue.hatsya.com/object/xp1 ... zcfc/b3s23

Even worse, the envelopes don’t even overlap, they just touch.

Code: Select all

#CSYNTH xp15_3v3y24r4z9g9y24r4zcfc costs 7 gliders (pseudo).

The worse case:

Code: Select all

x = 385, y = 259, rule = B3/S23
15$213b2o$212bobo$206b2o4bo$204bo2bo2b2ob4o$204b2obobobobo2bo$207bobob
obo$207bobob2o$208bo2$221b2o$212b2o7bo$212b2o5bobo$219b2o7$209b2o$210b
o$207b3o9b2o$207bo11bobo$219bo10$172bo$172b3o$175bo$174b2o3$166b2o$
166bo$163b2obo49b2o$163bo2b3o4b2o40bobo$164b2o3bo3b2o34b2o4bo$166b4o
37bo2bo2b2ob4o$166bo15b2o23b2obobobobo2bo$167b3o12bobo25bobobobo$170bo
13bo25bobob2o$165b5o14b2o25bo$165bo$167bo56b2o$166b2o47b2o7bo$215b2o5b
obo$222b2o7$212b2o$213bo$210b3o$210bo19$254b2o$254bo$256bo$236b2o14b5o
$237bo13bo$237bobo12b3o$238b2o15bo$252b4o$247b2o3bo3b2o$247b2o4b3o2bo$
255bob2o$255bo$254b2o3$235b3o8b2o$237bo8bo61b2o$236bo10b3o58bo$249bo
60bo$290b2o14b5o$291bo13bo$291bobo12b3o$292b2o15bo$306b4o$301b2o3bo3b
2o$301b2o4b3o2bo$309bob2o$309bo$308b2o3$300b2o$300bo$301b3o$303bo11$
268bo$266b3o$265bo$265b2o$118bo$118b3o$121bo$120b2o3$112b2o141b2o$112b
o141bobo5b2o$109b2obo141bo7b2o$109bo2b3o4b2o132b2o$110b2o3bo3b2o$112b
4o151bo$112bo15b2o133b2obobo$113b3o12bobo131bobobobo$116bo13bo128bo2bo
bobobob2o$111b5o14b2o127b4ob2o2bo2bo$111bo151bo4b2o$113bo147bobo$112b
2o147b2o19$157bo$155b3o$154bo$154b2o7$144b2o$143bobo5b2o$143bo7b2o$
142b2o2$156bo$152b2obobo$151bobobobo$148bo2bobobobob2o$148b4ob2o2bo2bo
$152bo4b2o$150bobo$150b2o!

Code: Select all

x = 156, y = 165, rule = B3/S23
5$53b2o$52bobo$46b2o4bo$44bo2bo2b2ob4o51b2o$44b2obobobobo2bo50bobo$47b
obobobo47b2o4bo$47bobob2o46bo2bo2b2ob4o$48bo50b2obobobobo2bo$102bobobo
bo$61b2o39bobob2o$52b2o7bo41bo$52b2o5bobo$59b2o55b2o$107b2o7bo$107b2o
5bobo$114b2o4$49b2o$50bo$47b3o$47bo56b2o$105bo$102b3o$102bo8$12bo$12b
3o$15bo$14b2o3$6b2o$6bo$3b2obo$3bo2b3o4b2o$4b2o3bo3b2o$6b4o136b2o$6bo
15b2o122bo$7b3o12bobo123bo$10bo13bo103b2o14b5o$5b5o14b2o103bo13bo$5bo
123bobo12b3o$7bo122b2o15bo$6b2o136b4o$139b2o3bo3b2o$139b2o4b3o2bo$147b
ob2o$147bo$146b2o3$127b3o8b2o$129bo8bo$128bo10b3o$141bo31$10bo$10b3o$
13bo$12b2o2$148b2o$4b2o142bo$4bo145bo$b2obo125b2o14b5o$bo2b3o4b2o118bo
13bo$2b2o3bo3b2o118bobo12b3o$4b4o124b2o15bo$4bo15b2o124b4o$5b3o12bobo
118b2o3bo3b2o$8bo13bo118b2o4b3o2bo$3b5o14b2o125bob2o$3bo145bo$5bo142b
2o$4b2o2$140b2o$140bo$141b3o$143bo10$96bo$94bobo11bo$95b2o9b3o$105bo$
49bo55b2o$47b3o$46bo$46b2o4$95b2o$94bobo5b2o$94bo7b2o$36b2o55b2o$35bob
o5b2o$35bo7b2o62bo$34b2o67b2obobo$102bobobobo$48bo50bo2bobobobob2o$44b
2obobo49b4ob2o2bo2bo$43bobobobo53bo4b2o$40bo2bobobobob2o48bobo$40b4ob
2o2bo2bo48b2o$44bo4b2o$42bobo$42b2o!

[SecondTypist]

Here is a suggestion. It is probably clunky and can be improved:
Each period of the oscillator is composed of various polyplets. If, at any point in the evolution of the oscillator, any individual polyplet or group of polyplets can be removed from the oscillator and the tampered-with pattern evolves in such a way that after the tampered-with pattern has been run for however long it would take the untampered pattern to return to its original state, the tampered-with pattern returns to its original state (not the original state of the untampered pattern), and over the tampered with pattern’s evolution, no polyplets have been created that weren’t in the untampered pattern, no polyplets from the untampered pattern have been changed to different polyplets or moved to another period, and all polyplets remain (while being in the same exact period) that were from the untampered pattern and had part of the tampered-with pattern required for some of its cell’s birth, then it is not a single “strict” oscillator. If this is false for a specific pattern, then it is a single “strict” oscillator.
By this definition, the two unices sharing a duoplet is a single oscillator, which is how it should be.

[TheWayOfTheCon]

This is mainly a copied post from my sandbox thread.

I had a half-baked idea regarding measuring the frequency of evolutionary sequences.

The measuring process goes as follows:

• Take all n-plets with a certain number of cells

• See how many eventually evolve into the sequence of interest

• Divide the number of n-plets that evolved into the sequence by the total number of possible n-plets

Take this traffic light predecessor for example:

Code: Select all

x = 5, y = 3, rule = B3/S23
2bo$2ob2o$2bo!

Let's figure out its frequency among tetraplets. There are 22 tetraplets.

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x = 54, y = 31, rule = B3/S23
4o6b3o7b3o7b2obo6b2o8b2o$13bo8bo9bo9b2o8bo$53bo7$2o8b2o8b2o8b2o8b2o8b
2o$2bo9bo8b2o8bo9bo8b2o$2bo8bo20bo7bo7$obo7bo9bo9bo9bo9bo$bobo7b2o8b2o
8bobo7bo9bo$13bo7bo10bo9bo8bo$43bo6bo7$bo8bo9bobo7bo$obo7b2o9bo9b2o$b
o8bo11bo7bo!

And we see that two of them evolve into that specific predecessor.

So 2 out of 22 (or 1/11) of all tetraplets evolve into the sequence.

Thus, the sequence's frequency among tetraplets is 1/11, or 9.1%. You could scale this up for pentaplets, hexaplets, etc. or do it with different sequences. This method almost certainly isn't perfect, because I'm assuming that all n-plets have about the same rarity. Additionally, this method could undermine the perceived frequency of some sequences. But it could lead to something more strict regarding calculating how frequent certain sequences are.

EDIT: Remembered that all polymonioes are also polyplets, a lot of corrections.