Symmetry and parity in Life

[BobShemyakin]

Everyone knows that the symmetry of the population without the impact from the outside can only increase.
The main kinds of symmetry are reflected and turns, as well as their combinations.
Parity I call the following feature location axes of symmetry.
Axis of symmetry parallel to the coordinate axes can be carried out on the limits of the cells, then the population size in the direction perpendicular to the axis of the even.
It can pass through the centres of the cells, then the population size in the direction perpendicular to the axis of the odd.
And this parity is also saved with the development of the population.
Because the turn on 180° can be represented as a superposition of reflections on the x axis and the y axis, the amount of symmetrical populations can be even-even, odd-odd or even-odd.
Why I started this conversation.
In the study of symmetric random soups are applied is even-even soups.
In my opinion we are losing more than half of the results.
To illustrate, here are a few examples from the field of glider synthesis.
even-even:

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x = 89, y = 20, rule = B3/S23
2bobo$3b2o56bo$3bo57bobo$56bobo2b2o$57b2o$57bo22b2o$4bo8bo64b3obo$5bo
5b2o64bo4bo$3b3o6b2o11b2obo33b3o12bob3o$25bob2o25bo3b2o2bo15bo$29b2obo
22bo2b2o3bo15bo$4b2o6b3o14bob2o20b3o20b3obo$5b2o5bo62bo4bo$4bo8bo61bob
3o$60bo15b2o$59b2o$55b2o2bobo$14bo39bobo$13b2o41bo$13bobo!

odd-odd:

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x = 90, y = 30, rule = B3/S23
7$56bo$3bo53bo$4b2o49b3o$3b2o$25b2o51b2o$25b2o51b2o$8bobo59bobo$8b2o3b
2o10b4o28bobo10b2o6b4o$9bo2b2o11bo3bo28b2o11bo6bo3bo$14bo11b3o29bo3bo
17b2obo$62bo18bobo$o25b3o33bo3bo14bob2o$b2o2bo19bo3bo23bo11b2o15bo3bo$
2o3b2o19b4o23b2o10bobo15b4o$4bobo45bobo$28b2o55b2o$28b2o55b2o$10b2o$9b
2o56b3o$11bo55bo$68bo!

even-odd:

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x = 90, y = 30, rule = B3/S23
5$55bo$4bo48bobo$5bo48b2o$3b3o$14bo$12b2o13bo36bobo$13b2o11bobob2o32b
2o19b2o$27b2obo20bobo11bo19bo$3bo27bo20b2o29bobo$4bo5b3o13bob3o21bo7b
2ob2o18b2o$2b3o5bo13b3obo31b2ob2o7bo7b2o$11bo11bo47b2o6bobo$24bob2o31b
o11bobo5bo$2o21b2obobo30b2o17b2o$b2o24bo30bobo$o$9b3o$9bo59b2o$10bo58b
obo$69bo!

Bob Shemyakin

[dvgrn]

Why I started this conversation.
In the study of symmetric random soups are applied is even-even soups.
In my opinion we are losing more than half of the results.

If I'm understanding your point correctly, there are symmetry search options for apgsearch 1.x that handle all the odd/even variants you've mentioned -- it's just a matter of searching in D4 +1, D4 +2, or D4 +4, or other options given in the links below. For example, =https://catagolue.appspot.com/census/b ... golue page shows searches that were done with even/odd symmetry.

A nice explanation with words (biggiemac) and pictures (Alexey_Nigin) was done on the Help with Symmetries thread.

The description by biggiemac mentions that support for C2_2 needs to be added, but it looks like that has already been done. I don't remember that any likely options are missing from the list of supported symmetries (?)

[biggiemac]

The description by biggiemac mentions that support for C2_2 needs to be added, but it looks like that has already been done. I don't remember that any likely options are missing from the list of supported symmetries (?)

All options are present and have been since symmetric apgsearch began.

I was referring to apgnano in that comment, which at the time of posting was exclusively C1, as compared to the python script apgsearch which allowed symmetries.

I only brought up C2_2 as a specific example because 28P7.2 has C2_2 symmetry, and at the time of posting no p7 existed in B3S23 on catagolue. By this point there are a handful of p7 objects in the D8 symmetries, but none has arisen in C2_2.