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!
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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!
Code: Select all
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!