Searching everything symmetrical in a 10×10 area

[hotdogPi]

Both two-way rotational symmetry and two-way mirror symmetry. In both cases, there are 2^50 ≈ 10^15 possibilities to check. Is this too much for a computer to handle? (Diagonal symmetry requires 2^55, which takes 32 times as long.)

You can save some time by ending each simulation immediately if it has fewer cells than the starting number and is within the same 10×10 bounding box, as it duplicates another simulation.

You can also cut down the simulations by 1/4 (although it's still more than 2^49) by saying that the four center cells have three possibilities: all on, all off, or two on and two off; the last of the three categories has two configurations for each but can be reduced to one because it's the same soup flipped/rotated.

What we are looking for:

• Unknown oscillators with period 4 or greater (this is the main reason to do this)

• Unknown spaceships (much more likely in mirror symmetry than rotational symmetry)

• Quadratic growth

• 50000+ generations

[MathAndCode]

Searching random soups in general is a good for finding new things. There is already apgsearch, which typically uses 16×16 soups but has a variety of soup sizes. The only advantage that your idea might have is efficiency: A soup whose descendants would already be studied from another soup can be discarded, and if you're seeking to do a systematic search, then there will likely be a way to prevent searching the same soup twice. However, each option could be put into apgsearch and may already be there. Also, if you discard any soup that has a descendant that fits within a 10×10 bounding box, then you will miss any soup that never expands outside of that 10×10 bounding box, so you need to check that its descendant will be tested separately. Of course, this brings up the possibility that two separate 10×10 soups have a common descendant that is larger than 10×10, and it might not even be after the same number of generations.
If you are already planning to do this and merely want to make sure that it will not crash your computer or make it not respond, then this is not a question to ask us because we do not know how powerful your computer is. I would recommend testing successively larger subsets of all 10×10 soups, starting at a point that you're confident will not cause problems and increasing by a factor of four or eight each time. (I would recommend fixing some group of inner cells then trying all possible combinations of outer cells in order to get samples that are more representative of how long the average running time per soup for all symmetric soups.) If you get to a point where the computation lasts for more than a second or two, then you know to stop, at least until you've made your code more efficient. One recommendation for making your code more efficient is that in ConwayLife (or any isotropic rule), a symmetric pattern will only have descendants with the same symmetry or a higher symmetry that includes that symmetry, so you only have to do birth/death computations for half of the cells.
In addition, if humans' current state of technological progress allows such a search, then there is a possibility that someone else has already done it.

[Hunting]

However, each option could be put into apgsearch and may already be there.

A similar research was done in LeapLife.