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So this with regard to the excitement while trying to make Langton's Ant do something "surprising" and "unusual".

I was able to make the turtles create symmetry as they moved. I noticed that only an even number of turtles can lead to symmetry, and that is quite understandable. However, the surprising thing is that each even number would not lead to symmetry if moved a certain number of steps - for example, 2 turtles would not make symmetry if they were moved 8 steps forward, 10 turtles wouldnt work if moved 2 steps and so on and so forth. Another thing to notice was that 6 turtles never made symmetry, no matter how many number of steps and 8 turtles always made symmetry no matter how many number of steps. I was trying to look for a pattern in this pattern of symmetry, but couldnt find one.

Any thoughts?