Self similar pattern when ink dissolves in the ...

When I drop ink into the water very carefully, I thought this would be just simply chaotic process like in Rayleigh-Taylor instability with no well defined pattern; however, surprisingly, it turns out to be rather regular with self similar bifurcation where number three is preferred. I don't know why and I did not see this phenomenon elsewhere in the textbook; therefore, I upload it to see if anyone can give me some reasonable explanations of it.

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