Butterfly diagram from cooley-tukey algorithm

I am trying to understand the logic of this algorithm so i can implement my own but i am not understanding this diagram i see appearing many times in a fair few articles on the topic, i am teaching myself so i don’t have a computer science degree to help. But i understand the general idea behind the algorithm.

But this butterfly diagram is confusing me.

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How do you interpret this diagram from left to right mathematically speaking? It’s so confusing.. what are the arrows telling me to do in terms of math operations on the functions?