What are 'Butterfly Combinations' and why are they called this way?
So, a summary of the Wikipedia page on Butterfly Diagrams:


In Computing Science, a Butterfly is the portion of a computation that combines the results of (two) smaller computations into the larger one.
This is common in Discrete Fourier Transformation algorithms, as well as in the otherwise unrelated Viterbi Algorithm for finding the most likely sequence of hidden states.
It is called 'Butterfly' because of how it works in the base case where you combine two single-point results: (Image courtesy of Wikipedia)
The earliest occurrence in print of the term 'Butterfly' is thought to be in a 1969 MIT technical report: C. J. Weinstein (1969-11-21). Quantization Effects in Digital Filters.