About 3 years ago I coded a 2D random walk togheter with a coleague in C++, first it seemed to work properly as we obtained a diferent pattern each time. But whenever we decided to increase the number of steps above some threshold an apparent butterfly pattern appeared, we noticed that with each run of the code the pattern would repeat but starting on a different place of the butterfly. We concluded and reported then that it was due to the pseudorandom generator associated with srand() function, but today I found again this report and there are still some things that I would like to understand. I would like to understand better how the pseudorandom generator works in order to obtain this sort of symmetry and ciclic pattern. The pattern I'm talking about is this (The steps are color coded in a rainbow sequence to apreciate the progression of the walk):
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