The other day I found a mathematical puzzle in a textbook and after awhile I figured out a solution that involved taking one set of numbers in a pattern and associating them with another set of numbers in a pattern.
Anyways, I started to look closer at these new associated sets. I noticed that no matter what patterned set I associated with other patterned sets, even if my choice of sets were random, the result is always a new and alternating patterned set of numbers.
Surely this has to be an established axiom or I'm just a dumb-ass that noticed an arbitrary property. Anyways, I'm not sure where to look into this and ask questions.
Explanation, clarification, and 'brainlet' declaration are welcome.
>pic for visualization
bumping for help