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Patterned Sets

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File: 2017-07-25 (1).png (70KB, 938x764px) Image search: [Google]
2017-07-25 (1).png
70KB, 938x764px
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
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