Try the keywords "mnemonics" and "chunking".
The general problem of "how do you find the underlying pattern" is (probably) computationally intractable (in the general case) though it has not (to my knowledge) been proved (in the formal mathematical sense).
Using patterns to facilitate memorization can broadly be bucketed into two kinds.
Personally, I prefer spaced repetition software (pure rote) to mnemonics and chunking because mnemonics fills my head with extra intermediate junk that slows down recall speed and interferes with the identification of genuine patterns and connections.
There are other ways to improve memorization too (such as sexualizing things and engaging multiple senses) but they are beyond the scope of the question.
Thanks! There seems to be a lot of research into mnemonics/chunking and memorization, and surprisingly little-none that I can locate into finding/calling attention to true patterns.
I notice that I have a much easier time memorizing things when I find a pattern. Often, I fail to think to even look for a pattern. As an example, I had a hard time memorizing the unit circle until I realized that the numerator is just counting up and down from sqrt(n) <-> -sqrt(n), for n = 4, 3, 2, 1, 0 1, 2, 3, 4, starting at different points for sin and cos, while the denominator is always 2. Before I saw that pattern, I was trying to memorize the values of cos and sin at particular degrees - the values in the individual parentheses, one by one. I completely missed the pattern when I looked at it this way. Noticing the pattern required actively looking for one, and also noticing that 1 = sqrt(1).
Likewise I've found tremendous utility in learning math by reducing complex equations to simpler underlying forms. For example, take this equation:
It's much more legible when you realize that it has the form:
A * (B cos(wt) + C sin(wt))/(B^2 + C^2).
But you have to think to look for that, and notice that 4d^2w^2 = (2dw)^2.
I'd love to know if there's any research into memory formation that is about the difference for patterned vs. unpatterned data, or the educational utility of having students deliberately look for patterns. "Patterns memorization" on Google Scholar isn't turning up much. Do you have any ideas?