Patterns of patterns

Doug Hofstadter tells a tale about when he was sixteen years old. He was fascinated by numbers and sought out to be a grand mathematician. During his search for patterns in sets of numbers he came across an interesting repeating sequence inside of the union of squares and primes:

1, 1, 3, 4, 6, 9, 10, 15, 16, 21, 25 . . .

Between each of the squares (bold) there were either one or two primes, which become a new set of 2's and 1's. Sequences of 2 1 2 1, and so on are noted by Hofstadter. He further tries to extrapolate sequences from the new sequence, by attempting many different methods (counting breaks between a common subsequence, looking for very large periodic patterns, and more).

Eventually, he comes to the conclusion of counting 1's between the 2's and produced a new set entirely:

212112121211212112121211212112121121212112

1 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2

Upon further musing, he decided even to apply his counting idea to the new sequence, which led to:

212112121211212112121211212112121121212112

1 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2

2 1 2 1 1 2

The first and the third sequence are the same ! And, according to Hofstadter, they continue to be the same for quite some time.

I'd like to reflect a bit on pattern matching in humans, as I this is what Hofstadter was trying to illustrate by telling his sequence story from when he was sixteen.

Pattern matching in humans is obviously an instinct. We are driven to align the world (or microworld, such as number sets) from chaos to order. Why? Although we don't have time machines to look at our ancestor's behavior, we do have other animals which are (assumedly) of lower intelligence than us (atleast when it comes to pattern matching numbers). We can study them to learn something about how we may have evolved, specifically primates, because we share so much genetic heritage.

How do we go about deciding on patterns? It doesn't seem to be an instantaneous reaction to a set of mismatched data, but more of a mechanical process of rules that can be applied to develop a coherent result. Hofstadter used his own rules to decide where to break the sequences up, and what to count. This is probably alot of trial and error, especially without any advanced training in this sort of thing.

Is this how our ancestor's devised patterns, through trial, error, and reason? Maybe. Perhaps when they started caring about precise periodic events, such as tide, season, and constellation sequences.