The Astonishing Behavior of Recursive Sequences

In mathematics, simple rules can unlock universes of complexity and beauty. Take the famous Fibonacci sequence, which is defined as follows: It begins with 1 and 1, and each subsequent number is the sum of the previous two. The first few numbers are: 1, 1, 2, 3, 5, 8, 13, 21, 34 … Simple, yes, but this unassuming recipe gives rise to a pattern of far-reaching significance, one that appears to be…

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