Alex Stone in Quanta Magazine:
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 woven into the very fabric of the natural world. It’s seen in the whorls of nautilus shells, the bones in our fingers, and the arrangement of leaves on tree branches. Its mathematical reach extends to geometry, algebra and probability, among other areas. Eight centuries since the sequence was introduced to the West — Indian mathematicians studied it long before Fibonacci — the numbers continue to attract the interest of researchers, a testament to how much mathematical depth can underlie even the most elementary number sequence.
More here.