I'm not sure about most people, but it is quite pretty how we start with (1, 1, 1) and x^2 + y^2 + z^2 = 3xyz which is all nice and simple then ... kaboom. Suddenly there are patterns everywhere. Not just similar patterns either, but a big range of things. Setting numbers to constants gets other known sequences like Fibonacci numbers, meaningful patterns when permuting, meaningful patterns when ordering, links to trees, links to irrational numbers, links to linear transforms. And all this is going on while many basic-sounding properties are apparently hard to analyse.

There is a lot going on for summing 3 squares. It is fun and unexpected. All the weirder because they don't seem to have linked all this to pi, e or i yet in an obvious way looking at the wiki page.