John Carlos Baez on Nostr: At left you see two closeups of the set of all roots of polynomials of some large ...

At left you see two closeups of the set of all roots of polynomials of some large degree with coefficients ±1. At right you see "dragon sets" - fractals described in a simple way depending on where we do the closeup. They look very similar in character... but not exactly the same. Can you make this precise and prove it?

You can see a heuristic explanation here:

https://math.ucr.edu/home/baez/roots/

(Search the page for "dragon".) This has got to be the key to solving the puzzle - but nobody has yet turned this idea into a precise statement and proved it.

If you ever wanted to prove an interesting theorem about fractals, this could be your chance.

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