johncarlosbaez, 7 months ago (edited 7 months ago)

If you draw all roots of all polynomials whose coefficients are ±1, you get an amazing picture that raises lots of challenging puzzles!

I really hope someone reads our short article:

https://www.ams.org/journals/notices/202309/rnoti-p1495.pdf

and solves the main puzzle: why do the fractal regions of this set look so much like "dragon sets"? We have a good heuristic explanation, but no proof yet.

People sometimes get excited about math when they learn about fractals, and then disappointed when they discover rather few professional mathematicians prove theorems about fractals. If you ever wanted to prove a cool theorem about fractals, this could be your chance!

If you read part 2, I'll show you what I'm talking about.

(1/2)