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Since @rcorless was posting about Bohemian matrices a while ago, I thought I'd try some experiments of my own. Here's the result of plotting the eigenvalues of 4×4 upper Hessenberg matrices with zero diagonal and the other entries chosen among the cube roots of -1.

This one, on the other hand, came from 5×5 upper Hessenberg matrices with the same rules for the superdiagonal entries, but with a zero diagonal and a subdiagonal of -1.

Clearly, there's a lot of things to try out; I might come back to this subject every so often. (Both pictures were generated thanks to the function featured in mathematica.stackexchange.com/ .)

@rcorless Thank you for sharing these Bohemian pictures, and I might as well take the opportunity to thank you for your Maple books as well!

@tpfto you are very welcome :) I guess it's time to wrie a third edition... We'll see! I'm thinking of the tagline "not your parent's Maple"!

@tpfto very very nice! Your visualization scheme is different! What did you do, exactly?

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