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 @c30feace - nice!  Is this page yours?

The set I wrote about (K = 1, N → ∞)  is connected.  I like how some of the sets you drew are not.

 @218dc8a6

https://media.mathstodon.xyz/media_attachments/files/111/156/222/561/705/633/original/62c32cf8d64efde3.png 
 @b4c50e1b @218dc8a6 @5fb5d869 @6278416d Yes, I messed with it a few years ago. Source code is available on Github https://github.com/kalvotom/ChristensenSet.jl

Of course, there are roots of polynomials up to some fixed degree, this is far from the limit 🙂. Also, the way you compose the final image plays a role (if I remember correctly, this is more like a density of roots, otherwise the picture would be huge).

If you are interested in some particular section of the image, I might give it another try and produce it in more detail.